Some modal and temporal translations of generalized basic logic

Fussner, Wesley; Zuluaga Botero, William (2021). Some modal and temporal translations of generalized basic logic. In: Relational and Algebraic Methods in Computer Science. RAMiCS 2021. Lecture Notes in Computer Science: Vol. 13027 (pp. 176-191). Cham: Springer 10.1007/978-3-030-88701-8_11

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We introduce a family of modal expansions of Łukasiewicz logic that are designed to accommodate modal translations of generalized basic logic (as formulated with exchange, weakening, and falsum). We further exhibit algebraic semantics for each logic in this family, in particular showing that all of them are algebraizable in the sense of Blok and Pigozzi. Using this algebraization result and an analysis of congruences in the pertinent varieties, we establish that each of the introduced modal Łukasiewicz logics has a local deduction-detachment theorem. By applying Jipsen and Montagna’s poset product construction, we give two translations of generalized basic logic with exchange, weakening, and falsum in the style of the celebrated Gödel-McKinsey-Tarski translation. The first of these interprets generalized basic logic in a modal Łukasiewicz logic in the spirit of the classical modal logic S4, whereas the second interprets generalized basic logic in a temporal variant of the latter.

Item Type:

Book Section (Book Chapter)

Division/Institute:

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

UniBE Contributor:

Fussner, Daniel Wesley

Subjects:

500 Science > 510 Mathematics

ISSN:

0302-9743

ISBN:

978-3-030-88700-1

Series:

Lecture Notes in Computer Science

Publisher:

Springer

Language:

English

Submitter:

George Metcalfe

Date Deposited:

14 Apr 2022 11:21

Last Modified:

05 Dec 2022 16:13

Publisher DOI:

10.1007/978-3-030-88701-8_11

BORIS DOI:

10.48350/166730

URI:

https://boris.unibe.ch/id/eprint/166730

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