Belief Sets and Commitment Stores

In this paper we compare central elements of Dialogue Logic and Belief Revision theory. Dialogue Logic of the Hamblin/Mackenzie style, or Formal Dialectic, contains three main features. First, there is a rule governed interaction between dialogue participants—the minimal case being two participants. Second, each participant has a commitment store which changes as the dialogue progresses. Third, the changes in the commitment store are governed by rules for additions and withdrawals of material. Withdrawal of material is one major source of difficulty in proposing rules for commitment store change. The classic Belief Revision theory is the AGM (Alchourrón, Gärdenfors and Makinson) theory. AGM theory is a theory about ideal rational believers who change their sets of beliefs by either expansion or contraction. Contraction is a major source of difficulty in belief revision theory. We claim that the commitment stores of dialogue logic include, in a sense, the belief sets of belief revision theory. Further, withdrawal and contraction are essentially the same process. We consider various kinds of withdrawal and contraction, and show how approaches to these processes illuminate certain of the formal fallacies

Proof and Dialogue in Aristotle

Jan Łukasiewicz’s analysis of Aristotle’s syllogism drew attention to the nature of syllogisms as conditionals rather than premise-conclusion arguments. His further idea that syllogisms should be understood as theorems of an axiom system seems a step too far for many logicians. But there is evidence to suggest that Aristotle’s syllogism was to regularise some of the steps made in ‘dialogue games.’ This way of seeing the syllogism is explored in the framework of modern formal dialogue systems. A modern formal syllogistic game, DLSyll, is set out and analysed in use

Logical fiction: Real vs. ideal

Formal systems for knowledge and belief, from Lemmon 13 and Hintikka lj to present day Belief Revision systems 5, have often been described as models of “ideal rational agents.” From the first, there has been extensive controversy about the validity of the models. 17, 14, 18 A series of topics have given focus to the controversy. They include distinguishing knowing from believing, formalising positive and negative introspection, omniscience of various kinds, the contrast between finite and infinite, and contradictory belief. We consider the extent to which a range of formal models of knowledge and belief are reasonable and realistic. We conclude with comments on the persistence of unreal models and the lack of discussion of their structure