Relevance logics, paradoxes of consistency and the K rule II. A non-constructive negation | Zendy

José M. Méndez | Zendy; Gemma Robles | Zendy

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Relevance logics, paradoxes of consistency and the K rule II. A non-constructive negation

Author(s) -

José M. Méndez,

Gemma Robles

Publication year - 2007

Publication title -

logic and logical philosophy

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.416

H-Index - 10

eISSN - 2300-9802

pISSN - 1425-3305

DOI - 10.12775/llp.2006.011

Subject(s) - negation , axiom , consistency (knowledge bases) , constructive , mathematics , law of excluded middle , intuitionistic logic , t norm fuzzy logics , relevance (law) , constructive set theory , discrete mathematics , algebra over a field , calculus (dental) , pure mathematics , axiom of choice , epistemology , computer science , propositional calculus , programming language , set theory , philosophy , artificial intelligence , fuzzy logic , law , geometry , dentistry , process (computing) , membership function , fuzzy set , political science , medicine , set (abstract data type)

The logic B+ is Routley and Meyer's basic positive logic. We define the logics BK+ and BK0+ by adding to B+ the K rule and to BK+ the characteristic S4 axiom, respectively. These logics are endowed with a relatively strong non-constructive negation. We prove that all the logics defined lack the K axiom and the standard paradoxes of consistency.

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