Multi-Agent Only Knowing

TL;DR

This paper revisits the concept of 'only knowing' in multi-agent systems, simplifying previous proofs, identifying issues, and proposing a new axiom system with a satisfiability operator for better formalization.

Contribution

It reexamines the multi-agent 'only knowing' logic, simplifies proofs, addresses earlier issues, and introduces a new axiom system with a satisfiability operator.

Findings

Provides a simplified completeness proof for the logic

Identifies problems with earlier definitions of 'only knowing'

Introduces an axiom system with a satisfiability operator

Abstract

Levesque introduced a notion of ``only knowing'', with the goal of capturing certain types of nonmonotonic reasoning. Levesque's logic dealt with only the case of a single agent. Recently, both Halpern and Lakemeyer independently attempted to extend Levesque's logic to the multi-agent case. Although there are a number of similarities in their approaches, there are some significant differences. In this paper, we reexamine the notion of only knowing, going back to first principles. In the process, we simplify Levesque's completeness proof, and point out some problems with the earlier definitions. This leads us to reconsider what the properties of only knowing ought to be. We provide an axiom system that captures our desiderata, and show that it has a semantics that corresponds to it. The axiom system has an added feature of interest: it includes a modal operator for satisfiability, and thus provides a complete axiomatization for satisfiability in the logic K45.