Intransitive temporal multi-agent’s logic, knowledge and uncertainty, plausibility

Abstract

© Springer International Publishing Switzerland 2016. We study intransitive temporal logic implementing multiagent’s approach and formalizing knowledge and uncertainty. An innovative point here is usage of non-transitive linear time and multi-valued models - the ones using separate valuations Vj for agent’s knowledge of facts and summarized (agreed) valuation together with rules for computation truth values for compound formulas. The basic mathematical problems we study here are - decidability and decidability w.r.t. admissible rules. First, we study general case - the logic with non-uniform intransitivity and solve its decidability problem. Also we consider a modification of this logic - temporal logic with uniform non-transitivity and solve problem of recognizing admissibility in this logic