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August 2021 Two Variants of Noncontingency Operator
Jie Fan
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Notre Dame J. Formal Logic 62(3): 491-525 (August 2021). DOI: 10.1215/00294527-2021-0025

Abstract

By slightly adapting two equivalent semantics of noncontingency operator, we obtain two variants, ⊡ and ⊞, with nonequivalent semantics. We show that on the class of models satisfying any of five basic properties (i.e., seriality, reflexivity, transitivity, symmetry, Euclideanness), the logic L(), which has ⊡ as the sole modal primitive, is less expressive than the logic L(), which has ⊞ as the sole modal primitive. We investigate the frame definability of both languages. We then axiomatize L() and L() over various classes of bimodal frames. Among other results, a notion of morphisms, called ⊞-morphisms, are provided to show the completeness of axiomatizations of L() over serial frames and also over symmetric frames.

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Jie Fan. "Two Variants of Noncontingency Operator." Notre Dame J. Formal Logic 62 (3) 491 - 525, August 2021. https://doi.org/10.1215/00294527-2021-0025

Information

Received: 3 July 2020; Accepted: 1 April 2021; Published: August 2021
First available in Project Euclid: 6 October 2021

Digital Object Identifier: 10.1215/00294527-2021-0025

Subjects:
Primary: 03B45

Rights: Copyright © 2021 University of Notre Dame

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Vol.62 • No. 3 • August 2021
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