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Complexity of logics for multi-agent systems with restricted modal context. (English) Zbl 1277.68255
Summary: We present a modal context restriction for multimodal logics with iterated modalities combining axioms $$\mathbf K$$, $$\mathbf D$$, $$\mathbf 5$$ and $$\mathbf{45}$$, for which the satisfiability problem is PSPACE-complete and putting additional restriction on the modal depth of formulas makes it NPTIME-complete. We propose an extension of the tableau method, as presented in [J. Y. Halpern and Y. Moses, Artif. Intell. 54, No. 3, 319–379 (1992; Zbl 0762.68029)], for checking the satisfiability of the formulas with restricted modal context. The case of axiom $$\mathbf T$$ is also discussed.
##### MSC:
 68T27 Logic in artificial intelligence 03B45 Modal logic (including the logic of norms) 03B62 Combined logics 68T42 Agent technology and artificial intelligence
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