A Logic for Reasoning about Explicit Knowledge in Finite Agents (Abstract)

The Problem Epistemic logics are logics for reasoning about knowledge in systems of agents. Traditional modal epistemic logics are information-theoretical, in the sense that they consider knowledge about propositions and that agents know everything that follows from the information they possess. Although proved useful in many applications, this view is unrealistic when modeling explicit knowledge – i.e. knowledge that agents have computed and can act upon. Hintikka (1975) called this the logical omniscience problem, and when epistemic logic is used to explain concepts in game theory, the idea of logical non-omniscience is closely related to the idea of bounded rationality. Finding more realistic epistemic logics modeling how explicit knowledge is obtained has been a popular research topic. Our goal in this paper is different. First, instead of describing closure conditions on explicit knowledge, we assume that explicit knowledge has been obtained, and we construct a logic for reasoning about static explicit knowledge in a group of agents. A framework for reasoning about static knowledge is useful for analyzing the knowledge in a group of agents at an instant in time (or a time span when no epistemic changes are made), for example between computing deductions. Second, we consider ascribing knowledge of propositions to agents in multiagent systems to be unrealistic. Instead, we assume that the agents posses and process syntactical objects. (Of course, neither of these ideas are new; we briefly discuss related work in the last section). We make the following semantic assumptions: