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Summer 1999 Kripke Completeness of Infinitary Predicate Multimodal Logics
Yoshihito Tanaka
Notre Dame J. Formal Logic 40(3): 326-340 (Summer 1999). DOI: 10.1305/ndjfl/1022615613


Kripke completeness of some infinitary predicate modal logics is presented. More precisely, we prove that if a normal modal logic $ \bf L$ above $ \bf K$ is $ \cal {D}$-persistent and universal, the infinitary and predicate extension of $ \bf L$ with BF$\scriptstyle \omega_{{1}}$ and BF is Kripke complete, where BF$\scriptstyle \omega_{{1}}$ and BF denote the formulas $ \bigwedge_{{{i\in\omega}}}^{{}}$ $ \Box$ pi $ \supset$ $ \Box$ $ \bigwedge_{{{i\in\omega}}}^{{}}$pi and $ \forall x \Box \varphi \supset \Box \forall x \varphi$, respectively. The results include the completeness of extensions of standard modal logics such as $ \bf K$, 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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Yoshihito Tanaka. "Kripke Completeness of Infinitary Predicate Multimodal Logics." Notre Dame J. Formal Logic 40 (3) 326 - 340, Summer 1999.


Published: Summer 1999
First available in Project Euclid: 28 May 2002

zbMATH: 1007.03016
MathSciNet: MR1845628
Digital Object Identifier: 10.1305/ndjfl/1022615613

Primary: 03B45

Rights: Copyright © 1999 University of Notre Dame


Vol.40 • No. 3 • Summer 1999
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