Notre Dame Journal of Formal Logic 37 (3):440-451 (1996)

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.
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DOI 10.1305/ndjfl/1039886520
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References found in this work BETA

Investigations Into Logical Deduction.Gerhard Gentzen, M. E. Szabo & Paul Bernays - 1970 - Journal of Symbolic Logic 35 (1):144-145.
The Logic of Contradiction.Nicolas D. Goodman - 1981 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 27 (8-10):119-126.
The Logic of Contradiction.Nicolas D. Goodman - 1981 - Mathematical Logic Quarterly 27 (8‐10):119-126.
A Remark on Gentzen's Calculus of Sequents.Johannes Czermak - 1977 - Notre Dame Journal of Formal Logic 18 (3):471-474.

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Logical Pluralism, Meaning-Variance, and Verbal Disputes.Ole Thomassen Hjortland - 2013 - Australasian Journal of Philosophy 91 (2):355-373.

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