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

TL;DR

This paper presents an exponential-time tableau-based decision procedure for the multi-agent epistemic logic MAEL(CD), establishing its ExpTime-completeness and providing a complexity-optimal algorithm for satisfiability checking.

Contribution

It introduces a new tableau-based decision procedure for MAEL(CD) that is both sound and complete, matching the known lower bound for complexity.

Findings

The procedure operates in deterministic exponential time.

It proves MAEL(CD)-satisfiability is ExpTime-complete.

The method is often more efficient in practice.

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.