Kripke Completeness of Infinitary Predicate Multimodal Logics

Notre Dame Journal of Formal Logic 40 (3):326-340 (1999)

Abstract

Kripke completeness of some infinitary predicate modal logics is presented. More precisely, we prove that if a normal modal logic above is -persistent and universal, the infinitary and predicate extension of with BF and BF is Kripke complete, where BF and BF denote the formulas pi pi and x x, respectively. The results include the completeness of extensions of standard modal logics such as , and its extensions by the schemata T, B, 4, 5, D, and their combinations. The proof is obtained by extending the correspondence between the representation of modal algebras and the completeness of propositional modal logic to infinite

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References found in this work

A Logic Stronger Than Intuitionism.Sabine Görnemann - 1971 - Journal of Symbolic Logic 36 (2):249-261.
The Structure of Lattices of Subframe Logics.Frank Wolter - 1997 - Annals of Pure and Applied Logic 86 (1):47-100.
Game Logic and its Applications I.Mamoru Kaneko & Takashi Nagashima - 1996 - Studia Logica 57 (2-3):325 - 354.
Kripke Completeness of Infinitary Predicate Multimodal Logics.Yoshihito Tanaka - 1999 - Notre Dame Journal of Formal Logic 40 (3):326-340.

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