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research-article

One-variable fragments of intermediate logics over linear frames

Authors:

Xavier Caicedo,

George Metcalfe,

Ricardo Rodríguez,

Olim TuytAuthors Info & Claims

Volume 287, Issue C

https://doi.org/10.1016/j.ic.2021.104755

Published: 01 September 2022 Publication History

Abstract

A correspondence is established between one-variable fragments of (first-order) intermediate logics defined over a fixed countable linear frame and Gödel modal logics defined over many-valued equivalence relations with values in a closed subset of the real unit interval. It is also shown that each of these logics can be interpreted in the one-variable fragment of the corresponding constant domain intermediate logic, which is equivalent to a Gödel modal logic defined over (crisp) equivalence relations. Although the latter modal logics in general lack the finite model property with respect to their frame semantics, an alternative semantics is defined that has this property and used to establish co-NP-completeness results for the one-variable fragments of the corresponding intermediate logics both with and without constant domains.

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One-variable fragments of intermediate logics over linear frames

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cover image Information and Computation

Information and Computation Volume 287, Issue C

Sep 2022

220 pages

ISSN:0890-5401

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Academic Press, Inc.

United States

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Published: 01 September 2022

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