Multiagent temporal logics with multivaluations

We study multiagent logics and use temporal relational models with multivaluations. The key distinction from the standard relational models is the introduction of a particular valuation for each agent and the computation of the global valuation using all agents' valuations. We discuss this approach, illustrate it with examples, and demonstrate that this is not a mechanical combination of standard models, but a much more subtle and sophisticated modeling of the computation of truth values in multiagent environments. To express the properties of these models we define a logical language with temporal formulas and introduce the logics based at classes of such models. The main mathematical problem under study is the satisfiability problem. We solve it and find deciding algorithms. Also we discuss some interesting open problems and trends of possible further investigations.