One-variable fragments of intermediate logics over linear frames

Caicedo, Xavier; Metcalfe, George; Rodriguez, Ricardo; Tuyt, Olim (2022). One-variable fragments of intermediate logics over linear frames. Information and computation, 287, p. 104755. Elsevier 10.1016/j.ic.2021.104755

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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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Metcalfe, George, Tuyt, Olim Frits

Subjects:

500 Science > 510 Mathematics

ISSN:

0890-5401

Publisher:

Elsevier

Language:

English

Submitter:

George Metcalfe

Date Deposited:

19 Sep 2022 10:48

Last Modified:

05 Dec 2022 16:24

Publisher DOI:

10.1016/j.ic.2021.104755

BORIS DOI:

10.48350/173011

URI:

https://boris.unibe.ch/id/eprint/173011

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