Tableau-based decision procedure for the multi-agent epistemic logic with all coalitional operators for common and distributed knowledge
This provides a decision procedure for a complex logic used in multi-agent systems, which is incremental as it builds on existing tableau methods for epistemic logics.
The paper tackles the problem of testing satisfiability in the full multi-agent epistemic logic CMAEL(CD) with operators for common and distributed knowledge for all coalitions, and it develops a tableau-based decision procedure that constructs satisfying Hintikka structures for satisfiable inputs and closes for unsatisfiable ones.
We develop a conceptually clear, intuitive, and feasible decision procedure for testing satisfiability in the full multi-agent epistemic logic CMAEL(CD) with operators for common and distributed knowledge for all coalitions of agents mentioned in the language. To that end, we introduce Hintikka structures for CMAEL(CD) and prove that satisfiability in such structures is equivalent to satisfiability in standard models. Using that result, we design an incremental tableau-building procedure that eventually constructs a satisfying Hintikka structure for every satisfiable input set of formulae of CMAEL(CD) and closes for every unsatisfiable input set of formulae.