Exploiting Belief Bases for Building Rich Epistemic Structures
This work addresses foundational issues in formal logic and AI, offering a more efficient approach to modeling knowledge and belief, though it appears incremental in its methodological contributions.
The paper tackles the problem of constructing semantics for epistemic logic by introducing a belief base abstraction, which simplifies and compacts the universal epistemic model compared to existing inductive constructions. It provides semantic equivalence results for basic and extended epistemic languages and a lower bound complexity result for model checking.
We introduce a semantics for epistemic logic exploiting a belief base abstraction. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and epistemic alternative are primitive, in the proposed semantics they are non-primitive but are defined from the concept of belief base. We show that this semantics allows us to define the universal epistemic model in a simpler and more compact way than existing inductive constructions of it. We provide (i) a number of semantic equivalence results for both the basic epistemic language with "individual belief" operators and its extension by the notion of "only believing", and (ii) a lower bound complexity result for epistemic logic model checking relative to the universal epistemic model.