# Rethinking Epistemic Logic with Belief Bases

## TL;DR

This paper proposes a novel semantics for epistemic logic based on multi-agent belief bases, offering a new perspective that defines possible worlds and alternatives from belief bases, with proven completeness, decidability, and complexity results.

## Contribution

It introduces a new belief-base-based semantics for epistemic logic, differing from traditional Kripke models, and provides axiomatization, decidability, and complexity analysis.

## Key findings

- Complete axiomatization of the new logic.
- Decidability established via finite model property.
- Polynomial embedding into existing awareness logic.

## Abstract

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.