A paraconsistent approach to speech acts

This paper discusses an implementation of speech acts in a paraconsistent framework. We analyze four speech acts: assert, concede, request and challenge as building blocks of agents’ interactions. A natural four-valued model of interaction yields multiple new cognitive situations. They are analyzed in the context of communicative relations, which partially replace the concept of trust. These assumptions naturally lead to six types of situations: perceiving inconsistent information, perceiving previously inconsistent information, perceiving previously unknown information, perceiving unknown information, perceiving compatible information and perceiving contradictory information. These new situations often require performing conflict resolution and belief revision. The particular choice of a rule-based, DATALOG¬¬-like query language 4QL as a four-valued implementation framework ensures that, in contrast to the standard two-valued approaches, tractability of the model is maintained. The work concludes with a discussion of an example. 1 Modeling Assumptions The development of contemporary multiagent systems (MAS) demands an adequate and precise logical modeling of the environment. Recently, there is a wide choice of knowledge representation methods. Each time, these methods should be selected carefully on an application-specific basis. When confining to logic-based approaches and formalisms, traditionally two-valued logics prevail. They fail, however, to express richer modeling possibilities when some values or properties are simply not known, or when the available information is inconsistent. A natural remedy for such situations is introducing four logical values [3, 23, 27]. This work aligns with a whole line of research concerning logical modeling, reasoning and communicating about the surrounding reality, under the assumption that we deal with four types of situations, encoded in the four logical values: ? Supported by the Polish National Science Centre grant 2011/01/B/ST6/02769. 2 B. Dunin-Kȩplicz et al. – fact a holds, – fact a does not hold, – it is not known whether a holds, – information about a is inconsistent. This reflects the current informational stance of an agent, which is dynamic in nature, exhibiting the dynamism of its environment. Whenever a change occurs, a belief revision is performed to account for the alteration in question. This paper opens our research programme on paraconsistent modeling of communication in the four-valued framework. We start from a paraconsistent model of speech acts, aiming ultimately at achieving a four-valued formalization of dialogues and argumentation. If argumentation-based dialogues are considered as communicative games between two or more agents, speech acts can be viewed as their building blocks. They are used to compose complex dialogues, such as persuasion, deliberation, information seeking, negotiation or inquiry and can be seen as the underlying reactive layer of communication (see [35] for the definitions of various dialogue types, and [1,4,10,14,16,17,29,30,32] for investigations in multi-agent argumentation-based dialogue). In the process of exchanging messages, we naturally treat the sender and the receiver as two independent information sources, which try to expand, update, and revise their beliefs through communication. Usually, the level of trust between agents influences this process. We intend to disregard the heavily computational theory of trust [6, 7] in favor of three model situations, which take place in traditional communication. Instead of introducing the levels of trust between the sender and receiver, we consider three communicative relations between the two agents involved: – communication with authority, – peer to peer communication, – communication with subordinate. When deciding on what four-valued formalism to adopt, we directed out attention to 4QL [26, 27], a rule-based, paraconsistent language, due to its low complexity and unique features distinguishing it from other similar formalisms. Keeping in mind our goal: adequate modeling of human-computer interactions in time-critical systems, we are prepared to pay the price of some expressiveness limitations concerning dialogues in order to maintain those important properties of 4QL. This four-valued approach to speech acts, based on 4QL, is most likely new in the literature. The aim of this paper is to give foundations for communication in multiagent systems based on 4QL. We analyze perceiving speech acts and propose a specific conflict resolution method. A natural four-valued model of interaction yields multiple new cognitive situations. Therefore we distinguish six types of them: perceiving inconsistent information, perceiving previously inconsistent information, perceiving previously unknown information, perceiving unknown information, perceiving compatible information and perceiving contradictory information. We analyze them one by one, providing a sort of semantics of four selected speech acts: assert, concede, request and challenge. It is given in terms of triples consisting of preconditions, speech acts and A Paraconsistent Approach to Speech Acts 3 complex post actions. Along with defining rules for perceiving speech acts, we indicate their detailed impact on the receiver’s informational stance. The paper is structured as follows. First, in Section 2, we introduce speech acts theory. Section 3 is devoted to a four-valued logic which is used throughout the paper and to basic information on 4QL, a rule language suitable as an efficient implementation tool. Section 4 discusses the main technical contribution of the paper. Section 5 illustrates our ideas by an example. Finally, Section 6 concludes the paper. 2 Drawing upon Speech Acts Theory Since the early 20th century linguists and philosophers of language have been studying speech acts. Their theory originates from J.L. Austin’s book [2], where he stated an observation that some utterances cannot be verified as true or false. This led to the division of speech acts into constatives, which can be assigned a logical truth value, and the remaining group of performatives. Austin’s successor, Searle, created perhaps the most popular taxonomy, identifying: assertives, directives, commissives, expressives and declaratives [33]. The aim of an assertive act is to make a commitment to the truth of the expressed proposition. A way in which an assertive can be assessed is with respect to the truth or falsity of the asserted proposition. Some examples of assertives include: suggesting, hypothesizing, stating. Directives are aimed at getting the hearer to do something, for example: inviting, begging, pleading and challenging. A special case of directives are questions. The purpose of commissives is to commit the speaker to some future action, for example, promising or swearing. The goal of uttering an expressive act is to express a psychological state (thanking, apologizing, congratulating). The essence of a declarative is reflected in the expression “saying makes it so”. For example, by uttering “I pronounce you husband and wife”, a couple is declared to be married. Other examples of such speech acts are christening or declaring war. This theory views communication as complex actions changing the mental states of dialogue participants. Various speech acts, viewed as typical actions can be represented in dynamic logic, by characterizing their preand post-conditions. Austin defined the effects of illocutionary acts as perlocutionary acts: the effects on the attitudes and actions of the hearer. We define them in terms of the changes in agents’ beliefs and actions (see also [10, 14, 16, 17]). Speech acts have been extensively used in modeling communication in MAS to express intentions of the sender [22]. There have been many approaches to defining their semantics [1,24,29,30], some based on Belnap’s four-valued logic [25]. Still, some researchers view them as primitive notions [31]. Within the most popular mentalistic approach, reflected in languages such as KQML and FIPA ACL [22], speech acts are defined through their impact on agents’ mental attitudes. The current paper clearly falls in that approach (see especially Subsection 4.6). 4 B. Dunin-Kȩplicz et al. 3 Four-valued Framework 3.1 The Underlying Logic To model phenomena such as lack and inconsistency of information, a commonly used logic is the four-valued logic proposed in [3]. However, as discussed, e.g., in [12, 34], the approach of [3] is problematic. Namely, in areas we focus on it often provides results deviating from intuitions. Our approach is strongly influenced by ideas underlying the 4QL query language [26, 27] which does not share such problems. In what follows all sets are finite except for sets of formulas. We deal with the classical first-order language over a given vocabulary without function symbols. We assume that Const is a fixed set of constants, V ar is a fixed set of variables and Rel is a fixed set of relation symbols. A literal is an expression of the form R(τ̄) or ¬R(τ̄), with τ̄ ∈ (Const ∪ V ar), where k is the arity of R. Ground literals over Const, denoted by G(Const), are literals without variables, with all constants in Const. If ` = ¬R(τ̄) then ¬` def = R(τ̄). Though we use the classical first-order syntax, the presented semantics substantially differs from the classical one. Namely, – truth values t, i, u, f (true, inconsistent, unknown, false) are explicitly present;5 – the semantics is based on sets of ground literals rather than on relational structures. This allows one to deal with the lack of information as well as inconsistencies (indicated respectively by truth values u and i). The semantics of propositional connectives is summarized in Table 1. Observe that definitions of ∧ and ∨ reflect minimum and maximum w.r.t. the ordering