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09-06-2017 | Foundations

A representation of residuated lattices satisfying the double negation law

Author: Ivan Chajda

Published in: Soft Computing | Issue 6/2018

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Abstract

Every residuated lattice can be considered as an idempotent semiring. Conversely, if an idempotent semiring is finite, then it can be organized into a residuated lattice. Unfortunately, this does not hold in general. We show that if an idempotent semiring is equipped with an involution which satisfies certain conditions, then it can be organized into a residuated lattice satisfying the double negation law. Also conversely, every residuated lattice satisfying the double negation law can be considered as an idempotent semiring with an involution satisfying the mentioned conditions.

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Title: A representation of residuated lattices satisfying the double negation law
Author: Ivan Chajda
Publication date: 09-06-2017
Publisher: Springer Berlin Heidelberg
Published in: Soft Computing / Issue 6/2018
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-017-2673-9

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