A note on a deductive scheme of Dummett in classical and fuzzy logics

Authors:
I. GarcíA-Honrado;E. Trillas
Affiliations:
University of Oviedo, Spain;European Centre for Soft Computing, Mieres, Asturias, Spain
Venue:
Fuzzy Sets and Systems
Year:
2013

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Abstract

The main subject of logic is the study of the processes of deductive reasoning and, in particular, the validity of the so-called 'schemes' of such type of reasoning. In this paper, a first and partial study of the validity of the following deductive scheme is presented,IfA,thenBIfnot-A,thenBB.This study is done assuming that the statements A and B are representable in Boolean algebras, De Morgan algebras, orthomodular lattices, or in standard algebras of fuzzy sets, and with the conditional statements 'If/then' translated into several conditional operators by taking always into account the consequence operator.