First Order Classical Modal Logic

Abstract
This 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 in the first part of the paper a series of new completeness results for salient classical systems of first order modal logic
Keywords First-order modal logic  neighborhood semantics  general frames
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Minghui Ma (2010). Toward Model-Theoretic Modal Logics. Frontiers of Philosophy in China 5 (2):294-311.
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