Logics of time and computation
Logics of time and computation
What does a conditional knowledge base entail?
Artificial Intelligence
Reasoning about knowledge
For the sake of the argument: Ramsey test conditionals, inductive inference, and nonmonotonic reasoning
Vicious circles: on the mathematics of non-wellfounded phenomena
Vicious circles: on the mathematics of non-wellfounded phenomena
First-order modal logic
Modal logic
Probabilistic Reasoning Under Coherence in System P
Annals of Mathematics and Artificial Intelligence
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The paper focuses on extending to the first order case the semantical program for modalities first introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we offer a series of new completeness results for salient classical systems of first order modal logic. Among other results we show that it is possible to prove strong completeness results for normal systems without the Barcan Formula (like FOL + K) in terms of neighborhood frames with constant domains. The first order models we present permit the study of many epistemic modalities recently proposed in computer science as well as the development of adequate models for monadic operators of high probability. We conclude by offering a general completeness result for the entire family of first order classical modal logics (encompassing both normal and non-normal systems).