Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 37, Number 3 (1996), 440-451.
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.
Notre Dame J. Formal Logic Volume 37, Number 3 (1996), 440-451.
First available in Project Euclid: 14 December 2002
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03B53: Paraconsistent logics
Secondary: 03B20: Subsystems of classical logic (including intuitionistic logic) 03B25: Decidability of theories and sets of sentences [See also 11U05, 12L05, 20F10] 03B55: Intermediate logics 03E70: Nonclassical and second-order set theories 03F05: Cut-elimination and normal-form theorems 03F55: Intuitionistic mathematics
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.