We introduce the notion of ideals in implicative semigroups, and then state the characterizations of the ideals. 2000 Mathematics Subject Classification. 20M12, 06F05, 06A06, 06A12.

Recently W. McCune and D. A. Sands have considered, in a note Amer Math. Monthly 103 (1996), 888{892], implicative axioms in groups of the form if u = v, then w = t, where u, v, w, t are group words in some variables. Their interest is in such identical implications that deene the variety of groups, or the variety of abelian groups. What I want to present is, slightly more generally, identical ...

Natural language processing systems, even when given proper syntactic and semantic interpretations, still lack the common sense inference capabilities required for genuinely understanding a sentence. Recently, there have been several studies developing a semantic classification of verbs and their sentential complements, aiming at determining which inferences people draw from them. Such construc...

We prove that the variety of nuclear implicative semilattices is locally finite, thus generalizing Diego’s Theorem. The key ingredients our proof include coloring technique and construction universal models from modal logic. For this we develop duality theory for finite semilattices, Köhler duality. main result remains true bounded give an alternative Theorem, provide explicit description free ...

This paper introduces the implicative derivations and gives some of their characterizations on MTL-algebras. Furthermore, we provide representation MTL-algebras by obtain Boolean algebra via all derivations. Finally, explore relationship between derivation other operators show that there exists a bijection sets multiplier IMTL-algebras. The results this can common properties in t-norm-based fuz...