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Fall 1999 Completeness and Definability in the Logic of Noncontingency
Evgeni E. Zolin
Notre Dame J. Formal Logic 40(4): 533-547 (Fall 1999). DOI: 10.1305/ndjfl/1012429717

Abstract

Hilbert-style axiomatic systems are presented for versions of the modal logics K$ \Sigma$, where $ \Sigma$ $ \subseteq$ {D, 4, 5}, with noncontingency as the sole modal primitive. The classes of frames characterized by the axioms of these systems are shown to be first-order definable, though not equal to the classes of serial, transitive, or euclidean frames. The canonical frame of the noncontingency logic of any logic containing the seriality axiom is proved to be nonserial. It is also shown that any class of frames definable in the noncontingency language contains the class of functional frames, and dually, there exists a greatest consistent normal noncontingency logic.

Citation

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Evgeni E. Zolin. "Completeness and Definability in the Logic of Noncontingency." Notre Dame J. Formal Logic 40 (4) 533 - 547, Fall 1999. https://doi.org/10.1305/ndjfl/1012429717

Information

Published: Fall 1999
First available in Project Euclid: 30 January 2002

zbMATH: 0989.03019
MathSciNet: MR1858241
Digital Object Identifier: 10.1305/ndjfl/1012429717

Subjects:
Primary: 03B45
Secondary: 03B42

Rights: Copyright © 1999 University of Notre Dame

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Vol.40 • No. 4 • Fall 1999
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