Intersubjective consistency of knowledge and belief (Q2702559)

The paper is devoted to the problems of common belief and common knowledge (in a multiagent environment). Common belief deserves special attention -- it may exhibit epistemically counterintuitive properties. NEWLINENEWLINENEWLINEThe paper is aiming to understand rational properties of common belief, to characterize conditions for well-behaved common belief. Intuitively, the problem is in intersubjective consistency of epistemic states. An intersubjective system of knowledge and belief is regular when the logic of common belief and the relationship between common belief and common knowledge are the same as for the individuals. NEWLINENEWLINENEWLINEIn the paper regularity is characterized in terms of properties of individual beliefs and their implications for intersubjective consistency conditions are studied. NEWLINENEWLINENEWLINEThe formal system of knowledge and belief is defined in the event-based framework which is common in game theory and economics. The relationship between the event-based and the syntactic approach (usual in logic) is discussed. NEWLINENEWLINENEWLINEThereafter the main results of the paper are presented. Some important intersubjective properties of belief and knowledge are defined (negative introspection of common belief, awareness of common belief, caution about common belief, disagreement, truth of common belief, equivalence of common belief and common knowledge). Similarly, properties called truth of individual beliefs and equivalence of belief and knowledge for every individual are defined. In terms of these properties, theorems which characterize the properties of common belief, its relations to common knowledge and to individual beliefs (knowledge) are proven. NEWLINENEWLINENEWLINEThe results of the paper are interesting from the viewpoints of artificial intelligence, computer science, philosophy and game theory.NEWLINENEWLINEFor the entire collection see [Zbl 0939.00009].