Open AccessParaconsistent da Costa Weakening of Intuitionistic Negation: What does it mean?
Author(s) -
Zoran Majkić
Publication year - 2022
Publication title -
international journal of pure mathematics
Language(s) - English
Resource type - Journals
ISSN - 2313-0571
DOI - 10.46300/91019.2022.9.9
Subject(s) - paraconsistent logic , gödel , intuitionistic logic , negation , classical logic , t norm fuzzy logics , monoidal t norm logic , mathematics , many valued logic , negation as failure , discrete mathematics , fuzzy logic , algebra over a field , autoepistemic logic , pure mathematics , higher order logic , computer science , artificial intelligence , linear logic , description logic , multimodal logic , fuzzy set , programming language , fuzzy number
In this paper we consider the systems of weakening of intuitionistic negation logic mZ, introduced in [1], [2], which are developed in the spirit of da Costa's approach. We take a particular attention on the philosophical considerations of the paraconsistent mZ logic w.r.t. the constructive semantics of the intuitionistic logic, and we show that mZ is a subintuitionistic logic. Hence, we present the relationship between intuitionistic and paraconsistent subintuitionistic negation used in mZ. Then we present a significant number of examples for this subintuitionistic and paraconsistent mZ logics: Logic Programming with Fiting's fixpoint semantics for paraconsistent weakening of 3-valued Kleene's and 4-valued Belnap's logics. Moreover, we provide a canonical construction of infinitary-valued mZ logics and, in particular, the paraconsistent weakening of standard Zadeh's fuzzy logic and of the Godel-Dummet t-norm intermediate logics.