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.

中文翻译：

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用信念基础重新思考认知逻辑

我们基于多智能体信念库的概念为显式和隐式信念的逻辑引入了新的语义。与现有的认知逻辑的克里普克式语义不同，其中可能世界和信念/认知替代的概念是原始的，在我们的语义中，它们是非原始的，但从信念基础的概念中定义。我们提供了一个完整的公理化，并通过有限模型论证证明了我们的逻辑的可判定性。我们还将我们的逻辑多项式嵌入到 Fagin & Halpern 的一般意识逻辑中，并通过嵌入为我们的逻辑建立复杂性结果。