A small set of axioms for residuated logic

Authors:
Nehad N. Morsi
Affiliations:
Department of Basic Science, Arab Academy for Science, Technology & Maritime Transport, Heliopolis, Cairo, Egypt
Venue:
Information Sciences: an International Journal
Year:
2005

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Abstract

We show that a set of three axioms, together with modus ponens, suffices to build up a formal system for the class R of all quadruples (L, ≤, T,J), in which (L,≤) is a partially ordered set with a top element, and T is a triangular norm on (L,≤) that has a residuated implication J. We show that this R is not a variety.