Uniqueness of normal proofs in implicational intuitionistic logic

Journal of Logic, Language and Information

Volumn 8, Issue 2, 1999, Pages 217-242

  Aoto, Takahito ^a  

^a JAPAN ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY   (Japan)

Author keywords

Coherence; Komori's problem; Minimal formulas; Natural deduction; Non prime contraction; Uniqueness of normal proofs

Indexed keywords

EID: 18944408433     PISSN: 09258531     EISSN: 15729583     Source Type: Journal    
DOI: 10.1023/A:1008254111992     Document Type: Article

References (21)

1. Aoto, T., 1995, "Unique normal proof property for implicational minimal formulas in the intuitionistic logic," Research Report IS-RR-95-0015F, School of Information Science, JAIST.
2. Aoto, T. and Ono, H., 1994a, "Non-uniqueness of normal proofs for minimal formulas in implication-conjunction fragment of BCK," Bulletin of the Section of Logic 23(3), 104-112.
3. Aoto, T. and Ono, H., 1994b, "Uniqueness of normal proofs in {→, ∧)-fragment of NJ," Research Report IS-RR-94-0024F, School of Information Science, JAIST.
4. Gentzen, G., 1934/1935, "Untersuchungen über das logische Schliessen," Mathematische Zeitschrift 39, 176-405, 405-431.
5. Hindley, J.R. and Seldin, J.P., 1986, Introduction to Combinators and λ-Calculus, London Mathematical Society Student Texts, Vol. 1, Cambridge: Cambridge University Press.
6. Hirokawa, S., 1993, "Principal types of BCK-lambda-terms," Theoretical Computer Science 107, 253-276.
7. Jaśkowski, S., 1963, "Über Tautologien, in welchen keine Variable mehr als zweimal vorkommt," Zeitschrift für mathematische Logik and Grundlagen der Mathematik 9, 219-228.
8. Jay, C.B. and Ghani, N., 1995, "The virtue of eta-expansion," Journal of Functional Programming 5(2), 135-154.
9. Kashima, R., 1997, "Contraction-elimination for implicational logics," Annals of Pure and Applied Logic 84, 17-39.
10. Klop, J.W., 1992, "Term rewriting systems," pp. 1-116 in Handbook of Logic in Computer Science, Vol. 2, S. Abramsky and D.M. Gabbay, and T.S.E. Maibaum, eds., Oxford: Oxford University Press.
11. Komori, Y., 1987, "BCK algebras and lambda calculus," pp. 5-11 in Proceedings of 10th Symposium on Semigroups, Sakado, 1986.
12. Komori, Y. and Hirokawa, S., 1993, "The number of proofs for a BCK-formula," Journal of Symbolic Logic 58(2), 626-628.
13. MacLane, S., 1982, "Why commutative diagrams coincide with equivalent proofs," Contemporary Mathematics 13, 387-401.
14. Mints, G.E., 1979, "A coherence theorem for cartesian closed categories (abstract)," Journal of Symbolic Logic 44(3), 453-454.
15. Mints, G.E., 1992, "A simple proof of the coherence theorem for Cartesian closed categories," pp. 213-220 in Selected Papers in Proof Theory, G.E. Mints, ed., Napoli: Bibliopolis.
16. Ono, H., 1990, "Structural rules and a logical hierarchy," pp. 95-104 in Mathematical Logic, P.P. Petkov, ed., New York: Plenum Press.
17. Prawitz, D., 1965, Natural Deduction, A Proof-Theoretical Study, Acta Universitatis Stockholmiensis Stockholm Studies in Philosophy, Vol. 3, Stockholm: Almqvist & Wiksell.
18. Takeuti, G., 1987, Proof Theory, second edition, Studies in Logic and the Foundations of Mathematics, Vol. 81, Amsterdam: North-Holland.
19. Tatsuta, M., 1993, "Uniqueness of normal proofs of minimal formulas," Journal of Symbolic Logic 58(3), 789-799.
20. Van Benthem, J., 1995, Language in Action: Categories, Lambdas, and Dynamic Logic, Cambridge, MA: The MIT Press.
21. Van Dalen, D., 1994, Logic and Structure, third edition, Berlin: Springer-Verlag.