Reasoning about Knowledge and Belief: A Syntactical Treatment

The study of formal theories of agents has intensified over the last couple of decades, since such formalisms can be viewed as providing the specifications for building rational agents and multi-agent systems. Most of the proposed approaches are based upon the well-understood framework of modal logics and possible world semantics. Although intuitive and expressive, these approaches lack two properties that can be considered important to a rational agent's reasoning: quantification over the propositional attitudes, and self-referential statements. This paper presents an alternative framework which is different from those found in the literature in two ways: Firstly, a syntactical approach for the representation of the propositional attitudes is adopted. This involves the use of a truth predicate and syntactic modalities which are defined in terms of the truth predicate itself and corresponding modal operators. Secondly, an agent's information state includes both knowledge and beliefs. Independent modal operators for the two notions are introduced and based on them syntactic modalities are defined. Furthermore, the relation between knowledge and belief is thoroughly explored and three different connection axiomatisations for the modalities and the syntactic modalities are proposed and their properties investigated

Common Knowledge: A Survey

This paper discusses the motivation behind common knowledge. Common knowledge has been argued to be necessary for joint action in general and for language use as a particular kind of joint action. However, this term has been broadly interpreted. Two major issues must be addressed: (1) What mental state corresponds to common knowledge, i.e., is knowledge, belief or supposition the appropriate mental attitude? (2) What inference process allows agents to achieve common knowledge? Most generally, common knowledge is used to describe the knowledge that is evidenced in reflexive reasoning. The term has also been used to refer to facts or objects which are mutually salient. One of the main problems for a theory of common knowledge is whether knowledge is the appropriate mental attitude. It seems as though probabilistic beliefs might approximate the cognitive phenomenon of common knowledge more closely than knowledge. The main problem with a usable notion of common knowledge is that inference must play a critical role in what becomes common knowledge. I discuss the nature of conversational inference. It has a number of properties that distinguish it from other inferential systems, such as being apparently abductive and probabilistic, but a precise characterization of it is an unsolved problem. I suggest that in cases where ensuring common knowledge really matters, participants in dialogue accomplish this is by exploiting opportunities for redundancy in conversation

Morality as Social Software

The dissertation research is a project to understand morality better through the concept of ‘Social Software.’ The dissertation is, consequently, to argue that the morality in a human society functions as a form of social software in the society. The three aspects of morality as social software are discussed in detail: the evolutionary, anti-entropic, and epistemic game-theoretic aspect. We humans ‘usually’ think that, for example, (a) killing other humans without any necessary reason is morally wrong, and (b) helping other humans in need is morally right. We want to know, in this dissertation research project, why we think in such ways. Myriads of answers to this question have already been offered. We will pursue an answer that has more explanatory power and enlightening lucidity. The term, ‘Social Software’ was coined by Rohit Parikh to connote, broadly, social “procedures that structure social reality” (van Eijck and Parikh 2009, p. 2). The term can be understood, “more or less equivalently,” (Parikh 2002-1, note 2) as ‘social procedure,’ ‘social algorithm,’ or ‘social game.’ (1) The first aspect of ‘morality as social software,’ to be discussed is the evolutionary: human morality has emerged and developed further through the process of evolution; (2) the second aspect is the anti-entropic: human morality is human resistance against the universal law of entropy that tends to annihilate everything from order to disorder; (3) the third aspect is the epistemic game-theoretic: human morality is understood better by epistemic game theory, which is a combination of ‘classical game theory’ and relatively new ‘epistemic logic.’ As more specific case studies for the epistemic game-theoretic aspect, the concepts of backward induction and “the less we know, the more rational and moral,” are discussed. Finally, a thorough discussion on the naturalistic fallacy instills more philosophical rigor into the dissertation