Specification of agents’ activities in past, present and future

Organon F 30 (1) 2023: 66–101 ISSN 2585-7150 (online) https://doi.org/10.31577/orgf.2023.30105 ISSN 1335-0668 (print) * VSB-Technical University of Ostrava https://orcid.org/0000-0002-5393-6916  Department of Computer Science FEI, VSB-Technical University of Ostrava, Czech Republic  [email protected] © The Author. Journal compilation © The Editorial Board, Organon F. This article is distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International Public License (CC BY-NC 4.0). RESEARCH ARTICLE Specification of Agents’ Activities in Past, Present and Future Marie Duží* Received: 5 September 2022 / Revised: 11 November 2022 / Accepted: 9 December 2022 Abstract: The behaviour of a multi-agent system is driven by messaging. Usually, there is no central dispatcher and each autonomous agent, though resource-bounded, can make less or more rational decisions to meet its own and collective goals. To this end, however, agents must communicate with their fellow agents and account for the signals from their environment. Moreover, in the dynamic, permanently changing world, agents’ behaviour, i.e. their activities, must also be dynamic. By communicating with other fellow agents and with their environment, agents should be able to learn new concepts and enrich their knowledge base. Processes and events that happened in the past may be irrelevant in the present or have a significant impact in the future, and vice versa. Therefore, the finegrained analysis of agents’ activities as well as events within or beyond the system is very important so that the system can run smoothly without falling into inconsistencies. Moreover, as the system should communicate with its environment, the analysis should be as close to natural language as possible. The goal of this paper is a proposal for such an analysis. To this end, I apply Transparent Intensional Logic (TIL) because TIL is particularly apt for a finegrained analysis of processes and events specified in the present, past Specification of Agents’ Activities in Past, Present and Futures 67 Organon F 30 (1) 2023: 66–101 or future tense with reference to the time when they happened, happen or will happen. Keywords: Activity; Communication of agents; Transparent Intensional Logic; Natural language processing; Sentences in different tenses. 1. Introduction A multi-agent system (MAS) is a distributed system of (more or less) intelligent agents who are active in their perceiving environment and acting to achieve their individual and collective goals.1 The agents are autonomous in the sense of not being controlled by a central dispatcher; the system is driven only by messaging.2 To obtain a needed piece of information, the agents must be able to ask their fellow agents. Yet, they need to put forward not only Yes-No questions but also, in particular, Wh-questions. While there is just one type of answer to a Yes-no question, the class of Whquestions is much more abundant in types. From the logical point of view, the type of possible answer determines the type of Wh-question. In regular communication, we ask by using different pronouns in interrogative sentences, and these pronouns indicate the type of possible answer. We can integrate logical and linguistic views to classify Wh-questions into more detailed classes. For instance, by ‘who’, we ask for a person; by ‘where’, for a location or position; ‘when’ means asking for the time. A proposal for such a more detailed classification of Wh-questions has been introduced in (Číhalová, Duží 2022). Each specialised subtype of a Wh-question conveys specific instructions for an agent on how and where to find the corresponding answer. Detailed classification of queries thus improves agents’ communication and intelligent behaviour. In particular, the specific types of Whquestions are apt for the communication of agents concerning their dynamic 1 By ‘intelligent’ I do not mean human intelligence in case of software agents, of course. Instead, I am talking about artificial intelligence, which is actually not an intelligence, as Roger Penrose in his 1994 book argues. Anyway, in this paper I use the term ‘intelligence’ for both. 2 See, for instance Wooldrige (2009). 68 Marie Duží Organon F 30 (1) 2023: 66–101 activities. The agents need to know who is the actor of an activity, when the activity starts and ends, by which instruments it is performed, etc. The systems of erotetic logic are valuable, as they render many exciting features of Yes-No questions and answers.3 However, many other essential features of questions stem from their presuppositions. Yet, to my best knowledge, none of the systems of erotetic logic deals with Wh-questions and presuppositions of questions in a plausible way. This is unsatisfactory, as Wh-questions are even more frequent than Yes-No questions in our everyday vernacular.4 To obtain a literal analysis of natural language sentences, I am going to apply Tichý’s (1988) Transparent Intensional Logic (TIL) with its procedural semantics, namely, its version as introduced in (Duží, Jespersen and Materna 2010). The analysis of empirical Wh-questions transforms in the TIL formalism into λ-terms denoting procedures that produce α-intensions (functions with the domain of possible worlds ω and times τ, and values of type α) where α is not a truth-value. The sought answer should provide an object of type α, which is the value of the α-intension asked for in the actual world at the time of evaluation. Since ordinary erotetic logics do not usually deal with Wh-questions, (Duží and Fait 2021) adjusted Gentzen’s system of natural deduction for TIL so that the system can answer not only YesNo questions by keyword searching but also answer Wh-questions by inferring computable knowledge from natural-language texts.5 The paper 3 See, for instance, Harrah (2002) or Peliš and Majer (2011). For a system based on relevant logic that can provide axioms and rules for dealing with Yes-No questions, see, for instance (Punčochář 2020). 4 There are a few systems dealing with Wh-questions, see, for instance, Groenendijk (2003), Haida (2008), Hamblin (1973), Essberger (online) or Kartunen (1977). Yet, none of them covers this issue in a satisfactory way. Their summary and appraisal from the point of view of application in TIL can be found in Číhalová, Duží (2022). 5 Computable or inferable knowledge has been introduced as a golden middle way between two extremes, namely explicit and implicit knowledge. Classical epistemic systems deal with explicit and implicit knowledge. The former prevents the paradox of logical/mathematical omniscience by depriving the agents of any inferential abilities, as they know only those pieces of knowledge that are explicitly recorded in their knowledge base. On the other hand, dealing with implicit knowledge Specification of Agents’ Activities in Past, Present and Futures 69 Organon F 30 (1) 2023: 66–101 describes a useful logical technique of deriving answers to Wh-questions based on a given knowledge base that can be both an agent’s base or even natural language texts. It consists of enriching the system of natural deduction with special rules rooted in the rich semantics of a natural language. In addition, special technical rules are specified to operate into hyperintensional contexts; see Duží, Jespersen (2015) and Jespersen, Duží (2022). In (Číhalová, Duží 2022) the analysis of agents’ activities is briefly outlined. The goal of this paper is to propose a detailed analysis of agents’ dynamic activities both from the point of view of their specifications and answering questions on such activities. The analysis takes account of time, i.e. sentences in the past, present or future tenses with reference to the time when this or that happened, is happening or will happen. The rest of the paper is organised as follows. Section 2 summarises the basic principles of Transparent Intensional Logic (TIL). In Section 3, I briefly reproduce the conceptual-oriented classification of Wh-questions as of (Číhalová, Duží 2022). The main novelty of this paper is presented in Section 4; it is the analysis of agents’ dynamic activities specified in past, present or future tenses together with the agents’ learning new concepts by questioning and answering. Concluding remarks and proposals for further research can be found in Section 5. 2. Basic Principles of TIL Pavel Tichý, the Transparent Intensional Logic (TIL) founder, was inspired by Frege’s semantic triangle. Frege characterised the sense of an presupposes that the agents would be able to derive all the logical consequences of their explicitly recorded pieces of knowledge, if only they had an infinite amount of time and resources at their disposal. Hence, implicit knowledge inevitably yields the paradox of logical/mathematical omniscience. Since both notions are not realistic in case of modelling behaviour of intelligent but resource bounded agents, we introduce the notion of inferable knowledge. The idea is simple. Having an agent with some inferential abilities and an explicit knowledge base, we compute maximal limit of knowledge they are able to infer by applying the rules of inference the agent masters. For details, see Duží, Menšík (2017). 70 Marie Duží Organon F 30 (1) 2023: 66–101 expression as the ‘mode of presentation’. Tichý defines this mode of presentation as an abstract, algorithmically structured procedure that produces the object denoted by the expression or, in rigorously defined cases, fails to produce a denotation if there is none.6 This is because there are non-denoting terms that have a perfect meaning, like ‘the greatest prime number’ or ‘the value of the cotangent function at the number π’. Mathematicians had obviously to understand the sense of these terms first, and only then could they prove that there are no such numbers. Hence, in TIL, the meaning of an expression is understood as a context-invariant procedure encoded by a given expression. By ‘context invariant’, we mean this. The procedure encoded by an unambiguous expression is one and the same (up to procedural isomorphism) independently of the context in which the expression is used.7 If the expression is ambiguous, it is furnished with more than one procedure corresponding to its different meanings. Tichý defined six kinds of meaning procedures and called them constructions. There are two kinds of atomic constructions that supply input objects to be operated on by molecular constructions. They are Trivialization and Variable. A Trivialisation presents an object X without the mediation of any other procedures. Using the terminology of programming languages, the Trivialisation of X, denoted by ‘0X’, is just a pointer or reference to X. Trivialization can present an object of any type, even another construction C. Hence, if C is a construction, 0C is said to present the construction C, whereby C occurs hyperintensionally, i.e. in the non-executed mode. Variables produce objects dependently on valuations; they are said to v-construct. The execution of a Trivialisation or a variable never fails to produce an object. However, since TIL is a logic of partial functions, the execution of some of the molecular constructions can fail to present an object of the type 6 See Tichý (1988). A similar philosophy of meaning as a ‘generalized algorithm’ can be found in (Moschovakis 2006); this conception has been further developed by Loukanova (2009). TIL procedural viewpoint is also not far from the idea of algorithmic logic, see Li, B. (2022). 4936. https://doi.org/10.20935/AL4936. 7 For the definition of procedural isomorphism, see (Duží 2019). Briefly, there is no unique criterion for procedural isomorphism and any language, any discourse. In practice, procedures are isomorphic if their specification is identical up to α-equivalence or restricted β-equivalence. Specification of Agents’ Activities in Past, Present and Futures 71 Organon F 30 (1) 2023: 66–101 they are typed to produce. When this happens, we say that a given construction is v-improper. There are two kinds of molecular constructions, which correspond to λ - abstraction and application in the λ-calculi, namely Closure and Composition. λ-Closure, [λx1…xn X], is the very procedure of producing a function with the values v-produced by the procedure X, by abstracting over the values of the variables x1, …, xn to provide functional arguments. No Closure is v-improper for any valuation v, as a Closure always v-constructs a function (which may be, in an extreme case, a degenerate function undefined at all its arguments). Composition, [X X1…Xn], is the very procedure of applying a function f produced by X (if any) to the tuple argument 〈a1, …, an〉 (if any) produced by the procedures X1, …, Xn. A Composition is v-improper as soon as f is a partial function not defined at its tuple argument or if one or more of its constituents X, X1, …, Xn are v-improper.8 TIL being a hyperintensional system, each construction C can occur not only in execution mode so as to produce an object (if any) when being executed but also as an object in its own right on which other (higher-order) constructions operate. The Trivialisation of C causes C to occur just presented as an argument, as mentioned above. Yet sometimes, we need to cancel the effect of Trivialisation and trade the mode of C for execution mode. Double Execution, 2C, does just that; it executes C twice over. If C v-constructs a construction D that in turn v-constructs an entity E, then 2C v-constructs E. Otherwise, 2C is v-improper. Hence, for any construction C, this law is valid: 20C=C. DEFINITION 1 (construction) (i) Variables x, y, … are constructions that construct objects (i.e., elements of their respective ranges) dependently on a valuation function v; they v-construct. 8 In the rest of this section, I draw on the standard exposition of the fundamentals of TIL, as presented in other papers (for instance in Jespersen, Duží (2022) or Duží, Fait (2021)), with just a few minor adjustments. True, since TIL has become a wellknown system, this exposition could have been more condensed; yet, in the effort of making everything comprehensive and convenient for a reader, I leave this part in full details. 72 Marie Duží Organon F 30 (1) 2023: 66–101 (ii) Where X is an object whatsoever (even a construction), 0X is the construction Trivialisation that constructs X without any change. (iii) Let X, Y1, …, Yn be arbitrary constructions. Then the Composition [X Y1…Yn] is the following construction. For any v, the Composition [X Y1…Yn] is v-improper if one or more of X, Y1, …, Yn are v-improper, or if X does not v-construct a function that is defined at the n-tuple of objects v-constructed by Y1, …, Yn. If X does v-construct a v-proper function, then [X Y1…Yn] v-constructs the value of this function at the n-tuple. (iv) (λ-) Closure [λx1…xm Y] is the following construction. Let x1, x2, …, xm be pair-wise distinct variables and Y a construction. Then [λx1…xm Y] v-constructs the function f that takes any members B1, …, Bm of the respective ranges of the variables x1, …, xm into the object (if any) that is v(B1/x1,…,Bm/xm)-constructed by Y, where v(B1/x1,…,Bm/xm) is like v except for assigning B1 to x1, …, Bm to xm. (v) Where X is an object whatsoever, 1X is the construction Single Execution that v-constructs what X v-constructs. Thus, if X is a v-improper construction or not a construction as all, 1X is v-improper. (vi) Where X is an object whatsoever, 2X is the construction Double Execution. If X is not itself a construction, or if X does not v-construct a construction, or if X v-constructs a v-improper construction, then 2X is v-improper. Otherwise 2X v-constructs what is v-constructed by the construction v-constructed by X. (vii) Nothing is a construction, unless it so follows from (i) through (vi). With constructions of constructions, constructions of functions, functions, and functional values in TIL stratified ontology, we need to keep track of the traffic between multiple logical strata. The ramified type hierarchy discharges that task. The type of first-order objects includes all objects that are not constructions. Therefore, it includes not only the standard objects of individuals and truth values but also sets, functional mappings and functions defined on possible worlds (i.e., the intensions germane to possibleworld semantics, PWS intensions). The type of second-order objects includes constructions of first-order objects and functions with such Specification of Agents’ Activities in Past, Present and Futures 73 Organon F 30 (1) 2023: 66–101 constructions in their domain or range. The type of third-order objects includes constructions of firstor second-order objects and functions with such constructions in their domain or range; and so on ad infinitum. DEFINITION 2 (ramified hierarchy of types). Let B be a base, where a base is a collection of pair-wise disjoint, non-empty sets. Then: T1 (types of order 1). i) Every member of B is an elementary type of order 1 over B. ii) Let α, β1, ..., βm (m > 0) be types of order 1 over B. Then the collection (α β1 ... βm) of all m-ary partial mappings from β1 × ... × βm into α is a functional type of order 1 over B. iii) Nothing is a type of order 1 over B unless it so follows from (i) and (ii). Cn (constructions of order n) i) Let x be a variable ranging over a type of order n. Then x is a construction of order n over B. ii) Let X be a member of a type of order n. Then 0X, 1X, 2X are constructions of order n over B. iii) Let X, X1, ..., Xm (m > 0) be constructions of order n over B. Then [X X1... Xm] is a construction of order n over B. iv) Let x1, ..., xm, X (m > 0) be constructions of order n over B. Then [λx1...xm X] is a construction of order n over B. v) Nothing is a construction of order n over B unless it so follows from Cn (i)-(iv). Tn+1 (types of order n + 1) Let *n be the collection of all constructions of order n over B. Then i) *n and every type of order n are types of order n + 1. ii) If m > 0 and α, β1, ..., βm are types of order n + 1 over B, then (α, β1, ..., βm) (see T1 ii)) is a type of order n + 1 over B. 74 Marie Duží Organon F 30 (1) 2023: 66–101 iii) Nothing is a type of order n + 1 over B unless it so follows from (i) and (ii). For the purposes of natural-language analysis, we are usually assuming the following base of ground types: ο: the set of truth-values {T, F}; ι: the set of individuals (the universe of discourse); τ: the set of real numbers (doubling as times); ω: the set of logically possible worlds (the logical space). We assume that the universe of discourse ι is multi-valued and consists of at least two elements, though here I leave aside the cardinality of this basic type. Empirical expressions denote empirical conditions, which may or may not be satisfied at the world/time pair selected as points of evaluation. These empirical conditions are modelled as (PWS-)intensions. Intensions are entities of type (βω): mappings from possible worlds to an arbitrary type β. The type β is frequently the type of the chronology of α-objects, i.e., a mapping of type (ατ). Thus α-intensions are mostly functions of type ((ατ)ω), abbreviated as ‘ατω’.9 Extensional entities are entities of a type α where α ≠ (βω) for any type β. Where the variable w ranges over β and t over τ, the following outline of a Closure essentially characterises the logical syntax of empirical language: λwλt […w….t…]. Examples of frequently used α-intensions are: propositions of type οτω, properties of individuals of type (οι)τω, binary relations-in-intension between individuals of type (οιι)τω, offices of type ιτω and hyperintensional attitudes of type(οι∗n)τω. Logical objects like truth functions and quantifiers are extensional: ∧, ∨, ⊃ are of type (οοο), and ¬ of type (οο). 9 We define (PWS-)intensions as functions with the domain of possible worlds. True, most frequently, time plays the role of the second modal parameter, though not always. For instance, assuming that physical laws of nature are nomically but not analytically necessary, as physics is an empirical science, we model these intensions by construction of this form: λw ∀t […] → οω. Specification of Agents’ Activities in Past, Present and Futures 81 Organon F 30 (1) 2023: 66–101 Note that the question transforms into a construction of an individual office, as it should be. The agent would like to know the value of this office. Another frequent type of intensions is the property of individuals, an object of type (οι)τω. For instance, the direct answer to the question “Which are the private hospitals located in Lowestoft?” should convey a set (of type (οι)) of individuals. There are two kinds of possible direct answers. An exhaustive answer conveys a complete list of individuals with the property of being a private hospital in Lowestoft, while an incomplete answer provides just some of them. Anyway, in both cases, the answer should be conclusive; it means that the individuals belonging to this list should be referred to directly. An indirect description of an individual would not be satisfactory.16 For instance, the answer “They are the private hospitals located in the most eastern city of England” is not conclusive. The agent would have to go on asking, “Which is the most eastern city of England?” and “Which are the private hospitals in the most eastern city of England?” and so on. Thus, the exhaustive answer to the question would be, for instance, the set: {Carlton Court, Airey Close, Beccles Hospital Inpatients, East Point Consulting Rooms, Andaman Surgery, James Paget Hospital, East Coast Community, The Veterinary Surgery, Crest View Medical Centre}. The analysis of the question that constructs a property of individuals (that are asked for) is this. λwλt [λx [[[0Private 0Hospital]wt x] ∧ [0Located-inwt x 0Lowestoft]]] → (οι)τω Types. x → ι: the variable ranging over individuals; Private/((οι)τω(οι)τω): property modifier: an analytic function that assigns to a property another (modified) property;17 Hospital/(οι)τω; Located-in/(οιι)τω; Lowestoft/ι. One can also ask for the value of an attribute at an argument like the salary of somebody. The possible answer to the question “What is John’s salary?” is a number, and the question denotes a magnitude of type ττω. 16 This problem has been dealt with in Duží (2022). 17 The analyses of property modifiers has been introduced in Jespersen, Carrara, Duží (2017) or in Duží (2017). 82 Marie Duží Organon F 30 (1) 2023: 66–101 3.1 Classification of Wh-questions Číhalová & Duží (2022) introduce the classification of Wh-questions based on the type of a possible answer. They show that for our purpose, the linguistic classifications are too coarse-grained and non-plausibly oriented. For the needs of a multi-agent system, we classify questions not only from the linguistic point of view but also from the logical point of view, with respect to a domain of interest and the structure of the agent’s knowledge base. The authors distinguish between static entities, like necessary relations between properties of individuals and dynamic entities, like activities which form processes. Active actions and passive events are activities. Each activity can involve other objects that are called their participants. The specification of activities is based on the linguistic theory of verb valency frames.18 From the logical point of view, we deal with the verb phrases as denoting a function that is applied to its arguments. The number of arguments is controlled by the content verb valency. There are several types of valency. An impersonal (avalent) verb has no subject or a dummy subject. “It rains.” is a typical example. Here the grammatic subject ‘it’ is just a dummy subject because it does not refer to any concrete object.19 An intransitive (monovalent) verb has just one argument, the subject S; “John 18 For the linguistic theory of verb valency frames, see Horák (1998) or Rambousek, Hlaváčková (2011). Číhalová (2016) proposed ontology of events based on the theory of verb valency frames. This theory is not unlike Chomsky’s θ-theory, which is concerned with the distribution and assignment of thematic roles to arguments. The theta criterion describes the specific match between arguments and thematic roles in the logical form of a sentence. (I am grateful to the anonymous reviewer for drawing my attention to this theory.) Yet, since our research is a part of a broader project on linguistic and logical natural language analysis and processing, and since in this project we cooperate with the centre for computational linguistics in Masaryk University of Brno, we vote for the theory of verb valency frames. This theory is supported by the centre, where the lexicon of verb valencies (VerbaLex) has been developed. 19 Lots of languages, including Romance and Slavonic ones, drop the dummy subject (‘it’, ‘es’, …) altogether, and make sentences just with a verb in third person singular. Specification of Agents’ Activities in Past, Present and Futures 83 Organon F 30 (1) 2023: 66–101 (S) is singing.” A transitive (divalent) verb has two arguments, an agent (A) and a patient (P), as in “John (A) kicked the ball (P).” A ditransitive verb has three arguments, an agent and two patients, for instance, in “John (A) passed the ball (P) to Tom (P).” There are also a few verbs with more than three arguments (polyvalent, like tritransitive); yet they mostly arise by valency increasing, where causatives or applicatives are typical valency increasing devices.20 Verb valency frames determine the obligatory and facultative arguments, i.e. thematic roles of a given verb, together with their types. Facultative arguments can be missing, of course. For instance, the verb ‘buy’ can occur in several sentences with a different number of arguments like “Tom bought a book”, “Tom bought a book in Paris”, “On Friday, Tom bought a book”, “Tom bought a book for Jane in Paris”, etc. In our analysis, we have to take these varieties into account. Linguists have created many classifications based on verb valency frames, for instance, VALLEX or VerbaLex.21 John Sowa (2000) proposed a specification tool for knowledge representation, where he adopted a linguistic approach to verbs. He developed the system of conceptual graphs in which Peirce’s logic is combined with the semantic networks known from artificial intelligence. For the valency participants, Sowa uses the term ‘thematic roles’ or ‘case relations.’ His summary of all the thematic roles can be found in (Sowa 2000, pp. 506-510) or in the web source Thematic roles. Sowa distinguishes several types of thematic roles, for instance, Agent, Beneficiary, Destination, Duration, Effector, Experiencer, Instrument, Location, Matter, Patient and so on.22 Thematic role or the type of a participant expresses the role that a noun phrase plays for the activity described by a governing verb. From the viewpoint of logic, it is the relation between two entities where one is an activity (expressed by the verb), and the other is an attribute (expressed mostly by a noun, adverb, number or adjective). The number and the categories of participants depend on the respective domain of interest and the functions of the system of agents. In this paper, 20 For details, see Dixon (2000). 21 See, for instance Lopatková et al. (2006) and Hlaváčková, Horák (2006). 22 For details, see Sowa (2000, 508-510). 84 Marie Duží Organon F 30 (1) 2023: 66–101 I will use the following frequent kinds of attributes that can be assigned to an activity: Pat – object affected by the activity Ben – beneficient (somebody who has benefited from the activity) Man – the manner of the activity execution (measure, speed etc.) Inst – instrument Time – when Loc – the place of activity Dir1 – the direction of activity – from where Dir2 – the direction of activity – which way Dir3 – the direction of activity – where to Wh-questions concern the participants of activities; we ask for their values in a world and time of evaluation. Hence, we can distinguish questions about the process itself (what is going on?) from Wh-questions on the primary agent and other participants of a given activity. For instance, assume we have the sentence “John (the agent) is going (the activity) to London (Dir3) by car (Inst) in an average speed of 50 miles per hour (Man).” Then we can ask, “What is John doing?”, “Who is going to London?”, “How quickly does John go to London?” etc. 3.2 Hyperintensional questions about concepts A particular category of questions concerns hyperintensional questions about a given concept. The agents should be able to learn from experience through mutual communication with their fellow agents. In such a communication, it may happen that a receiving agent b does not ‘know’ a concept that is a constituent of a sender’s message. By ‘knowing a concept’ C, we mean having the concept C in one’s ontology. In such a situation, the receiving agent b can ask for an explication or a definition of the unknown concept. When asking for the explication of concept C the agent does not talk about the object produced by C. Rather, the concept, i.e. the closed Specification of Agents’ Activities in Past, Present and Futures 85 Organon F 30 (1) 2023: 66–101 construction C itself, is a subject matter that is asked for. Such a context where the construction C is just presented as an argument rather than executed to produce an object is hyperintensional. In (Duží & Vojtáš 2008), a special kind of question is introduced, namely a question with the performative Unrecognized, the argument of which is an unknown concept C. The answer is then of type Refine, where the message provides a concept C’, which refines the unknown concept C. Refinement has been rigorously defined above (Def.5). Briefly, by refining an atomic concept of an object O, we mean discovering a molecular concept that produces the same object O. In mathematics, refining usually concerns definitions like “a group is a set G equipped with a binary operation that combines any two elements of G to form another element of G in such a way that group axioms are satisfied, namely associativity, the existence of the neutral element in G and invertibility.” Here the atomic concept to be refined is that of a ‘group’. The molecular concept refining ‘group’ is encoded by the definiens, namely ‘a set G equipped with a binary operation that combines any two elements of G to form another element of G in such a way that group axioms are satisfied, namely associativity, the existence of the neutral element in G and invertibility’. In the case of empirical concepts, it is more plausible to speak about explication. The reason is this. To say that a molecular concept C is a refinement of an atomic empirical concept D is risky. It would be a refinement only if the molecular concept C were analytically equivalent to the original concept D, which means that both are the concepts of the same object O/ατω. However, in the most interesting cases of empirical concepts of PWS-intensions we use a Carnapian explication rather than a definition proper. Then equivalence is undoubtedly not guaranteed, for one can hardly check the identity of the intensions produced by the two concepts. Rather, a new molecular concept C (explicatum) should define an intensional object O that is as close as possible to the object referred to by an inexact (prescientific) concept D (explicandum). In Meaning and Necessity (1947), Carnap characterises explication as follows: The task of making more exact a vague or not quite exact concept used in everyday life or in an earlier stage of scientific or logical development, or rather of replacing it by a newly constructed, 86 Marie Duží Organon F 30 (1) 2023: 66–101 more exact concept, belongs among the most important tasks of logical analysis and logical construction. We call this the task of explicating, or of giving an explication for, the earlier concept […] (Carnap 1947, pp. 7-8) Keeping this difference in mind, I use the term ‘refinement’ for both cases, including the explication of empirical concepts. In most cases of explicating the concept unknown to an agent, this simplification is harmless. 4. Agents’ dynamic activities The basic idea of the analysis is due to (Tichý 1980). Its adjustment and simplification are introduced in (Duží 2010). Tichý draws a distinction between episodic and attributive verbs. Attributive verbs ascribe properties to individuals, and their structure is usually a copula followed by an adjective or noun; for instance, ‘is happy’, ‘is red’, ‘looks speedy’, ‘is a student’ are attributive verbs. On the other hand, episodic verbs express actions performed by objects. For instance, if John is getting up, it would be insufficient to analyse this activity by assigning the property of getting up to John. Rather, John is doing the activity of getting up. For example, the sentence “John is driving from Brussels to Paris at the average speed of 90 km/h” should be analysed as describing a time-consuming process consisting of a series of actions and events. In (Číhalová, Štěpán 2014), the basic idea of specifying event ontology by means of verb valency frames was introduced, and (Číhalová, 2016) proposed its further adjustment. It consists, in particular, in refining the type of action executed within a given process. For instance, the specification of the process Charles is driving from Prague to München by train at the speed of 90 km/h is determined by the sense of the verb ‘to drive’ together with its arguments (who is driving – the actor, when is (s)he driving, from where, to where, by what kind of a vehicle, in which speed, etc.). 4.1 Agents’ activities in the present From the logical point of view, an episodic verb denotes a relation-inintension Do between an individual of type ι (the actor) and an activity. Specification of Agents’ Activities in Past, Present and Futures 87 Organon F 30 (1) 2023: 66–101 Using a general placeholder α for the type of activity, Do thus obtains the type (οια)τω.23 As mentioned above, each activity has several participants (i.e. assignments of an attribute to the activity), and the valency of the verb determines the compulsory participants and the maximal number of facultative participants. The attributes can be of various kinds like individuals, properties, quantities, etc. Typical kinds of attributes have been specified above. They are Pat (object affected by the activity), Ben (who has a benefit from the activity), Manner (manner of the activity execution), Inst (instrument), Time (when), Time1 (time when the activity started), Time2 (time when the activity ended), Loc (location of the activity), Dir1 (direction of event – from where), Dir2 (direction of event – where through), Dir3 (direction of event – where to). If needed, other kinds of attributes can be specified. For the purpose of the system implementation, we only must keep the selected keywords fixed. The type of assigning an attribute to an activity is the relation in intension between an object of type β and the activity (type α); where β can be a property of individuals like being a train, or a number of type τ (time), individual ι (like John, Prague, Brussels) etc., according to the kind of an attribute. Thus, we have a general type of participant Part/(οβα)τω. It must be a relation-in-intension, as one and the same activity can be performed with different instruments at different times, and so like. For instance, John can go from Prague to Brussels by train, and next time he can vote for a plane. 23 In this paper, I often release typing and use instead placeholders like α, β, δ for entities too complicated from the typing point of view. As we all know well, typed languages and calculi are useful and easy to work with because typing prevents a user from making silly mistakes when specifying procedures. Yet, too strong typing can sometimes be restrictive. For this reason, typed functional programming languages are usually polymorphic, or type control is not too strict; in case of a typing error, the interpreter only informs the programmer and leaves the decision to them. As TIL is a typed lambda calculus, in its computational variant TIL-Script, we also aim to implement such useful features. Proposals of the polymorphic TIL system have been introduced in Duzi (1993), Pezlar (2020) and Pezlar (2022). For a benevolent type checking algorithm, see, e.g., Duží,Marie & Fait,Marie (2019). 88 Marie Duží Organon F 30 (1) 2023: 66–101 A general pattern for the analysis of an activity P → α with the actor A → ι and participants Part-i/(οβα)τω that assign attributes Xi → βi to P is this:24 λwλt [[0Dowt A P] ∧ [0Part-1wt X1 P] ∧ [0Part-2wt X2 P] ∧…∧ [0Part-nwt Xn P]] For instance, the analysis of the sentence “John goes to Brussels by train” comes down to this construction. λwλt [[0Dowt 0John 0Go]∧ [0Instwt 0Train 0Go] ∧ [0Dir3wt 0Brussels 0Go]] It may happen that at another time John will go to Brussels by plane. Then we have λwλt [[0Dowt 0John 0Go] ∧ [0Instwt 0Plane 0Go] ∧ [0Dir3wt 0Brussels 0Go]] Wh-questions about John’s activity would be, for instance: What does John do? Where does John go? The content of these questions transforms into constructions like (variables what → α, where → ι) λ w λ t λ what [0Dowt 0John what] λ w λ t λ where [[0Dowt 0John 0Go] ∧ [0Dir3wt where 0Go]] The technique of deducing answers to such Wh-questions has been introduced in Duží, Fait (2020) and (2021). It is an adjusted system of natural deduction with special rules rooted in the rich semantics of natural language and some technical TIL rules stemming from the need to work within a hyperintensional context. Classical natural deduction rules can be applied only to constituents of a construction. For this reason, we need these special 24 The first proposal of such an analysis of activities with participants has been introduced in Duží (2021). In this paragraph, I introduce a slightly adjusted and corrected analysis. In particular, I do not apply the relation-in-intension Assign (an attribute to an activity), as this entity is superfluous and we can obtain a more elegant solution without it. Specification of Agents’ Activities in Past, Present and Futures 89 Organon F 30 (1) 2023: 66–101 technical rules.25 In principle, answers to such Wh-questions are derived by unifying matching terms by means of substituting the values for variables like what, where, and so like. In our simple example, the answers would be what = 0Go, where = 0Brussels. If agent b has in his ontology the specification of all the possible participants of an activity, and if b obtains an incomplete message where some participants are missing, then b can ask his fellow agents to complete the missing pieces of knowledge. For instance, when receiving the first message about John’s going to Brussels by train, the agent can send another query message asking from where does John go to Brussels. To this end, we apply the method of analysis of Wh-questions, as introduced above. The content of the query is then this. λwλt λd [[0Dowt 0John 0Go] ∧ [0Instwt 0Train 0Go] ∧ [0Dir1wt d 0Go] ∧ [0Dir3wt 0Brussels 0Go]] A possible answer to this Wh-question is the message with this content. λwλt [[0Dowt 0John 0Go] ∧[0Instwt 0Train 0Go] ∧ [0Dir1wt 0Prague 0Go] ∧ [0Dir3wt 0Brussels 0Go]] The answer is obtained by substituting Prague for the variable d using the agents’ knowledge base.26 In case there are two or more actors of the activity, we can apply the relation-in-intension Do’/(ο(οι)α)τω. For instance, the sentence “John and Tom go to Brussels by plane on April 1st” is furnished with this analysis. λwλt [[0Do’wt λx [[x= 0John] ∨ [x= 0Tom]] 0Go] ∧ [0Instwt 0Plane 0Go] ∧ [0Dir3wt 0Brussels 0Go] ∧ [0Timewt 0April1 0Go]] The above sentence is underspecified, as it is not clear whether John and Tom are going on their own or together. Yet, the analysis is unambiguous, 25 See, for instance, Duží,Marie, Jespersen, B. (2015) and Jespersen, B., Duží,Marie (2022), where the rules for existential quantification into hyperintensional contexts have been introduced. 26 For details on deducing answers to Wh-questions by applying the system of natural deduction adjusted to TIL, see Duží, Fait (2021). 90 Marie Duží Organon F 30 (1) 2023: 66–101 as John and Tom are the two actors of the same activity. Hence, they are going together. If they went each on their own, it would be two different activities with different actors, even if the other participants were identical.27 4.2 Agents’ activities in past or future Another advantage of this approach is this. Since in TIL, we have two modal parameters, time and possible worlds, we can easily specify activities executed in past or future and model the dynamic behaviour and reasoning of agents. If an activity was executed in the past or will be executed in future, the sentence should contain a reference to the time when this or that happened or will happen. For instance, the sentence “John will go to Brussels by plane” receives this analysis. λwλt ∃t' [[0Dowt’ 0John 0Go] ∧ [t’ > t] ∧ [0Instwt 0Plane 0Go] ∧ [0Dir3wt 0Brussels 0Go]] Note that the attributes Inst and Dir3 are extensionalised with respect to time t of evaluation rather than to time t’ > t, as we assign these attributes now. The situation can change; of course, John can later vote for a car, for instance. In such a case, the sentence is not true. Anyway, the piece of information conveyed by the sentence seems to be incomplete, as one is tempted to ask, “When will John go to Brussels?” It is so because sentences in the past or future should contain a constituent referring to time T → (οτ), the time interval when this or that happened or will happen. In such a case, the sentence is associated with a presupposition that the current time t is in the proper relation with respect to T. Roughly, it means that for sentences in future, t comes before the end of the reference time T, while for sentences in past, t comes after T; if it is not so, then the proposition denoted by the sentence has a truth-value gap. For instance, the sentence “John will go to Brussels on January 1st, 2023” can be true or false till January 1st, 2023, 24:00. Later, it has no truth value. Involving presupposition is reasonable, of course. Imagine a situation when 27 I am grateful to the anonymous reviewer for this remark, which lead me to the specification of an activity that is not ambiguous. Specification of Agents’ Activities in Past, Present and Futures 97 Organon F 30 (1) 2023: 66–101 happened or will happen to be done together with the frequency of the activity in the reference time. Further research will concentrate on a still more detailed analysis of messages in different grammatical tenses, presuppositions of such messages, and on dynamic aspects of agents’ activities. Here we will also apply the results obtained in the application of Gentzen’s natural deduction adjusted for TIL so that these methods can be integrated into one intelligent system. Acknowledgements This research has been supported by the Grant of SGS No. SP2022/123, VŠBTechnical University of Ostrava, Czech Republic, “Application of Formal Methods in Knowledge Modelling and Software Engineering V”, and by the University of Oxford project ‘New Horizons for Science and Religion in Central and Eastern Europe’ funded by the John Templeton Foundation. I am grateful to two anonymous reviewers whose comments significantly contributed to improving the quality of the paper. References Carnap, Rudolf. 1947. Meaning and Necessity. Chicago: Chicago University Press. Číhalová, Martina. 2016. “Event Ontology Specification Based on the Theory of Valency Frames”. In Frontiers in Artificial Intelligence and Applications, Information Modelling and Knowledge Bases XXVII (pp. 299–313). Amsterdam: IOS Press. Číhalová Martina, Duží, Marie. 2022. “Modelling Dynamic Behaviour of Agents in a Multi-agent System; Logical Analysis of Wh-questions and Answers”. 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