Cut-elimination for a logic with definitions and induction

Theoretical Computer Science

Volumn 232, Issue 1-2, 2000, Pages 91-119

  McDowell, Raymond ^a,c   Miller, Dale ^b  

^a WIDENER UNIVERSITY   (United States)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

^c KALAMAZOO COLLEGE   (United States)

Author keywords

Cut elimination; Definitions; Induction; Logic specifications

Indexed keywords

EID: 0012713211     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(99)00171-1     Document Type: Article

References (29)

1. J.-M. Andreoli, Logic programming with focussing proofs in linear logic, J. Logic Comput. 2(3) (1992) 297-347.
2. J. Chirimar, Proof theoretic approach to specification languages, Ph.D. Thesis, University of Pennsylvania, February 1995.
3. A. Church, A formulation of the simple theory of types, J. Symbolic Logic 5 (1940) 56-68.
4. K.L. Clark, Negation as failure, in: J. Gallaire, J. Minker (Eds.), Logic and Data Bases, Plenum Press, New York, 1978, pp. 293-322.
5. L.H. Eriksson, A finitary version of the calculus of partial inductive definitions, in: L.-H. Eriksson, L. Hallnäs, Schroeder-Heister (Eds.), Proceedings of the Second International Workshop on Extensions to Logic Programming, Vol. 596 of Lecture Notes in Artificial Intelligence, Springer, Berlin, 1991, pp. 89-134.
6. L.-H. Eriksson, Pi: an interactive derivation editor for the calculus of partial inductive definitions, in: A. Bundy (Ed.), Proceedings of the 12th International Conference on Automated Deduction, Vol. 814 of Lecture Notes in Artificial Intelligence, Springer, Berlin, June 1994, pp. 821-825.
7. G. Gentzen, Investigations into logical deductions, 1935, in: M.E. Szabo (Ed.), The Collected Papers of Gerhard Gentzen, North-Holland, Amsterdam, 1969, pp. 68-131.
8. J.-Y. Girard, Une extension de l'interprétation de Gödel à l'analyse, et son application à l'émination des coupures dans l'analyse et la théorie des types, in: J.E. Fenstad (Ed.), Proceedings of the Second Scandinavian Logic Symposium, Vol. 63, Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam, 1971, pp. 63-92.
9. J.-Y. Girard, A fixpoint theorem in linear logic, A message posted on the linear@cs.stanford.edu mailing list, http://www.csl.sri.com/linear/mailing-list-traffic/www/07/mail_3.html, February 1992.
10. J. Hannan, Extended natural semantics, J. Funct. Programm. 3(2) (1993) 123-152.
11. G. Huet, A unification algorithm for typed λ-calculus, Theoret. Comput. Sci. 1 (1975) 27-57.
12. P. Martin-Löf, Hauptsatz for the intuitionistic theory of iterated inductive definitions, in: J.E. Fenstad (Ed.), Proceedings of the Second Scandinavian Logic Symposium, Vol. 63, Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam, 1971, pp. 179-216.
13. R. McDowell, Reasoning in a logic with definitions and induction, Ph.D. Thesis, University of Pennsylvania, December 1997.
14. R. McDowell, D. Miller, A logic for reasoning with higher-order abstract syntax, in: G. Winskel (Ed.), 12th Annual IEEE Symposium on Logic in Computer Science, IEEE Computer Society Press, Silver Spring, MD, June 1997.
15. R. McDowell, D. Miller, C. Palamidessi, Encoding transition systems in sequent calculus: Preliminary report, in: Proceedings of the 1996 Workshop on Linear Logic, volume 3 of Electronic Notes in Theoretical Computer Science. Elsevier, Amsterdam, 1996.
16. R. McDowell, D. Miller, C. Palamidessi, Encoding transition systems in sequent calculus, Theoret. Comput. Sci. Preliminary version appeared as [15], to appear.
17. D. Miller, Forum: a multiple-conclusion specification language, Theoret. Comput. Sci. 165 (1996) 201-232.
18. D. Miller, G. Nadathur, F. Pfenning, A. Scedrov, Uniform proofs as a foundation for logic programming, Ann. Pure Appl. Logic 51 (1991) 125-157.
19. G. Nadathur, D. Miller, Higher-order horn clauses, J. ACM 37(4) October (1990) 777-814.
20. D. Patterson, J. Hennessy, Computer Architecture: A Quantitative Approach, Morgan Kaufman Publishers, Los Altos, CA, 1990.
21. C. Paulin-Mohring, Inductive definitions in the system coq: rules and properties, in: Proceedings of the International Conference on Typed Lambda Calculi and Applications, 1993, pp. 328-345.
22. F. Pfenning, The practice of logical frameworks, in: Hèlène Kirchner (Ed.), Proceedings of the Collaquium on Trees in Algebra and Programming, Vol. 1059, Lecture Notes in Computer Science, April 1996, Springer, Berlin, pp. 119-134.
23. F. Pfenning, C. Elliot, Higher-order abstract syntax, in: Proceedings of the ACM-SIGPLAN Conference on Programming Language Design and Implementation, ACM Press, New York, June 1998, pp. 199-208.
24. P. Schroeder-Heister, Cut-elimination in logics with definitional reflection, in: D. Pearce, H. Wansing (Eds.), Nonclassical Logics and Information Processing, Vol. 619, Lecture Notes in Computer Science, Springer, Berlin, 1992, pp. 146-171.
25. P. Schroeder-Heister, Rules of definitional reflection, in: M. Vardi (Ed.), Proceedings, Eighth Annual IEEE Symposium on Logic in Computer Science, IEEE Computer Society Press, Silver Spring, MD, June 1993, pp. 222-232.
26. C. Schürmann, F. Pfenning, Automated theorem proving in a simple meta-logic for LF, CADE-15, Lindau, Germany, July 1998, pp. 286-300.
27. J. Slaney, Solution to a problem of Ono and Komori, J. Philos. Logic 18 (1989) 103-111.
28. R.F. Stärk, Cut-property and negation as failure. International Journal of Foundations of Computer Science, 5(2) (1994) 129-164.
29. W.W. Tait, Intensional interpretations of functionals of finite type I: Journal of Symbolic Logic 32(2) (1967) 198-212.