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

摘要

We develop a conceptually clear, intuitive, and feasible decision procedurefor testing satisfiability in the full multi-agent epistemic logic CMAEL(CD)with operators for common and distributed knowledge for all coalitions ofagents mentioned in the language. To that end, we introduce Hintikka structuresfor CMAEL(CD) and prove that satisfiability in such structures is equivalent tosatisfiability in standard models. Using that result, we design an incrementaltableau-building procedure that eventually constructs a satisfying Hintikkastructure for every satisfiable input set of formulae of CMAEL(CD) and closesfor every unsatisfiable input set of formulae.