Dynamic Temporal Logical Operations in Multi-Agent Logics

Abstract

We study temporal multi-agent logics using a new approach to defining time for individual agents. It is assumed that in any time state each agent (in a sense) generates its own future time, which will only be available for analysis in the future. That is, the defined time interval depends both on the agent and on the initial state where the agent starts to act. It is also assumed that the agent may have intervals of forgotten (lost) time. We investigate problems of unification and problems of computable recognizing admissible inference rules. An algorithm is found for solving these problems based on the construction of a finite computable set of formulas which is a complete set of unifiers. We use the technique of projective formulas developed by S. Ghilardi. It is proved that any unifiable formula is in fact projective and an algorithm is constructed which creates its projective unifier. Thereby we solve the unification problem, and based at this, find the solution to the open problem of computable recognizing admissible inference rules.