Abstract
A pair of deductive systems (S,S’) is Leibniz-linked when S’ is an extension of S and on every algebra there is a map sending each filter of S to a filter of S’ with the same Leibniz congruence. We study this generalization to arbitrary deductive systems of the notion of the strong version of a protoalgebraic deductive system, studied in earlier papers, and of some results recently found for particular non-protoalgebraic deductive systems. The necessary examples and counterexamples found in the literature are described.
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Dedicated to Professor Ryszard Wójcicki on the occasion of his 80th birthday
Special issue in honor of Ryszard Wójcicki on the occasion of his 80th birthday Edited by J. Czelakowski, W. Dziobiak, and J. Malinowski
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Font, J.M., Jansana, R. Leibniz-linked Pairs of Deductive Systems. Stud Logica 99, 171 (2011). https://doi.org/10.1007/s11225-011-9359-6
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DOI: https://doi.org/10.1007/s11225-011-9359-6
Keywords
- Leibniz operator
- Leibniz filters
- protoalgebraic logics
- strong version
- truth-equational logics
- abstract algebraic logic