A Hybrid of Tense Logic S4T and Multi-Agent Logic with Interacting Agents

Abstract

In this paper we introduce a temporal multi-agent logic S4IA T , which implements interacting agents. Logic S4IA T is defined semantically as the set of all formulas of the appropriate propositional language that are valid in special Kripke models. The models are based on S4-like time frames, i.e., with reflexive and transitive time-accessibility relations. Agents knowledge-accessibility relations Ri, defined independently for each individual agent, are S5-relations on R-time clusters, and interaction of the agents consists of passing knowledge along arbitrary paths of such relations. The key result of the paper is an algorithm for checking satisfiability and recognizing theorems of S4IA T . We also prove the effective finite model property for the logic S4IA T .