Branching time logics with multiagent temporal accessibility relations

Under study are the branching time temporal logics with temporal accessibility relations for the agents different in length and content. We find an algorithm for solving the problems of satisfiability and decidability of the logic through describing finite satisfiable models of computable size (through the size of the input formulas). We remove the constraints on the size of all temporal accessibility intervals for the agents (to be all inside a common temporal accessibility interval at any local time point); i.e., all constraints can be arbitrary. Also, we formulate some open problems.