Strengthening Effect Algebras in a Logical Perspective: Heyting-Wajsberg Algebras |
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Authors: | Martinvaldo Konig |
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Institution: | 1. Via I. Nievo 11, 50129, Firenze, Italy
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Abstract: | Heyting effect algebras are lattice-ordered pseudoboolean effect algebras endowed with a pseudocomplementation that maps on the center (i.e. Boolean elements). They are the algebraic counterpart of an extension of both ?ukasiewicz many-valued logic and intuitionistic logic. We show that Heyting effect algebras are termwise equivalent to Heyting-Wajsberg algebras where the two different logical implications are defined as primitive operators. We prove this logic to be decidable, to be strongly complete and to have the deduction-detachment theorem. |
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