On Paraconsistent Weakening of Intuitionistic Negation

2011/02/09 by Zoran Majkic, Majkic, Zoran
Computer Science · #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #cs.LO

paper · pdf · doi:10.48550/arxiv.1102.1935

10 pages

arxiv created 2011/02/09 · arxiv updated 2011/02/10

Abstract

In [1], systems of weakening of intuitionistic negation logic called Z_n and CZ_n were developed in the spirit of da Costa's approach(c.f. [2]) by preserving, differently from da Costa, its fundamental properties: antitonicity, inversion and additivity for distributive lattices. However, according to [3], those systems turned out to be not paraconsistent but extensions of intuitionistic logic. Taking into account of this result, we shall here make some observations on the modified systems of Z_n and CZ_n, that are paraconsistent as well.

Related

• Proofs of some Propositions of the semi-Intuitionistic Logic with Strong Negation
• Propositional Calculus with Multiple Negations
• Negational Fragment of Intuitionistic Control Logic
• A basic system of paraconsistent Nelsonian logic of conditionals
• Sequent systems for negative modalities