Nontransitive temporal multiagent logic, information and knowledge, deciding algorithms

Multiagent and temporal logics are active domains in Information Sciences, CS, and AI. Attention has predominantly focused on the logics based on transitive relational models, with particular emphasis on transitive time. But this does not seem rather reliable assumption. Nontransitivity of passing information may be demonstrated with relative ease through persuasive examples. Therefore, we introduce and study multiagent temporal logics that are based on nontransitive linear time. Another innovative step is consideration of incomplete information: the information/knowledge with lacunas – the linear time with forgettable intervals of time in the past. Technically, the most important problems are problems of satisfiability and decidability of suggested logics. The main results are the algorithms that compute satisfiability and solve decidability (and so provide solutions to these problems). The paper concludes by posing a series of open problems.