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Representations for logics and algebras related to revised drastic product t-norm

Published in: Soft Computing | Issue 7/2019

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Abstract

We obtain a functional representation of RDP logic formulas and a combinatorial representation for finite RDP algebras. As the variety of RDP algebras includes the varieties of Gödel, DP, and EMTL algebras, we derive analogous representations for such varieties and their corresponding logics.

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MTL algebras are commutative integral bounded residuated lattices satisfying prelinearity (Galatos et al. 2007).

A multiset is a family whose members have multiple instances (a set is a multiset whose members have exactly one instance).

Note that, if \(g :J \rightarrow J'\) is an open map such that \(g(\max (J))=\max (J')\), then \(|J'| \le |J|\).

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Title: Representations for logics and algebras related to revised drastic product t-norm
Publication date: 22-09-2018
Published in: Soft Computing / Issue 7/2019
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-018-3541-y

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