Families of local involutive integral residuated lattice-ordered commutative monoids admitting Boolean term

2023/12/20 by Antoni Torrens, Torrens, Antoni
Computer Science · Decision Sciences · #06D35 Secondary #08A30 #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Logic (math.LO) #Primary:06D99 #Quantum Algebra (math.QA) #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.2312.13255

openalex publication_date 2023/12/20 · openalex created_date 2023/12/22 · openalex updated_date 2026/07/28

Abstract

We present a family of local involutive integral bounded residuated lattice-ordered commutative monoids (involutive residuated lattices, for short) having Boolean term, radical term (see \citeCT12 and \citeT23), and satisfying GAP (Generalized Appel property) (see \citeT23).The construction of this family is based in the examples given in \cite[Subsection 5.1]CT12, by taking \bfm\LLn in place of \bfmL_n+1 and \bfmL_p+1 in place of the two element Boolean algebra. In some sense this paper is a companion of the paper \citeT23, in which the General Apple Property (GAP) and Boolean terms are studied.

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