Another Look at Modi!cation in Spatial Prepositions

an International Journal of Theoretical Linguistics Ángel L. Jiménez-Fernández Editor-in-Chief Universidad de Sevilla Pilar Barbosa Universidade do Minho Victoria Camacho-Taboada Universidad de Sevilla Michelle Sheehan University of Cambridge Volume 5 Issue 2, December 2013 ISSN: 1989-8525 Editorial Team Editors Ángel L. Jiménez-Fernández, Editor-in-Chief, Universidad de Sevilla, Spain Pilar Barbosa, Universidade do Minho, Portugal Victoria Camacho-Taboada, Universidad de Sevilla, Spain Michelle Sheehan, University of Cambridge, UK Layout editor Pedro J. Carrillo-Gomez, Chief Layout Editor, Universidad de Sevilla, Spain Victoria Camacho-Taboada, Universidad de Sevilla, Spain Alicia González Seco, Universidad de Sevilla, Spain Estefanía Guerrero Robles, Universidad de Sevilla, Spain Copy editors Megan Devlin, University of Ulster, UK Rebecca Woods, University of York, UK Proofreaders Victoria Camacho-Taboada, Universidad de Sevilla, Spain Pedro J. Carrillo-Gomez, Universidad de Sevilla, Spain Principal Contact Ángel L. Jiménez-Fernández, Phd Phone: (+34) 954 551 546 Fax: (+34) 954 551 516 Email: [email protected] Support Contact Pedro J. Carrillo-Gomez Phone (+34) 620 581 485 pe[email protected] Mailing Address Facultad de Filología Universidad de Sevilla C/ Palos de la Fra. s/n 41004 Sevilla (Spain) Volume 5 Issue 2, December 2013 ISSN: 1989-8525 Scienti�c Committee Caroline Heycock, University of Edinburgh, UK Anders Holmberg, University of Newcastle, UK Selçuk Issever, Ankara University, Turkey Mary Kato, State University of Campinhas, Brazil Michael Kenstowicz, MIT, USA Itziar Laka, University of the Basque Country, Spain Alazne Landa, University of the Basque Country, Spain Mark Jary, University of Roehampton, UK Maria-Rosa Lloret, Universitat de Barcelona, Spain, Spain Manuel Leonetti, Universidad de Alcalá, Spain Ángel J. Gallego, Centre de Lingüística Teòrica & Universitat Autònoma de Barcelona, Spain Mireia Llinas, Universitat Autònoma de Barcelona, Spain Giuseppe Longobardi, University of Trieste, Italy Ana Maria Martins, University of Lisbon, Portugal Jürgen M. Meisel, University of Hamburg, Germany and University of Calgary, Canada Amaya Mendikoetxea, Autonomous University of Madrid, Spain Shigeru Miyagawa, MIT, USA Andrew Nevins, Harvard University, USA Jairo Nunes, University of São Paulo, Brazil Ana Ojea, University of Oviedo, Spain Francisco Ordoñez, Stony Brook University, USA Javier Ormazabal, University of the Basque Country, Spain Sumru Ozsoy, Boğaziçi University, Turkey Orin Percus, University of Nantes, France Josep Quer, Institució Catalana de Recerca i Estudis Avançats & University of Pompeu i Fabra, Spain Andrew Radford, University of Essex, UK Eduardo Raposo, University of California at Santa Barbara, USA Gemma Rigau, Universitat Autònoma de Barcelona, Spain Luiggi Rizzi, University of Siena, Italy Ian Roberts, University of Cambridge, UK Juan Romero, University of Extremadura, Spain Alain Rouveret, University Paris 7, France Vieri Samek-Lodovici, University College London, UK Uli Sauerland, Centre for General Linguistics, Typology and Universals Research (ZAS), Germany Vassilis Spyropoulos, University of Athens, Greece Esther Torrego, University of Massachusetts, USA Ana Maria Brito, University of Porto, Portugal Ignacio Bosque, Universidad Complutense de Madrid, Spain Zeljko Boskovic, University of Connecticut, USA Jonathan Bobaljik, University of Connecticut, USA Elena Benedicto, Purdue University, USA Adriana Belletti, University of Siena, Italy Artemis Alexiadou, University of Stuttgart, Germany Gorka Elordieta, University of the Basque Country, Spain Utpal Lahiri, University of the Basque Country, Spain Gabriela Matos, University of Lisbon, Portugal Ines Duarte, University of Lisbon, Portugal Maria Joao dos Reis de Freitas, University of Lisbon, Portugal David Adger, University of London, UK Teresa Cabre, Autonomous University of Barcelona, Spain Hector Campos, Georgetown University, USA Anna Cardinaletti, University of Venice, Italy Juan Uriagereka, University of Maryland, USA Myriam Uribe-Etxebarria, University of the Basque Country, Spain Susanne Wurmbrand, University of Connecticut, USA Francisco Garrudo, University of Seville, Spain Maria del Pilar Garcia-Mayo, University of the Basque Country, Spain Teresa Fanego, University of Santiago de Compostela, Spain María Victoria Escandell, UNED, Spain David Embick, University of Pennsylvania, USA Violeta Demonte, Autonomous University of Madrid, Spain Hamida Demirdache, University of Nantes, France Paola Crisma, University of Trieste, Italy Joao Costa, New University of Lisbon, Portugal Guglielmo Cinque, University of Venice, Italy Cedric Boeckx, Institució Catalana de Recerca i Estudis Avançats & Universitat Autònoma de Barcelona, Spain Olga Fernández-Soriano, Autonomous University of Madrid, Spain Luis Eguren, Autonomous University of Madrid, Spain Víctor Acedo, Universitat Autònoma de Barcelona, Spain Volume 5 Issue 2, December 2013 ISSN: 1989-8525 an International Journal of Theoretical Linguistics Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini Stockholms Universitet [email protected] Nobuaki Akagi Macquarie University [email protected] Volume 5.2, 2013 38-84 ISSN: 1989-8525 doi:tba Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini Stockholms Universitet [email protected] Nobuaki Akagi Macquarie University [email protected] Abstract The goal of this paper is to propose a uni�cation of two strands of research within the semantics of spatial prepositions. The �rst strand focuses on the socalled modi�cation problem, which can be stated as follows. Some, but not all spatial prepositions can occur in sentences including measure phrases, such as ten meters (Mario went ten meters in front of the car). The second strand focuses on so-called prepositional aspect: the fact that some but not all spatial prepositions can occur with temporal adverbial phrases such as in one hour. A uni�ed account is proposed, based on a minimal version of Type-Logical syntax combined with situation semantics. This uni�ed account is shown to explain and predict why, for instance, telic prepositions cannot occur with measure phrases (viz. *ten meters to the park). A compositional analysis of the contribution to lexical aspect of measure phrases, and their compositional interplay with spatial prepositions and temporal adverbials, is o�ered in detail. The main conclusion is that measure phrases do contribute to the lexical aspect reading of a sentence, but do so in fairly subtle (and compositionally-based) ways. Keywords: spatial prepositions, degree semantics, lexical aspect, measure phrases; morpho-semantics. 1 Introduction⇤ Spatial Prepositions (henceforth: SPs) have been the focus of much recent syntactic and semantic research. Current syntactic analyses of SPs have uncovered their �ne-grained syntactic structure in thorough and accurate detail (Asbury 2008, Pantcheva 2011, the works in Asbury et al. 2008, Cinque & Rizzi 2010, a.o.). Recent semantic works have also thoroughly investigated SPs and their many dimensions of meaning (Zwarts & Winter 2000, Kracht 2002, Zwarts 2005, Gehrke ⇤We thank two anonymous reviewers for the thorough feedback, which we believe that helped us in vastly improving our initial draft. We also would like to thank Clelia LaMonica, Andrew Cooper, Aijun Huang, Oleksandr Kapranov, Raphael Domange and other colleagues for suggestions, proof-reading support and judgments. The �rst author would like to thank his princess for the support, and Captain Harlock, as always, for the inspiration. The usual disclaimers apply. Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 38 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi 2008, a.o.). Given their novel insights on this category, these works seem to o�er a theoretical platform from which certain well-known problems can be solved. In this paper, we focus on one such problem: the interplay between SPs, Measure Phrases (henceforth: MPs) such as ten meters, and Temporal Adverbial Phrases (henceforth: TAPs) such as in/for X time (Dowty 1979, 1989). We start from MPs, in our discussion. In recent work, Morzycki (2006: 279) observes that only certain SPs can occur with MPs, as shown in (1)-(2): (1) The osprey is �ying ten meters above the lake (2) #The osprey is �ying ten meters near the lake Examples (1)-(2) show that while above can freely occur in a sentence containing the MP ten meters, the SP near cannot do so. The related sentence results is awkward or uninterpretable, a fact we represent via the symbol “#”. As Morzycki (2006) suggests, SPs that have this distribution include a monotonicity property de�ned over the model-theoretic objects belonging to their denotation. In this case, Morzycki (2006) follows Zwarts & Winter (2000) in assuming that both SPs and MPs denote (sets of) vectors. Simplifying matters somewhat, SPs di�er on whether they denote sets of vectors that can vary in possible “length”, or sets that only include vectors within a certain interval of length. Only the �rst group of SPs denotes sets of vectors which share one key property, monotonicity. The sets of vectors in their denotation can be ordered along an increasing/decreasing scale of length. Those SPs that do not have this monotonicity property cannot occur with MPs (e.g. near).1 This work does not explore in further detail a more �ne-grained analysis of which types of SPs have monotonic denotations. However, this analysis can lend itself to an interesting starting point for a more thorough account of these modi�cation patterns. One aspect discussed within this analysis provides an interesting problem in need of a solution, which can be de�ned as follows. If MPs combine with verb phrases (VPs), then they can do so only when they denote a set of eventualities that are aspectually atelic, or cumulative.2Otherwise, they cannot combine with VPs, lest a sentence be uninterpretable. We show this pattern in examples (3)-(4): (3) The osprey �ew one kilometer in one hour 1We employ the more intuitive notions of “occurrence” and ”distribution” for the introduction and section 2, in which we discuss our data. We will use more precise and formally de�ned notions in section 3 and 4, when we will have a clear picture status on the order and structure of the three phrases under discussion (SPs, MPs, TAPs). 2Here and in the remainder of the paper, we use the labels telicity and telic as interchangeable with noncumulativity and non-cumulative, depending on which label makes the prose more �uid. Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 39 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi (4) #The osprey few one kilometer for one hour As Morzycki (2006: 284) observes, the verb �ycan receive an either atelic or telic interpretation, as events of �ying seem to lack such a necessary “end-point". When an MP, one kilometer, appears as the argument of this verb, then only one type of TAP can combine with this phrase: the telic in one hour. The atelic four one hour renders the sentence uninterpretable.3This pattern is tightly related to the pattern displayed in (1)-(2), and to the fact that MPs can occur with SPs insofar as the modi�cation condition is met. A natural conclusion from these facts is that, if MPs can only combine with phrases that denote atelic predicates, then SPs occur within these “atelic" phrases if they also denote atelic predicates. Interestingly, works such as Zwarts (2005) show in detail how a distinction between telic and atelic SPs can be made precise. This distinction is particularly clear with so-called directional SPs, and is based on their distributional patterns with TAPs: (5) The car went to the park in one hour/*for one hour (6) The car went towards the park *in one hour/for one hour According to Zwarts (2005), certain directional SPs can only occur when telic TAPs, such as in one hour (e.g. to, from, into, and so on) also occur in a sentence. More accurately, an MP can act as a modi�er of a complex verb and preposition phrase, only if it occurs with a certain sub-set of directional SPs. Other directional SPs, instead, can only occur in sentences including atelic TAPs, such as for one hour (e.g. along, towards). Hence, if we look at TAP and their distribution with SPs, then some SPs seem to form a class of atelic predicates (above, towards), while others form a telic class (near, to). An obvious question, brie�y mentioned in Morzycki (2006), Zwarts (2008), is how the distributions of SPs with respect to MPs, and that of SPs with respect to TAPs are logically connected. A simple, pre-theoretical intuition is that both phenomena are licensed when certain semantic conditions are met. However, the exact nature of these conditions, and how they compositionally interact, is still poorly understood. An interesting but understudied pattern can be de�ned as follows. If an SP can denote an atelic predicate, then it can occur in a sentence containing an MP. If an atelic SP and an MP are part of a sentence, then a TAP can only occur when it denotes a telic predicate. This subtle distributional pattern is shown in (7)-(9): (7) #The car went ten meters to the park 3Our discussion of TAPs as inherently telic or atelic is slightly imprecise, as both TAPs and MPs can be seen as phrases that highlight the lexical aspect of an SP. However, this imprecision will allow us to better highlight how these parts of speech interact, with respect to aspect. We will solve this imprecision by sections 3 and 4, as well. Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 40 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi (8) The car went ten meters towards the park (9) The car went ten meters towards the park in one hour/#for one hour Examples (7)-(8) show that atelic towards, but not telic to, can occur when the MP ten meters occurs in a sentence. Example (9) shows that, once towards and ten meters occur in a sentence, then the intended interpretation is telic, instead. In fact, the TAP that can combine with the modi�ed verb and SP unit is the telic in one hour, not the atelic for one hour. Previous works contemplate the emergence of this pattern; however, they leave for future research its exact description and account. The goal of this paper is to address this empirical void, and o�er a formal account of the novel data that also makes correct, systematic predictions about their distribution. We aim to reach this goal by studying the connections among these three syntactic categories (MPs, SPs and TAPs), and the relevance of this analysis for a compositional theory. Our contention is that, if we o�er a correct analysis of these categories, then we can actually predict the observed patterns in (1)-(9), as the compositional result of the interpretation of these categories. Speci�cally, we aim to de�ne a uni�ed analysis of the lexical aspect properties shared by ten meters, towards, in one hour and other members of the three categories under discussion. From this uni�ed analysis, we aim to show that standard assumptions about compositionality can predict which sentences including one more of these elements are interpretable, and which are not. Therefore, we will ultimately suggest that we can account these patterns by considering them a re�ection of how these three categories can (or cannot) contribute to lexical aspect. By aiming to reach this goal, we also wish to reach two related, speci�c subgoals. First, we wish to expand previous �ndings on SPs, and o�er a more thorough analysis of their distributional patterns with respect to MPs and TAPs. Since these data seem to be still understudied, we think that our analysis can shed light on these patterns. Second, we wish to o�er a formal treatment of these connections, and suggest that we can explain why these patterns occur via this formal treatment. Therefore, we also aim to shed light on how MPs, and in general measure expressions can contribute to lexical aspect, as suggested in the literature (e.g. Morzycki 2006, Zwarts 2008).The paper is organized as follows. Section 2 presents in more thorough detail the data at hand, and outlines the empirical explananda that we aim to account. Section 3 proposes a formal framework for our analysis, which is based on a fragment of type-logical syntax, with a situation semantics interpretation. Section 4 o�ers an analysis of the data, and section 5 o�ers the conclusions to the paper. Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 41 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi 2 General background: Notions and Data The goal of this section is to outline key notions about the semantics of SPs. We �rst discuss general notions and well-documented data about SPs (section 2.1). We then move onto a discussion of the novel data about this category, and its distribution with MPs and TAPs (section 2.2). It is generally acknowledged that SPs denote a relation between a located entity, or �gure, and a landmark object that de�nes a spatial “reference system", aground (Talmy 1978, 2000). Furthermore, SPs are generally assumed to be partitioned in two basic categories: locative and directional SPs. Locative SPs denote a “static" relation between �gure and ground, as the �gure remains in one certain position over a given interval of time. Directional SPs denote a “dynamic" relation, instead, as in the case of to or towards. The �gure is understood to reach, leave or occupy a certain set of changing positions, over an interval of time (Cresswell 1978, Jackendo�1983, 1990, Wunderlich 1991, 1993, a.o.). Furthermore, locative SPs are usually divided into non-projective and projective SPs, with examples being respectively at and behind (Cresswell 1978, Zwarts 1997, a.o.). Examples that present these notions are (10)-(12): (10) (locative, non-projective SP)The man sits at the desk (11) (locative, projective SP)The man sits behind the desk (12) (directional SP)The man has gone to the desk In (10)-(12), the de�nite phrase (DP) the man denotes the �gure, while the DP the desk denotes the ground. The SPs at,behind,to denote the spatial relations that hold between �gure and ground. Each SP denotes a distinct, speci�c spatial relation that holds between the �gure and ground. For instance, at denotes a relation in which a given man is sitting close to the desk, although the speci�c position is not mentioned (Herskovits 1986: ch.4). Instead, behind denotes a relation in which this man sits in one position that is located on the depth axis of the desk, in its “negative" verse (Zwarts 1997). So, to denotes a relation in which the �gure has reached the ground, after having moved in direction of this ground (Jackendo�, 1983, a.o.). Overall, SPs can be divided in a tri-partite, slightly asymmetric taxonomy, with respect to their semantic content.4 This tri-partite distinction plays a role in the discussion of MP modi�cation. This topic has been investigated in detail in one line of research known as Vector Space Semantics (henceforth: VSS, Zwarts 1997, 2010, Zwarts & Winter 2000, Winter 2001, 2005, 2006, Morzycki 2006, Svenonius 2008, Bohnemeyer 2012). VSS has 4This distinction plays a role for SPs, when they receive their spatial (i.e. literal) meaning. Other uses, especially when aspect is taken in consideration, may involve di�erent partitions of the semantic space (Fong 1997, 2001, Roy & Svenonius, 2009, Gehrke 2008, a.o.). Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 42 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi of TAPs is sensible, for the most part, to the subtle semantic properties of the complex constituent that SP and MP form, which in turn acts as an argument of a verb. Both “geometrical” distinctions (i.e. locative vs. directional), and lexical aspect distinctions (telic vs. non-telic) play a role. So, our semantic properties seem to follow certain hierarchical, inherently compositional patterns of distribution. Another set of data that highlights the distribution of MPs, TAPs and SPs, and their hierarchical distribution involves the distribution of locative SPs with a certain sub-type of verbs of motion. It is known that a class of verbs of motion, such as swim or �oat, can denote either “directed” or “located” motion (Talmy 1983, Fong 1997, Folli 2002, 2008, Gehrke 2008, a.o.). A less discussed aspect of this distribution is that projective SPs can occur with MPs and verbs denoting these two slightly di�erent types of motion.10 When this happens, TAPs can occur as well, but the interpretation that emerges as a result depends on the TAP that occurs in a sentence. We show some examples involving swim and �oat in examples (56)-(61): (56) The canoe �oated 50 meters inside the cave (57) The canoe �oated 50 meters inside the cave in one hour/for one hour (58) The girl swam 50 meters below the bridge (59) The girl swam 50 meters below the bridge in one hour/for one hour (60) The canoe �oated inside the cave in one hour/for one hour (61) The girl swam below the bridge in one hour/for one hour The sentence in (56) includes the verb �oated and SP phrase inside the cave, and can furthermore include either the TAP in one hour or the TAP for one hour, as (57) shows. The same holds for the sentence in (58), which includes the verb swam and the SP phrase below the bridge: both TAPs can occur as well, as (59) shows. However, in both (56) and (58) the sentential-level interpretation is ambiguous with respect to lexical aspect. When a TAP occurs, only one possible interpretation becomes accessible. For instance, when in one hour occurs with floated 50 meters inside the cave, the sentence has a telic reading: the canoe moved 50 meters by �oating. When for one hour occurs with this verb and SP phrase, the sentence has an atelic reading: the canoe �oated at a 50 meters’ distance from e.g. the walls of the cave. Note that the same pattern emerges when MPs do not occur in a sentence but SPs and TAPs do, as discussed in previous literature (viz. also (60)-(61)). So, verbs add a further layer of complexity in the “computation" of lexical aspect, with respect to the distribution of MPs, SPs and TAPs. Before we attempt to o�er an analysis for this complex set of data, we summarize our discussion in this section, and outline how we reached our �rst goal. 10We thank an anonymous reviewer for bringing this topic to our attention, as we did not discuss it in a previous version of the paper. Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 49 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi Our discussion of the novel data in (22)-(61) suggests that the interplay of our three syntactic categories (four, if we include verbs) is quite subtle. MPs such as one kilometer can occur with projective (locative) and cumulative (directional) SPs (in front of, through; among others). MPs cannot occur with non-projective or non-cumulative SPs (at, to; respectively). The combination of a projective SP and an MP is inherently cumulative, regardless of the MP’s contribution. So, only a cumulative TAP can occur with this complex constituent. For instance, one meter in front of the desk can only occur with the TAP for one hour, but not with the TAP in one hour. Furthermore, the combination of a cumulative directional SP and an MP becomes non-cumulative. Only an MP such as one kilometer can occur with an SP phrase such as towards the park, but not with a TAP such as for one hour. Directional and locative SPs, when they can occur with MPs, display di�erent interactional properties with respect to TAPs. Furthermore, di�erent types of verbs can occur with these three categories. Verbs that are ambiguous between a directed and a located motion interpretation may be disambiguated by TAPs as modi�ers. When this happens, SPs and MPs may (or may not) contribute to the overall lexical aspect reading. This synopsis of the distributional patterns suggests that we have reached our �rst goal, that of presenting a broader and more accurate picture of the connections among these three categories. As we can easily observe, these distributional patterns also suggest that the compositional, piece-meal interaction of our three target constituents (SPs, MPs, TAPs) follows a certain syntactic and semantic “order” of realization. Therefore, we can assume that, if we propose an appropriate formal analysis of these constituents and their properties, then we can predict how these distributional patterns can emerge, in a compositional way. This formalization represents our second goal, which we pursue in sections 3 and 4. 3 The Formal apparatus In this section we o�er our syntactic and semantic assumptions about our constituents that will pave the way for our account in section 4. Section 3.1 offers the syntactic account, in which we �rst suggest which the most appropriate structure is for our four categories, and then implement a derivational, categorial analysis. Section 3.2 o�ers a semantic account, in which we o�er a theory-neutral interpretation of our categories and their interpretations. 3.1 The Formal Apparatus: Morpho-Syntax The goal of this section is to o�er a morpho-syntactic account of SPs, TAPs, MPs and verbs that paves the way for our semantic analysis. Given our semantic goals, we will mostly focus on two aspects. The �rst is to capture the syntactic structures of our examples, and how our target phrases are hierarchically combined. The second is to give a syntactic account that allows a transparent mapping Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 50 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi onto a compositional semantics. 3.1.1 Morpho-Syntax: The Structural Analysis The goal of this section is to motivate our morpho-syntactic analysis. We start by providing a brief survey of current proposals on the structure of SPs. Classical works on the structure of this category contend that SPs can be decomposed into two distinct, hierarchically arranged heads, known as “Path” and “Place”, or “Dir(ection)” and “Loc(ative)”. Most works follow this structural analysis (van Riemsdjik 1978, 1990, Jackendo�1983, 1990, Wunderlich 1991, 1993, Tortora 2005, 2008, Folli 2008, a.o), at times implementing di�erent labels (Kracht 2002, 2004, 2008 a.o.). While this approach has been quite in�uential, recent research in the cartographic approach suggests that a more �ne-grained analysis of SPs and their structure is possible. Such an analysis stems from one core assumption of cartography. The core assumption states that each identi�able morpheme in an SP can project its own (functional) head;11 hence, that SPs can involve several heads or “positions”. Several proposals exist, to this e�ect (Koopman 2000, Svenonius 2006, 2010, Asbury 2008, den Dikken 2010, Fábregas 2007, Pantcheva 2008, 2010, 2011, a.o.). However, to maintain the discussion clear, we discuss a relatively conservative version of the cartographic approach: den Dikken (2010) (cf. also Svenonius 2010). We present the classical analysis in (62), and this version of the cartographic approach in (63): (62) [DirP [MP ten meters ]to [LocP in front of [DP the table ]] (63) [DegP [ ten meters ] [DirP to [LocP in [Axpart front [KaseP of [DP the car ]]]]] The key di�erences between (62) and (63) can be de�ned as follows. In (63) we have three more heads or “positions”. Two of these heads are “Axpart” and “Kase”, which represent the speci�c projections of the morphemes front and of, part of the SP in front of. In the classical analysis, these morphemes are considered as forming a single lexical unit, hence projecting one head: “Loc”, in (62). The “Deg” head that introduces the MP ten meters, in the cartographic approach, is considered part of the extended projection of an SP. Hence, it represents the third new head in (63). So, the cartographic approach o�ers a more �ne-grained analysis on the morpho-syntax of SPs than the classical approach, although it builds over this approach to a good extent. While classical and cartographic approaches share a certain theoretical continuity, other proposals on the structure of SPs take a di�erent stance. One such 11We do not wish to investigate the complex question on whether SPs are a functional or a lexical category, since this fairly complex topic is orthogonal to our debate, and would lead us too far a�eld. Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 51 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi example is based on the “Lexical Syntax” framework, and its “P-within-P” hypothesis (Hale & Keyser 2002: ch.4, Mateu 2002, 2008). In Lexical Syntax, each morpheme can be associated to one of four types of heads, depending on how many argument phrases it can combine with (0, 1 or 2 arguments). Furthermore, Hale & Keyser (2002) only focus on the structural or abstract properties of lexical items; they do not employ a �ne-grained analysis of morpho-syntactic categories. So, no speci�c labels such as “Dir(ectional)” or “Loc(ative)” are employed, only labels such as the abstract “P” for a head with two arguments. The “P-within-P” hypothesis builds on these assumptions, and is based on one further central assumption. One morpheme of an SP acts as the “main” head; the other SPs are attached as (morphological) segments or “internal” elements of this head. Interestingly, variants of the classical approach exist, that o�er a similar analysis (Emonds 1985, 2000, Kayne 1994, 2004, van Riemsdijk & Huysbregts 2007, a.o.). We show the corresponding structures in (64)-(67): (64) (Lexical Syntax)[PP[Pin- ] -to [XP the car ]] (65) (Lexical Syntax)[PP[Pin- ] -side [XP the car ]] (66) (Lexical Syntax)[PP[Pin front ]] of [XP the car ]] (67) [DirP [Dir[Loc in- ]] -to] [DP the car ]] The structures in (64)-(66) read as follows. The SPs into, inside and in front of are analysed as the combination of a relational head (e.g. of, -side, -to), and a possibly complex phrase/argument SP in speci�er position (e.g. in, in front). The structure in (67) is based on van Riemsdijk & Huysbregts (2007), which analyses the “Loc” head as a segment of the “Dir” head. Overall, as the structures in (64)-(67) show, the subtle di�erences between these approaches and cartographic/classic ones correspond to the “position” in the clausal spine of each head, as well as their speci�c “quantity”. The intuition that SPs involve a complex structure, however, runs across each approach, although in di�erent formulations. Before we choose which structure of SPs to adopt, we look at the structure of our MPs ad TAPs. Standard approaches on MPs consider this category as a part of the so-called “Degree Phrases” (Kennedy 1999, 2007, Morzycki 2005, 2006), such as ten meters long. MPs such as ten meters are treated as a variant of (quanti�ed) DPs that sit in the speci�er position of a silent Degree head. Instead, APs such as long are placed in the complement position of this head. The structure of TAPs has been less studied, although an uncontroversial claim is that it involves a prepositional head, and a DP argument (Morzycki 2004, 2005, a.o.). We show these structures in (68)-(69): (68) [MeaP [DP ten meters ] (Mea) [AP long ]] Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 52 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi (69) [PP for [DP one hour ]] The structures for the MP ten meters long and the TAP for one hour should be straightforward to read, keeping in mind that we represent our silent Degree phrase as “(Mea)”. One crucial assumption that this analysis allows us to propose is that, if SPs are part of a sentence, then a Measure head takes an SP phrase as its complement phrase. We make this assumption for one simple reason. Certain locative phrases can appear as particle-like phrases (e.g. in front, ahead), in these and other cases of “argument demotion” (Svenonius 2010), and occur with MPs, viz. (70a)-(71a). In such a case, the resulting MP acts as a complement of a verb. Given these data, a simple account of their structure can be the one in (70b)-(71b): (70) a. Mario is sitting ten meters in front (of the car) b.[MeaP [DP ten meters ] (Mea) [SP in front ]] (71) a. Mario is sitting ten meters behind (the car) b.[MeaP [DP ten meters ] (Mea) [SP behind ]] The simple analysis of ten meters in front and ten meters behind which we can o�er via this assumption is shown in (70b) and (71b). Importantly, if we take this analysis of MPs, we must take Lexical Syntax as our framework of reference. The reason is as follows. In our discussion of the data, one element seems to play a key role in the overt expression of licensing patterns. As we have seen in examples (30)-(39), certain SPs such as in can combine with relational morphemes such as –side, the resulting SP (inside) being able to occur with an MP. The morphological features and semantic content of a head matter: into cannot combine with MPs, unlike –side. So, a single morphological unit seems to determine this licensing pattern, depending on whether this unit can in turn denote certain structural values or not. In other words, both inside and into seem to involve the combination of two morpheme into a larger unit, with one morpheme (-to or -side) determining if the SP can occur with an MP. Although this fact would not be easily captured (if at all) in a cartographic approach, it �nds a natural explanation in a Lexical Syntax analysis. The interpretation of the “main” head of an SP determines this licensing pattern, as the data suggest. Another important aspect is that the data in (70)-(71) seem to suggest that the “internal” SP forms a single unit: demotion cannot target segments of a word. So, we cannot have the string #in (front of the car): demotion, as instance of ellipsis, seems to target “word” units (Merchant 2001, 2004, Fábregas 2011, a.o.). Although this fact could �nd an explanation within cartographic approaches as well, it �nds a more natural explanation in an analysis that assumes that SPs consist of only two lexical units. Simplifying matters somewhat, this approach predicts that, if a head Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 53 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi SP and its complement are demoted (here, of the car), then the “internal” SP acts as a complement of the verb. This analysis is not directly accessible in a cartographic approach, as we have just discussed: ruling out in, but not in front, would require ad hoc assumptions. From these considerations, we can conclude that an optimal account for our data is one that divides SPs “only” in two lexical units, and takes the internal unit to be a phrase in its own right. Lexical Syntax is such an approach, as it allows us to o�er the structural analysis for SPs, as shown in (72). We then assume that SPs combine with Measure heads s as phrases sitting in the head’s complement, thus forming a phrase with the DPs such as ten meters. The resulting MP becomes the complement phrase of a verb, forming a minimal sentential structure, e.g. a VP such as Mario is sitting ten meters in front of the desk (cf. (51)). A TAP, then, modi�es this whole sentence, something that we represent by having a VP sitting in speci�er position of a silent “(M)” head, as standardly assumed (cf. Morzycki 2005: ch.1). This is shown in (73): (72) [SP [LocP in front] of [DP the desk ]] (73) [M0[VP sitting[MeaP[DP ten meters](Mea)[SP in front of the...]](M’)[PPfor[DP one hour]]] The simpli�ed structure in (73) says that a phrase such as ten meters in front of the desk, from (51), has the following structure. A silent measure head, labelled “(Mea)”, takes an SP phrase (in front of the desk) and a “measure” DP (ten meters) as arguments. A verb, in this case is sitting, takes this MeaP and a subject DP as arguments, to form a sentence, which we represent as a VP in (73).12 A second silent head, “(M’)” mediates the combination of this VP and the TAP for one hour into a larger M’P phrase. Note that the SP phrase in front of the car is in turn the combination of an SP head of, with a locative phrase in front and a ground DP the car, as shown in (72). As the structure indirectly suggests, the order of composition, when both MPs are present, is that of an MP being merged before a TAP. Intuitively, our syntactic analysis can now mirror the licensing semantic patterns that we discussed in previous section. Our choice appears germane for our semantic account, since it captures the fact that the distribution of TAPs is sensible to the distribution of MPs, SPs and verbs, to varying degrees. After this discussion, a caveat is in order. Although we make a certain theoretical choice in our proposal, other solutions could be possible. To our understanding, an equally acceptable semantic analysis can be o�ered, which is based on the classical/cartographic approaches we discussed so far. However, a cartographic approach would make the exact implementation of our analysis quite more complex, and perhaps more cumbersome than the necessary, when this analysis 12As it should be obvious, we abstract away from o�ering an analysis on any sentence-based functional structure. Hence, our sentences correspond to full VPs. Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 54 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi is possible at all. We will discuss more technical problems of the cartographic approach in section 3.1.2 once we have our theoretical apparatus at our disposal. Overall, we feel that opting for a simpler approach the syntax-semantics interface is an important goal, for us. Among other things, it allows us to focus on the main head SP (e.g. to,of,-side) as the locus at which semantic properties are ascribed. However, we leave open the question on whether our simpler approach is also the best approach, for a general theory of SPs. Our main concern, from this point onwards, is that of accounting how the structures in (70)-(73) can be derived, hence paving the way for our semantic analysis. 3.1.2 Morpho-Syntax: Type-Logical Syntax and Derivations The goal of this section is to show how our structures can be derived by combining (“merging”) the relevant lexical items together. Speci�cally, we aim to show how our constituents are merged together in an ordered way, so that we can capture how our “asymmetric” distributional patterns can emerge, as a result. For this purpose, we adopt some kernel assumptions of a syntactic framework known as type-logical calculi (Jäger 2005, Moortgat 2010, 2011, Morryll 1994, 2011, a.o.). More thorough presentations of this framework and its theoretical connections to other frameworks within the minimalist programme (e.g. Distributed Morphology: Harbour 2007, Harley 2012; a.o.), can be found in Ursini (2011, 2013a,b,c), Ursini & Akagi (2013b). In this paper, we simply o�er a more “compact” presentation of the framework that allows us to focus on our distributional data. Our assumptions are de�ned as follows. In type-logical calculi, syntactic categories or types are represented as either “complete” or “incomplete”. Complete types represent syntactic objects that can act as distinct, independent units. For instance, the type np is the type of noun phrases such as the boy, a syntactic unit that can be independently an argument of a verb. Incomplete categories must combine with other categories, to form a complete category. Under this assumption, an attributive adjective such as tall is assigned the type np/np. This means, for instance, that an adjective must combine with a noun phrase (e.g. man) in order to form a (more complex) noun phrase (tall man). The slash symbol “/” represents the Merge operation (cf. Chomsky 1999: 2-4, Morryll 2011: ch. 1, a.o.). This connective represents Merge as a binary,associative and idempotent operation. These properties are de�ned as follows. First, this operator takes two units and their types and merges them into one unit/type (binary property). Second, the order of application is not crucial, as long as the sequence of combined types is preserved (associativity). Third, if two constituents of the same type are combined, then the result will yield the same type (idempotence).13 13Formally, a connective “^" is binary i�:a ^b=(a, b); associative i�:(a^b)^c=a^(b^c); idem- Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 55 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi We will discuss the relevance of these properties when they will play a crucial role in our derivations. As we are mostly concerned with basic syntactic derivations, we only implement the right-associative version of Merge, which we call Merge right. We leave aside the possibility that other categorial connectives and “directions” of Merge can (or must) be implemented, in our treatment. We also have a second reason for this choice. Recall that the MeaP that results from merging an SP and a “quantity” DP (e.g. ten meters in front of the desk) acts as an argument of a verb. The resulting phrase determines which type of TAP is merged, successively. In linear order terms, we can assume that for SPs, derivations seem to proceed “left-to- right”. Furthermore, this assumption is in line with models of production that aim for psychological reality (Levelt 1989, Jarema & Libben 2007, see also Phillips 1997, 2003, 2006, for a non-type-logical, minimalist proposal). We take this as an appealing, though not crucial property for our approach; however, we will discuss which data seem support this approach, when relevant. We then implement a view of types that is based on, but not identical with Hale & Keyser’s (2002) theory of Lexical Syntax. Our main di�erence from their theory is as follows. We only assume one atomic type, from which the other three types are derived as incomplete types. We call this atomic type p, mnemonic for “phrase”. Via the de�nition of Merge right and our basic type, we can de�ne the closure set of recursive types in our analysis via the following set of rules:14 (74) 1. (lexical type)pis a syntactic type 2. (type formation)If xis a type and yis a type, then x/yis a type 3. (type reduction)If x/yis a type and yis a type, then (y/x)/x:=y,y/(y/x):=x 4. (closure property)Nothing else is a type The rules in (74) read as follows. Given the atomic (“lexical”) type of arguments p(rule 1), then one can recursively construct more complex types as the “association” of two (more) basic types (rule 2). Conversely, if one merges a complex type with a simple type, the result will be a “lower” type (rule 3). No other combinatoric options are available (rule 4). These rules allow us to spell out a minimal set of types that we can assign to our lexical items, which is the set TYPE={p, p/p,p/p/p}. This rather basic type set allows us to de�ne one fragment of typed constituents that we will employ in our derivations, which we present in (75): potent i�:a^a=a. These speci�c properties are not crucial, here. 14For the sake of simplicity, we use the (de�nitional) identity symbol “:=” in our derivations, which reads as “is de�ned as” or also “results in”, rather than the standard turn-style symbol “`”. Nothing crucial hinges on this notational change. Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 56 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi (75) a. p/p/p::={of, to,-side, (Mea), (M), is sitting, swam} b. p::={Mario, the canoe, ten meters ,one kilometre, the car, in front, in, in one hour, for one hour, 50 meters} As the type assignment in (75) shows, heads are assigned type p/p/p, since they can sequentially merge with two arguments of typep, and form a (complex) phrase of type p. Note that our phrases are all assigned the type p, because they always act as arguments of some other functional unit that acts as a head. No lexical items are assigned the type p/p, as this type plays a role in di�erent types of data (e.g. adjunction) that are not relevant, here. Note, though, that we can obtain this type when we merge two items, so we include it in our type set. Our assignment is incomplete, in the sense that we do not assign a type to each constituent we discuss in our examples. For instance, we assign the type pto the DP Mario, hence taking a very simpli�ed approach to DP structure. We also treat progressive and past verbal forms as a single (verbal) head (is sitting,swam). Furthermore, we do not analyse TAPs such as in one hour, directly assigning them the type of phrases. For our purposes, this simpli�cation allows us to discuss the distribution of verbs with our three categories, without any loss of precision. Although a more accurate analysis is possible (cf. Ursini 2013b,c), this simple approach to verbs and TAPs will su�ce, for our analysis of the data. For our derivations, we de�ne a simple pre-order as the pair of an interval set I, and an addition operation “+”, i.e. <I,+>. This pre-order represents an index set, which in turn allows to represents the steps in a derivation as ordered elements. We introduce the operations Lexical selection (henceforth: LS) and Merge introduction (henceforth: MI), as operations that respectively select an item from the enumeration, and merge items together. We show how this derivational system works by o�ering a derivation for the MP ten meters in front of the car, in (76): (76) (LS)t. [ ten metersp] (LS)t+1. [ (Mea)p/p/p ] (MI)t+2. [ ten metersp]/[ (Mea)p/p/p ]:=[p/p[ ten metersp ] (Mea)p/p/p ] (LS)t+3. [ in frontp] t+4. [p/p[ten metersp] (Mea)p/p/p ]]/[ in frontp]:= [p[ ten metersp] (Mea)p/p/p [ in frontp]] (MI) (LS)t+5. [ of p/p/p ] t+6. [p[ ten metersp] (Mea)p/p/p [ in frontp]]/[ ofp/p/p ]:= [p[ ten metersp] (Mea)p/p/p [p/p[ in frontp]] ofp/p/p ] (MI) (LS)t+7. [ the carp] The derivation in (76) reads as follows. From step tto step t+3, the complex constituent ten meters in front is derived, as phrase (of type p). This phrase, together the with ground (DP) phrase the car, is merged with of, from derivational steps t+4 to t+8. The result of this derivation is the phrase ten meters in front of Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 57 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi the car, which can then act as the complement phrase of a verb, such as is sitting15. Once we have shown how this type of phrases is derived, we can o�er a “compressed” derivation for (51), repeated in (77a) in its interpretable form (i.e. including the TAP for one hour): (77) a. The man is sitting one meter in front of the desk for one hour b. (LS)t. [the manp] (LS)t+1. [is sittingp/p/p] (MI)t+2. [the manp]/[is sittingp/p/p]:=[ p/p[ the manp] is sittingp/p/p] (LS)t+3. [in front of the deskp] t+4. [p/p[the manp]is sittingp/p/p]/[in front of the deskp]:= [p[the manp]is sittingp/p/p[in front of the deskp](MI) (LS)t+5. [(Mod)p/p/p] (MI)t+6. [the man...deskp]/[ (Mod)p/p/p]:=[p/p[the man...deskp](Mod)p/p/p] (LS)t+7. [for one hourp] t+8. [p/p[the man...deskp](Mod)p/p/p]/[for one hourp]:= [p[the man...deskp](Mod)p/p/p[for one hourp]] (MI) This derivation reads as follows. From the steps tto t+4, the “partial” sentence the man is sitting one meter in front of the desk is derived, although in a rather compressed format. Steps t+5 to t+8 show how this sentence can be then modi�ed by the TAP in one hour: a silent head, “(Mod)”, takes the whole sentence (here, a VP) as its speci�er phrase, and the TAP as its complement phrase. Note that we use elliptical forms (...desk) to simply maintain a certain compactness for our derivational steps. As a result, we are now able to capture standard structural analyses of this type of modi�cation (Dowty 1979, 1989, Morzycki 2005; a.o.) via our more “dynamic” derivational system. Importantly, these derivations also show that a cartographic analysis would run into trouble. If we would treat each morpheme as a head of type p/p/p, even the merge of in front with of would case a type mismatch, which would need quite complex assumptions, for the derivation to proceed successfully. Our approach avoids this problem in a rather straightforward manner, and paves the way for our semantic approach. However, before we move to semantic matters, we o�er some considerations on our derivations and the results they bring about.16 15This derivation also shows that our operation MI seems to “remove” structure, rather than introduce it: the type of the merged constituents is simpler than its input types. In this regard, our operation seems closer in purpose to “elimination” operations in TL calculi (cf. Morryll 2011: ch.1). However, we prefer the label “Merge Introduction”, as it highlights that that a structure-building operation is introduced in a derivation and “introduces” a new constituent in the derivational space. 16Note: of and the car merge with in front, rather than with the ten meters in front, as we assume of takes a spatial phrase as its speci�er. In this case, the co-application principle allows Merge to access the “smaller” phrase as a type input for the new head. The head of, of type pn/p/p, can access the phrase in front, of type p:=(p/p)/pn. Their Merge amounts to: Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 58 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi other (cf. (81)). A-cumulativity imposes a strict ordering on the situations of a predicate, whether these are simple or structured/sum situations. Similarly, a predicate Xis monotonic if, given a part-of relation de�ned over a set of situations, the predicate preserves this monotonic relation (cf. (82)). For commodity, we restrict ourselves to upward monotonicity, in our de�nition. Instead, a predicate Xis telic when it lacks proper parts that also belong to the denotation of the predicate under discussion (cf. (83)). According to this de�nition, then, telicity is akin to atomicity, in the sense that telic predicates denote atomic situations (cf. Krifka 1998, Zwarts 2005, Harbour 2007; a.o.). The linguistic import of these properties can be de�ned as follows. Cumulativity says that for all the distinct paths (as situations) that are “towards” a house, then their sum will be “towards” this house. Asymmetric cumulativity is represented via the disjointed conditions s’<s and s<s’, which in turn represent the fact that, for instance, the concatenation of two “towards” paths must come in a certain order. The relation “<pc” stands for the “precedence” relation which, simplifying matters somewhat, says that one element precedes another element, in a given (ordered) domain (Krifka 1998: 204). Monotonicity, instead, works as follows. Take two situations that are partially ordered, and are both in the denotation of an “in front” predicate. If this is the case, then one “in front” situation will be part of another “in front” situation. Instead, if a predicate is telic, then the situations in its denotation will not possibly stand in the part-of relation. A path/situation that is “to” the house” cannot be part of another path that is also “to” the house. Conversely, two paths that are “towards” the house can be combined into a longer “towards” path, and related via a precedence relation, which represents their internal linear order. An important consequence of these de�nitions is that they allow how to show why these properties stand in certain semantic relations. From (80) and (81), we can deduce that an A-cumulative predicate is also monotonic, but also that the monotonicity of a cumulative predicate can be derived. This is the case, because the existence of sum situations in the denotation of a predicate (X(s’Ls)) entails that a part-of relation between these situations can be de�ned. Simplifying matters somewhat, if a predicate has cumulative denotation, then for all the situations s, s’, s” we can assume that the relation X(s)X(s’Ls”) holds, as ss’Ls” holds, too. Furthermore, from (80), (81) and (82) we can deduce19 that cumulativity can be de�ned as the inverse relation of telicity, since telicity lacks a partial order that (indirectly) de�nes cumulativity. A-cumulativity and telicity share a di�erent relation, but we defer a discussion of the precise details to our discussion of a case in which these properties interact. 19A formal discussion (and proof) of these relations can be found in Krifka (1998), among others. We do not discuss this aspect here, as we think that it would make the prose too cumbersome. Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 65 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi We will discuss the actual linguistic realizations of these properties via the derivations of some examples. Now, we can o�er an interpretation of our lexical items based on our type assignments, and from which we can show how we can derive the interpretation of our examples. Some sample interpretations are shown in (84). Elements in the a.-list are of type <s,<s,s> >, items in the (b)-list are type <s>: (84) a. [[ of ]]:=x.y.MONs:P’(x,y), [[ (P) ]]=x.y.MONs:P’(x,y), [[ at ]]:= x.y.MONs:P’(x,y), [[ to ]]=x.y.TELs:to’(x,y), [[ -side ]]:=x.y.CUMs:side’(x,y),[[ (D) ]]=x.y.A-CUMs:P’(x,y), [[ (Mea) ]]:=x.y.MONs:Mea’(x,y),[[ (M) ]]:=x.y.s:(x^y) [[ �oat ]]=x.y.±A-CUMs:float’(x,y), [[ is sitting ]]=x.y.CUMs:sit’(x,y) b.[[ in front ]]:=in-fr,[[ in ]]:=in, [[ above ]]:=ab,[[ along ]]:=al, [[ the car ]]:=c,[[ the park ]]:=p,[[ the river ]]:=r,[[ the cloud ]]:=cl, [[the canoe]]=cn,[[ ten meters ]]:=10-mt,[[ one hundred meters ]]:=100-m, [[50 meters ]]:=50-m, [[ one kilometer ]]:=1-km, [[in one hour ]]:=TELs:one-H’(s),[[ for one hour ]]:=CUMs:one-H’(s) In prose, each head denotes a part-of (monotonic) relation that can combine with two arguments, and form a structured situation as a result. This structured situation is then speci�ed with respect to a structural property, whether this property is monotonicity, telicity or cumulativity. So, the speci�c interpretation of each head depends on whether it has the asymmetric cumulative property or not, such as silent Dheads (for “Directional”), or Projective heads P. Furthermore, each head can carry its own speci�c lexical content. For instance, the denotations of the verbs �oat and is sitting represent this lexical content as a property that identi�es the type of situation under discussion. A similar consideration applies to our SPs and TAPs, as the translations show. Note that, in our translations, we abstract away from both temporal and (grammatical) aspect morphology of verbs, as we do not o�er an interpretation for past and progressive morphemes. To the best of our understanding, this aspect is not crucial, for the correct analysis of our data. One important aspect of our translations for verbs is that we represent the semantic ambiguity of verbs such as �oat and swam (i.e. directed vs. located motion) as a rather simpli�ed form of lexical underspeci�cation (Poesio 2001: ch.4, Harbour 2007, Egg 2011, Ursini 2013c, a.o.). For instance, �oat is represented as either denoting an A-cumulative or not A-cumulative sequence of situations: that is, a directed or non-directed (located) structured situation. The symbol “±” represents that the interpretation of this verb is the set-theoretical union of these two possible (and disjointed) readings: CUM and A-CUM, or more accurately a cumulative and an a-cumulative reading. Note that, although A-cumulativity is not the exact complementary property of cumulativity, this notation will make our analysis easier to read. We defer to the next section an explanation of how this form Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 66 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi of underspeci�cation is solved. Other important aspects of our translations pertain to the translations we o�er for SPs and other heads. For instance, while we assume that of denotes the part-of relation, we take that other heads such as to or –side (as in inside) di�er in the speci�c type of relation they denote. Note that our head M, the head that allows the combination of a complex phrase with the TAPs in/for X time, has a conjunctive semantics.20 We take this to be a fairly uncontroversial assumption, as it parallels standard treatments of adverbs, from a semantic perspective (cf. Morzycki 2005: ch.1). Our minimal change consists in having a relational element, rather than an adjunct-like element, to capture this interpretation. Again, we show how this assumption derives the relevant interpretation in the next section. One distinction that we think being relevant for our analysis, based on the VSS approach, is that between non-projective and projective SPs. The main semantic di�erence between these two categories is that non-projective SPs lack a speci�c orientation for set of vectors they denote. Informally, the vectors in the denotation of at do not form a scale with respect to a given length and dimension (Zwarts & Winter 2000: 181, Bohnemeyer 2012). In our approach, this is captured as a property that we label as “¬MON”, and that represents the lack of an ordering over the situations within the denotation of at. This is in part inaccurate, as at seems to denote a structured, although not “ordered” set of situations (Nam 1995, Zwarts 2010, Ursini & Akagi 2013a for experimental evidence). For our purposes, an analysis of this lack of internal “order” seems to correctly capture the semantic di�erence between this non-projective SP and other projective SPs (e.g. in front of,above). More importantly, it su�ces to o�er an analysis of the distributional patterns that we are going to discuss next. 4.2 The Analysis: The Derivational Data We now show how and why our analysis can actually predict the data we have discussed so far. We do by directly o�ering interpreted versions of the basic syntactic derivations discussed in (76)-(77). Intuitively, while each sentence can receive the same type of syntactic derivation, the semantic interpretation of each speci�c sentence will determine the speci�c result of this interpretive process. For this reason, we do not explicitly represent Merge, but rather use brackets to mark arguments as opposed to relations. We then state the semantic types of lexical items and the operation involved, which is either interpretation (henceforth: Int) or function application (henceforth: FA), respectively the semantic counterparts of Lexical selection and Merge. We start by o�ering a derivation of our example (23), repeated here as (85): 20In our mereological approach, conjunction “^” and set intersection “\” are semantically equivalent. We maintain this distinction to better highlight the semantic contribution of TAPs. Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 67 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi (85) a. #The man walked one hundred meters into the park b. (type <s>, Int)t.[[ one hundred meters ]]:=100-m, (type <s,<s,s», Int)t+1.[[ (Mea) ]]:=x.y.MONs:Mea’(x,y) t+2.([[ one hundred meters ]])[[ (Mea) ]]:= (100-m)x.y.MONs:Mea’(x,y) = y.MONs:Mea’(100-m,y) (type <s,s> FA) (type <s>, Int)t+3.[[in]]:=in t+4.[[ one hundred meters (Mea) ]]([[ in ]]):= y.MONs:Mea’(100-m,y)(in)=MONs:Mea’(100m,in) (type <s>,FA) (type <s,<s,s», Int)t+5.[[ to ]]:=x.y.TELs’:to’(x,y) t+6.([[ one hundred meters (Mea) in ]])[[ to ]]:= (MONs:Mea’ (100-t,in)) x.y.TELs’ :to’ (x,y) = y.MONs:Mea’(100-m, TELs’:to’(in,y))= # (result unint., derivation crashes) The reason for the derivation crashing is simple. Telicity is de�ned as the lack of a part-of relation between situations (i.e. (¬s’s)), so a telic predicate cannot become part of a predicate that, in turn, is ordered via a part-of relation (i.e. s’s). If we employ explicit structural relations rather than their implicit operator counterparts, we have s¬(s”s’) as our situation structure for (85). This structure reads: there is a situation that should lack proper parts (the negated part), but these missing proper parts have parts on their own.21 This paradoxical relation is, of course, not a possible object if our model of discourse, unless we take the involved situations to correspond to the empty set {ø}. So, we correctly rule out that MPs such as one hundred meters,ten meters can combine with telic SPs such as to, into and so on. Therefore, our account can now predict the data in (22)-(25), by (correctly) deriving uninterpretable sentences as sentences that denote the null value in the model. One important observation is the following. Similar patterns are often modelled via presuppositions on predicates, in the literature (Krifka 1998: 216-217 on TAPs, Morzycki 2005: ch.1 on adjectival modi�cation). In our presupposition-less approach, we can derive and hence predict which phrases are uninterpretable by simply having their composition to denote an “impossible" situation. When to merges with ten meters in, function application yields an uninterpretable result: a situation with the wrong structure becomes part of another structured situation. This result, however, is not a possible result for the composition of an MP and an SP. We show how an interpretable phrase can emerge, by o�ering a derivation for (26), repeated here as (86): 21Step t+6 implicitly captures the semantic re�ex of co-application, since the relation denoted by to is “embedded” within the larger relation denoted by ten meters into the park. Formally, we have: (MONs:Mea’(100-t,in))x.y.TELs’:to’(x,y) = (y.(MONs:Mea’(100-t,y)))((in)x.y.TELs’:to’(x,y)) = (y.(MONs:Mea’(100-t,y)))(y.TELs’:to’(in,y)) = (y.(MONs:Mea’(100-t,TELs’:to’(in,y). In words, one argument (in) is “passed” onto the new relation, which is then composed with the previous function via function composition. See Moortgat (2010: ch. 2, 2011: §2) for discussion, once more. Uninterpretability emerges as a structural inconsistency that emerges from this derivation, then. Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 68 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi (86) a. The car traveled one kilometer along the river b. (type <s>, Int)t.[[ one kilometer ]]:= 1-km, (type <s,<s,s», Int)t+1.[[ (Mea) ]]:=x.y.MONs:Mea’(x,y) (type <s,s>,FA)t+2.([[ one kilometer ]])[[ (Mea) ]]:= (1-km)x.y.MONs:Mea’(x,y)=y.MONs:Mea’(1-km,y) (type <s>, Int)t+3.[[ along ]]:=al (type <s>,FA)t+4.[[ one kilometer (Mea) ]]([[ along ]]):= y.MONs:Mea’(1-km,y)(al)= MONs:Mea’(1-km,al) (type <s,<s,s», Int)t+5.[[ (D) ]]:=x.y.A-CUMs’:P’(x,y) (type <s,s>,FA)t+6.([[ one kilometer (Mea) along ]])[[ (D) ]]:= (MONs:Mea’(1-km,in))x.y.A-CUMs’:P’(x,y)= y.MONs:Mea’ (1-km, A-CUMs’:P(al,y)) = y.A-CUMs:Mea’(1-km,s:P(al,y)) t+7.[[ the river ]]:=r (type <s>,FA)t+8.[[ one kilometer (Mea) along (D) ]]([[ the river ]]):= y.A-CUMs:Mea’(1-km, s’:P(al,y))(r)= A-CUMs:Mea’(1-km, s’:P(al,r)) The derivation reads as follows. From steps tto t+4, the interpretation of ten meters along is derived, as a relation between a given length (one kilometer) and a speci�c spatial dimension to which this length is ascribed. When this phrase is merged with a silent head and the other argument the river, from steps t+5 to t+8, the ground object is speci�ed, with respect to which this “along” relation is de�ned. During step t+6, an important process of the derivation takes place. Recall that we de�ned asymmetric cumulativity as cumulativity with a precedence relation de�ned over the domain of its objects. When an asymmetric cumulative structured situation becomes part of a monotonic structured situation, the monotonicity property selects one of the two ordering relations: either s’<pcsor s<pcs’. So, the “global” situation becomes asymmetrically cumulative, via what could be considered a phenomenon of percolation/projection of one local semantic property to a more global domain (Harbour 2007: ch. 2-4, Adger 2010, for discussion).22 We represent this result by representing the projecting property, A-cumulativity, as the main operator for the resulting situation. This selection has another semantic consequence. Since one situation part will be de�ned as being having a certain lexical property, in this case being one kilometer along a river, there will not be any “whole” parts that will have this property as well. In other words, one kilometer along the river turns out to denote a telic predicate, as a logical consequence of the interaction between two non-telic meanings. We can now predict (26)-(29), since we can account why telic directional SPs 22If we consider semantic properties extensionally, then a part-of relation among properties can be established among properties. In this sense, the semantic e�ect of composing monotonic situation with a cumulative situation, to obtain a cumulative denotation, can be represented as follows: CUM [MON=CUM, by de�nition. The same holds for the other combinations of properties. See Zwarts (2008) for a more thorough discussion on the ordering relations among these properties. Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 69 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi cannot merge and compose with MPs, but also why (symmetric) cumulative SPs can do so. One further prediction is that non-projective locative SPs cannot merge with MPs, while projective SPs can do so. This is shown via (32) and (35), repeated here as (87)-(88): (87) a. #The man is sitting ten meters at the desk b. (type <s>, Int)t.[[ ten meters ]]:=10-m, (type <s,<s,s> >, Int)t+1.[[ (Mea) ]]:=x.y.MONs:Mea’(x,y) t+2.([[ ten meters ]])[[ (Mea) ]]:= (10-m)x.y.MONs:Mea’(x,y) = y.MONs:Mea’(100-m,y) (type <s,s ,FA) (type <s>, Int)t+3.[[ (s) ]]:=s (type <s>,FA)t+4.[[ ten meters (Mea) ]]([[ (s) ]]):= y.MONs:Mea’(10-m,y)(s)= MONs:Mea’(10-m,s) (type <s,<s,s> >, Int)t+5.[[ at ]]:=x.y.¬MONs’:at’(x,y) t+6.([[ ten meters (Mea) (s) ]])[[ at ]]:= (MONs:Mea’(10-m,(s)))x.y.¬MONs’:at’(x,y)=# (derivation crashes) (88) a. The osprey is hovering ten meters above the cloud b. (type <s>, Int)t.[[ ten meters ]]:=10-m, (type <s,<s,s> >, Int.)t+1.[[ (Mea) ]]:=x.y.MONs:Mea’(x,y) t+2.([[ ten meters ]])[[ (Mea) ]]:= (10-m)x.y.MONs:Mea’(x,y) = y.MONs:Mea’(10-m,y) (type <s,s>,FA) (type <s>, Int)t+3.[[ above ]]:=ab t+4.[[ ten meters (Mea) ]]([[ ab ]]):= y.MONs:Mea’(10-m,y)(ab)=MONs:Mea’(10-mt,ab) (type <s>,FA) t+5.[[ (P) ]]:=x.y.MONs’:P’(x,y) t+6.([[ ten meters (Mea) above ]])[[ (P) ]]:= (MONs:Mea’(10-m,ab))x.y.MONs’:P’(x,y)= y.MONs:Mea’(10-m,s’:P’(ab,y)) (type <s,s>, Int) t+7.[[ the cloud ]]:=cl t+8.[[ ten meters (Mea) above (P) ]]([[ the cloud ]]):= y.MONs:Mea’(10-m,s’:P’(ab,y))(r)= MON:Mea’(10-m,s’:P’(ab,r)) (type <s>,FA) These derivations closely mirror the derivations in (85)-(86). In the case of (87), the mismatch between properties is the following. A situation s’ is de�ned as being non-monotonic, as well as part of a monotonic situation s. A paradoxical model-theoretic object, an “impossible” situation, is derived; hence the corresponding phrase is uninterpretable. In the case of (88), the interpretation is a Monotonic, structured situation: a situation in which a distance of ten meters between cloud and the osprey’s position is de�ned as part of a larger situation. Again, we represent the percolation/projection of properties by removing redundant operators (here, MON). Overall, our account can now predict the data in (30)-(39), since it can account how MPs can merge with projective locative SPs (here, above), but not with non-projective SPs (here, at). Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 70 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi We can now focus on our most complex data, starting from the examples in (40)-(55). We show how MeaPs such as one kilometer towards the park can (indirectly) merge with certain TAPs but not others: in this case, in one minute. We start our derivations from the interpretations of the MeaPs, to maintain the discussion relatively simple. For space reasons, we employ the constants a and b for situations, aside the standard s. We also omit the part of the derivation that generates the full VP of which one kilometer towards the park is the complement. This is not problematic, as verbs do not play a crucial role, at least not in these examples (but see again (77) for a full derivation). We then repeat example (45) as (89), and split the two possible forms of the sentences into two parallel derivations, illustrated in (89b)-(89c): (89) a. The car went one kilometer towards the park in one minute/#for one minute b.t+k.[[ one kilometer towards the park ]]:= A-CUMaP’(a:Mea’(1-km,s’:(tw,p) (type <s>,FA) k+1. [[ (M) ]]:=x.y.s:(x^y) k+2.([[ one kilometer towards the park ]])[[ M]]:= (A-CUMaP’(a:Mea’(1-km,s’:(tw,p)))x.y.s:(x^y)= y.s:(A-CUMaP’(a:Mea’(1-km,s’:(tw,p)))^y) (type <s,s>,FA) (type <s>, Int)k+3.[[in one minute ]]:=TELb:one-min’(b) k+4.[[ one kilometer towards the park (M) ]]([[in one minute ]]):= y.s:(A-CUMaP’(a:Mea’(1-km,s’:(tw,p)))^y) (TELb:one-min’(b))= s:(A-CUMaP’(a:Mea’(1-km,s’:(tw,p)))^TELb:one-min’(b))= s:(A-CUMsP’(s:Mea’(1-km,s’:(tw,p)))^TELs:one-min’(s))= TELs:(a:P’(a:Mea’(1-km,s’:(tw,p)))^b:one-min’(b)) (type <s>,FA) c. t+k.[[ one kilometer towards the park ]]:= A-CUMaP’(a:Mea’(1-km,s’:(tw,p) (type <s>,FA) (type <s,<s,s> >, Int)k+1.[[ (M) ]]:=x.y.s:(x^y) k+2.([[ one kilometer towards the park ]])[[ M]]:= (A-CUMaP’(a:Mea’(1-km,s’:(tw,p)))x.y.s:(x^y)= y.s:(A-CUMaP’(a:Mea’(1-km,s’:(tw,p)))^y) (type <s,s>,FA) (type <s>, Int)k+3.[[ for one minute ]]:=CUMb:one-min’(b) k+4.[[ one kilometer towards the park (M) ]]([[for one minute ]]):= y.s:(A-CUMaP’(a:Mea’(1-km,s’:(tw,p)))^y) (CUMb:one-min’(b))= s:(A-CUMaP’(a:Mea’(1-km,s’:(tw,p)))^CUMb:one-min’(b))=# (d. crashes) Recall that this is a partial misrepresentation of the syntactic structure of these sentences, although it is inconsequential and explanatorily more immediate, since Mactually merges with a full VP. The derivations in (89b) and (89c) read as follows. In (89b), the two phrases one kilometer towards the park and in one minute denote an A-cumulative and a telic predicate, respectively. When they are conjoined via a silent head M, they both introduce conjoined structured situations that are bound by two distinct operators, A-CUM and TEL. The intersection of these conjoined structure is the set of situations that are ordered according to a Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 71 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi precedence relation, and lack proper parts: telic (and ordered) situations. So, we can simply apply a basic logical identity, and have the telic operator to bind the main situation s, as shown in (89b). In (89c), this is not possible: the conjunction of two situations aand bis de�ned as having two complementary properties at the same time. A structured situation s, is de�ned as being symmetrically and asymmetrically cumulative. This yields an uninterpretable situation, hence the derivation crashes. A symmetrical result yields for MeaPs involving projective SPs, such as ten meters above the cloud. We show this speci�c pattern via a “compressed” derivation of (55), repeated here as (90): (90) a. The osprey is hovering ten meters above the cloud #in one hour/for one hour b.t+m.[[ ten meters above the cloud (M) ]]([[ in one hour ]]):= y.s:(MONaP’(a:Mea’(10-m,s’:(ab,cl)))^y) (TELb:one-h’(b))= s:(MONaP’(a:Mea’(10-m,s’:(ab,cl)))^TELb:one-h’(b))=# (der. crashes) c. t+m. [[ ten meters above the cloud (M) ]]([[ for one hour ]]):= y.s:(MONaP’(a:Mea’(10-m,s’:(ab,cl)))^y) (CUMb:one-h’(b))= s:(MONaP’(a:Mea’(10-m,s’:(ab,cl)))^CUMb:one-h’(b))= MONs:P’(a:Mea’(10-m,s’:(ab,cl)))^b:one-min’(b)) (type <s>,FA) The derivations in (90) should be straightforward to read. The MeaP ten meters above the cloud denotes a cumulative structured situation, as we have seen in (88). When a cumulative MeaP combines with a TAP, only the cumulative for one hour will yield an interpretable result, as shown in (90c).When the merged TAP is the telic or non-cumulative in one hour, instead, the result will be an uninterpretable situation, as shown in (90b). Note that, since cumulativity entails monotonicity, the intersection of two situations having these two properties will correspond to a “larger” monotonic situation. This entailment is indirectly represented in (90c), in which the MON operator binds the “larger” situation variable s. The derivation in (90b) shows that, aside being disjointed properties, cumulativity and A-cumulativity have a di�erent semantic relation with telicity. Therefore, the distribution of phrases denoting cumulative predicates (e.g. ten meters above the cloud) is predicted to di�er from predicates denoting a-cumulative predicates (e.g. ten meters towards the park). The interplay of TAPs with these phrases con�rms these predictions, as we have seen so far. With these results in hand, we can conclude that our analysis can now account the data in (40)-(55). To account our �nal set of data, that discussed in (56)-(61), we need to present one �nal derivation that shows how an ambiguous verb such as �oat can merge with MeaPs. For this purpose, we repeat (57) as (91a), and employ a “full” syntactic structure. We show its partial derivation in (91b): (91) a. The canoe �oated 50 meters inside the cave in one hour/for one hour b. (type <s,s>, Int)t+k.[[ the canoe �oated ]]:=y.±A-CUMf:�oat’(c,y) Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 72 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi (<s>, I.)k+1.[[ 50 meters inside the cave ]]:=MONs:Mea’(50-m,s’side’:(in,cv)) k+2.([[ the canoe... �oated 50 meters ]]) [[ inside the cave]]:= y.±A-CUMf:float’(c,y)(MONs:Mea’(50-m,s’:side’:(in,cv)))= A-CUMf:float’(c,s:Mea’(50-m,s’side’:(in,cv)), CUMf:float’(c,s:Mea’(50-m,s’side’:(in,cv) The derivation in (91b) reads as follows. By the step t+k+2, two possible interpretations are derived for (91a), as in the case of (58). So, by this derivational step (91a) is ambiguous, or more accurately underspeci�ed. These interpretations are represented in set-theoretic format, for the sake of clarity. The �rst interpretation says that a situation in which a canoe �oats 50 meters inside the cave is a telic situation: the canoe covers a certain distance while �oating. The second interpretation says that a situation in which a canoe �oats 50 meters inside a cave is a situation in which this occurs at a certain distance from some implicit border. This situation is cumulative, in the sense that it includes proper situations located at the same distance, but not involving directed movement. Again, the cumulativity as a percolating property seems to determine the “global” properties of a structured situation. Recall also that our use of the symbol “±” is a short-hand for a situation being either A-cumulative or cumulative, rather than not cumulative. This notation allows us to represent these two properties as being mutually exclusive. We call these two situations dand z, respectively, and show in (92)-(93) what happens when they combine with in one hour and for one hour: (92) t+n.([[ the canoe...the cave (M)]])[[in one hour]]:= ({A-CUMd,CUMz^TELb:one-h’(b))=TEL(d^b:one-h’(b),Ø} (93) t+n.([[ the canoe...the cave (M)]])[[for one hour]]:= ({A-CUMd,CUMz^CUMb:one-h’(b))=Ø,CUM(z^b:one-h’(b)} In words, (92) says that only one of the two interpretations for this sentence is compatible with in one hour. Since in one hour denotes a telic, oriented and bounded situation, only the corresponding interpretation for the canoe �oated 50 meters inside the cave o�ers a non-empty interpretation. The inverse holds when for one hour s merged, for obvious reasons. So, we can capture our last set of data, those presented in (56)-(61). Overall, our analysis can now cover all the data presented in section 2 and as a consequence, our initial set of data that motivated our initial inquiry, those in (1)-(9). We think that this is a welcome result, as it suggests that we have reached our second goal, that of predicting our data via our compositional approach. We discuss some consequences of this result in the next section. 4.3 The Analysis: Discussion and Connections In this section we discuss the results that we obtained via our analysis. As it should be obvious from our discussion, we are now able to predict the patterns Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 73 Another Look at Modi�cation in Spatial Prepositions Francesco-Alessio Ursini & Nobuaki Akagi we have discussed so far, since we can systematically derive which phrases are interpretable, and which phrases are not. This result has become possible for one simple reason. We have de�ned a simple logic of structural properties, and explained how our three categories (MeaPs, SPs, TAPs) can include these properties in their denotations. We have then shown that this logic can be extended to the interplay of these three categories with verbs, although we have o�ered a perhaps less thorough analysis of this interplay. These properties (cumulativity, telicity, acumulativity, monotonicity), qua logical properties, can systematically constrain the range of possible combinations of constituents that can occur. We have then shown that, via basic principles of compositional semantics and the ability to compute the actual values of the properties composed together, certain interpretations can or cannot emerge. Therefore, we have shown that with an opportunely structured approach to compositional matters, it is possible to account our data in a straightforward way. One practical example is as follows. When ten meters and above compose together, the interpretation of the relevant Measure phrase corresponds to a certain structured situation. Given the structure of this situation, it is possible to predict which other situations can be composed further, and which cannot. Simplifying matters somewhat, if we compose the structured situation denoted by for one hour with ten meters above, we obtain a structured situation that can be de�ned in our model. If we compose the situation denoted by ten meters above with that denoted by in one hour, instead, the result will be an uninterpretable (i.e. empty) situation. Importantly, these simple assumptions are consistent with much literature on MeaPs (Morzycki 2005, 2006, a.o.). This is the case, as we show that monotonicity is a central property that governs the distribution of this category with other categories, in this case SPs and TAPs. These assumptions are also consistent with our knowledge of SPs, in particular with those works that study prepositional aspect in detail (Zwarts 2005, 2008, Ramchand & Tungseth 2006, a.o.). This is also the case, as we show that not only TAPs but also MeaPs can in�uence, somehow, prepositional aspect. If we consider that we implement a treatment of lexical aspect that imports broader assumptions about this category (e.g. Krifka 1998), the advantages of our theory should be clear. We have o�ered a uni�ed, thorough and compositional approach of seemingly distinct phenomena. This is a welcome result. One important aspect of our proposal is that we also o�er a simpli�ed treatment of semantic matters in which certain principles are derived from the compositional process. For instance, works on prepositional aspect suggest the (un)- interpretability of phrases such as walk to the store in one hour/#for one hour are a consequence of a “structural” mismatch. 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Zwarts, Joost, and Yoad Winter. 2000. Vector space semantics: a Model-Theoretic analysis of Locative Prepositions. Journal of Logic,Language and Information 9 (2) 169-211. Reception date: 05/02/2013 Revision date: 07/20/2013 Acceptation date: 12/01/2013 Francesco-Alessio Ursini Stockholms Universitet [email protected] Nobuaki Akagi Macquarie University [email protected] Iberia: IJTL |Volume 5.2, 2013, 38-84 ISSN: 1989-8525 doi: tba http://revistas.ojs.es/index.php/iberia/ 84