Branching time agents' logic, satisfiability problem by rules in reduced form

This paper considers the branching time logic on non-transitive intervals of agents' accessibility relations. The agents' accessibility relations are defined inside transitivity intervals and via neighboring limit points, they may be not complete and lose some states — the lacunas of forgotten time thought they may interfere. This approach is used for modeling computational processes and analysis of incomplete information for individual agents. A logical language for reasoning about models' properties which includes temporal and modal logical operations is suggested. Illustrative examples are provided. Mathematical part of the paper is devoted to the satisfiability and decidability problems for the suggested logic. We use instruments of reduced normal forms for rules and algorithms converting rules to such forms. We find algorithms solving the satisfiability problem. Some open problems are suggested.