Conservative expansions of substructural logics

Amidei, J.; Ertola-Biraben, R. C. and Montagna, F. (2022). Conservative expansions of substructural logics. In: Galatos, Nikolaos and Terui, Kazushige eds. Hiroakira Ono on Substructural Logics. Outstanding Contributions to Logic, 23. Springer, pp. 339–368.



In this paper we investigate several conservative expansions of substructural logics, and of fuzzy logics in particular. The most important are the expansion by Δ and the expansion by propositional quantifiers, with applications to Craig interpolation. In the last part of the paper we show that in several expansions of MTL it is possible to add conservatively the Łukasiewicz connectives, as well as a new kind of product.

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