Notre Dame Journal of Formal Logic

Dual-Intuitionistic Logic

Igor Urbas

Abstract

The sequent system LDJ is formulated using the same connectives as Gentzen's intuitionistic sequent system LJ, but is dual in the following sense: (i) whereas LJ is singular in the consequent, LDJ is singular in the antecedent; (ii) whereas LJ has the same sentential counter-theorems as classical LK but not the same theorems, LDJ has the same sentential theorems as LK but not the same counter-theorems. In particular, LDJ does not reject all contradictions and is accordingly paraconsistent. To obtain a more precise mapping, both LJ and LDJ are extended by adding a "pseudo-difference" operator which is the dual of intuitionistic implication. Cut-elimination and decidability are proved for the extended systems and , and a simply consistent but -inconsistent Set Theory with Unrestricted Comprehension Schema based on LDJ is sketched.

Article information

Source
Notre Dame J. Formal Logic Volume 37, Number 3 (1996), 440-451.

Dates
First available in Project Euclid: 14 December 2002

http://projecteuclid.org/euclid.ndjfl/1039886520

Digital Object Identifier
doi:10.1305/ndjfl/1039886520

Mathematical Reviews number (MathSciNet)
MR1434429

Zentralblatt MATH identifier
0869.03008

Citation

Urbas, Igor. Dual-Intuitionistic Logic. Notre Dame J. Formal Logic 37 (1996), no. 3, 440--451. doi:10.1305/ndjfl/1039886520. http://projecteuclid.org/euclid.ndjfl/1039886520.

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