Reasoning tractably about explicit belief: A model-theoretic approach
✍ Scribed by Kwang Mong Sim
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 273 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0884-8173
No coin nor oath required. For personal study only.
✦ Synopsis
Existing epistemic logics such as the logic of implicit and explicit belief and the logic of awareness adopt a deducti¨e-theoretic approach for characterizing belief. In this approach, an agent represents the state of the world with a conjunction of axioms in its knowledge Ž . base KB and evaluates queries by trying to prove or disprove that they follow from KB.
Ž . This paper presents a multi¨alued epistemic logic MEL that allows agents to reason both deductively and model theoretically about implicit and explicit belief. By characterizing an agent's KB with a class of finite models, the set of formulas that an agent believes can be determined by checking their validity in all these models. This rests on the fact that MEL Ž has a complete axiomatization sentences that are true in all these models will also be . provable . In this paper, the soundness, completeness, and decidability of MEL are proven. Furthermore, a polynomial time model-checking algorithm for determining the satisfiability of a sentence at a particular state in a given model of MEL is also presented.