The universe of discourse of modal logic

Journal of Applied Non-Classical Logics 6 (2):137-147 (1996)
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Abstract

ABSTRACT A new notion of model is presented which makes the Barcan formula and its converse hold in arbitrary frames without requiring constant, increasing or decreasing domains. Soundness and completeness of first order K is established for this class of new models. The failure of reasoning by substitution known as ? opacity ? is explained. An existenc predicate makes it possible to distinguish between actual and possible elements. The connections with the restricted Barcan formula are considered

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10.1080/11663081.1996.10510875

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Proof Methods for Modal and Intuitionistic Logics.Melvin Fitting - 1985 - Journal of Symbolic Logic 50 (3):855-856.
A tableau proof method admitting the empty domain.Melvin Fitting - 1971 - Notre Dame Journal of Formal Logic 12 (2):219-224.

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