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Summer 1996 Dual-Intuitionistic Logic
Igor Urbas
Notre Dame J. Formal Logic 37(3): 440-451 (Summer 1996). DOI: 10.1305/ndjfl/1039886520


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 ${\bf LJ}^{∸}$ and ${\bf LDJ}^{∸}$, and a simply consistent but $\omega$-inconsistent Set Theory with Unrestricted Comprehension Schema based on LDJ is sketched.


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Igor Urbas. "Dual-Intuitionistic Logic." Notre Dame J. Formal Logic 37 (3) 440 - 451, Summer 1996.


Published: Summer 1996
First available in Project Euclid: 14 December 2002

zbMATH: 0869.03008
MathSciNet: MR1434429
Digital Object Identifier: 10.1305/ndjfl/1039886520

Primary: 03B53
Secondary: 03B20 , 03B25 , 03B55 , 03E70 , 03F05 , 03F55

Rights: Copyright © 1996 University of Notre Dame

Vol.37 • No. 3 • Summer 1996
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