Rethinking Epistemic Logic with Belief Bases
This work addresses foundational issues in epistemic logic for AI and multi-agent systems, offering a novel approach to belief representation, but it appears incremental as it builds on existing frameworks like Fagin & Halpern's logic.
The paper tackles the problem of modeling explicit and implicit beliefs in multi-agent systems by introducing a new semantics based on belief bases, which redefines possible worlds and alternatives as non-primitive concepts derived from belief bases. The result includes a complete axiomatization, decidability proof via finite model argument, a polynomial embedding into an existing logic, and a complexity analysis.
We introduce a new semantics for a logic of explicit and implicit beliefs based on the concept of multi-agent belief base. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and doxastic/epistemic alternative are primitive, in our semantics they are non-primitive but are defined from the concept of belief base. We provide a complete axiomatization and prove decidability for our logic via a finite model argument. We also provide a polynomial embedding of our logic into Fagin & Halpern's logic of general awareness and establish a complexity result for our logic via the embedding.