Adding Proof Calculi to Epistemic Logics with Structured Knowledge

Abstract

Dynamic Epistemic Logic (DEL) is used in the analysis of a wide class of application scenarios involving multi-agents systems with local perceptions of information and knowledge. In its classical form, the knowledge of epistemic states is represented by sets of propositions. However, the complexity of the current systems, requires other richer structures, than sets of propositions, to represent knowledge on their epistemic states. Algebras, graphs or distributions are examples of useful structures for this end. Based on this observation, we introduced a parametric method to build dynamic epistemic logics on-demand, taking as parameter the specific knowledge representation framework (e.g., propositional, equational or even a modal logic) that better fits the problems in hand. In order to use the built logics in practices, tools support is needed. Based on this, we extended our previous method with a parametric construction of complete proof calculi. The complexity of the model checking and satisfiability problems for the achieved logics are provided.