Representation of Information and Satisfiability, Algorithms for Multi-Agent Logics

This paper studies logical properties of multi-agent logics based at relational models with elements of multi-agency. In particular, we introduce a multi-agent temporal logic PastL based at linear possible-worlds models with non-transitive and non-uniform accessibility relations. We consider the time directed to past, and use logical operation Since for non-transitive accessibility; Several formalizations for the conception knowledge/agent’s knowledge in terms of non-transitive time in past are suggested. A logics PastT based is this approach is studied, we consider main computational problems - satisfiability and decidability. Based at technique of reduced normal forms we solve these problems and find deciding algorithms. Several interesting open problems are suggested. In final part of the paper we extend obtained results on logics with different accessibility relations for different agents and consider the satisfiability problem for these logics.