A note on dual-intuitionistic logic

Mathematical Logic Quarterly

Volumn 49, Issue 5, 2003, Pages 519-524

  Kamide, Norihiro ^a  

^a KEIO UNIVERSITY   (Japan)

Author keywords

Dual intuitionistic logic; Goodman's logic; Nelson's logic; Strong negation

Indexed keywords

EID: 0042739689     PISSN: 09425616     EISSN: None     Source Type: Journal    
DOI: 10.1002/malq.200310055     Document Type: Article

References (15)

1. A. Almukdad and D. Nelson, Constructible falsity and inexact predicates. J. Symbolic Logic 49, 231 - 233 (1984).
2. O. Arieli and A. Avron, Reasoning with logical bilattices. Journal of Logic, Language and Information 5, 25 - 63 (1996).
3. J. P. Cleave, The notion of logical consequence in the logic of inexact predicates. Z. Math. Logik Grundlagen Math. 20, 307 - 324 (1974).
4. J. Czermak, A remark on Gentzen's calculus of sequents. Notre Dame J. Formal Logic 18, 471 - 474 (1977).
5. R. Goré, Dual intuitionistic logic revisited. Lecture Notes in Artificial Intelligence 1847, pp. 252 - 267 (Springer-Verlag, Berlin et al. 2000).
6. N. D. Goodman, The logic of contradiction. Z. Math. Logik Grundlagen Math. 27, 119 - 126 (1981).
7. J. Harland, Success and failure for hereditary Harrop formulae. J. Logic Programming 17, 1 - 29 (1993).
8. N. Kamide, Sequent calculi for intuitionistic linear logic with strong negation. Logic Journal of the IGPL 10, 653 - 678 (2002).
9. M. Kracht, On extensions of intermediate logics by strong negation. J. Philosophical Logic 27, 49 - 73 (1998).
10. D. Nelson, Constructible falsity. J. Symbolic Logic 14, 16 - 26 (1949).
11. D. Pearce, Reasonig with negative information II: Hard negation, strong negation and logic programs. Lecture Notes in Computer Science 619, pp. 63 - 79 (Springer-Verlag, Berlin et al. 1992).
12. R. H. Thomason, A semantical study of constructible falsity. Z. Math. Logik Grundlagen Math. 15, 247 - 257 (1969).
13. I. Urbas, Dual-intuitionistic logic. Notre Dame J. Formal Logic 37, 440 - 451 (1996).
14. H. Wansing, The logic of information structures. Lecture Notes in Artificial Intelligence 681, pp. 1 - 163 (Springer-Verlag, Berlin et al. 1993).
15. H. Wansing, Higher-arity Gentzen systems for Nelson's logics. In: Proceedings of the 3rd International Congress of the Society for Analytical Philosophy - Rationality, Realism, Revision (J. Nida-Rümelin, ed.), pp. 105 - 109 (Walter de Gruyter, Berlin-New York 1999).