Tableau-based decision procedure for the multi-agent epistemic logic with operators of common and distributed knowledge

Abstract

We develop an incremental-tableau-based decision procedure for the multi-agent epistemic logic MAEL(CD) (aka S5_n (CD)), whose language contains operators of individual knowledge for a finite set Ag of agents, as well as operators of distributed and common knowledge among all agents in Ag. Our tableau procedure works in (deterministic) exponential time, thus establishing an upper bound for MAEL(CD)-satisfiability that matches the (implicit) lower-bound known from earlier results, which implies ExpTime-completeness of MAEL(CD)-satisfiability. Therefore, our procedure provides a complexity-optimal algorithm for checking MAEL(CD)-satisfiability, which, however, in most cases is much more efficient. We prove soundness and completeness of the procedure, and illustrate it with an example.

To appear in the Proceedings of the 6th IEEE Conference on Software Engineering and Formal Methods (SEFM 2008)

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• Complexity and Expressivity of Branching- and Alternating-Time Temporal Logics with Finitely Many Variables
• Tableau-based decision procedures for logics of strategic ability in multi-agent systems
• Tableau-based decision procedure for the multi-agent epistemic logic with all coalitional operators for common and distributed knowledge