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The finite stages of inductive definitions

from Part II - Contributed Papers

Published online by Cambridge University Press:  23 March 2017

Robert F. Stärk
Affiliation:
University of Pennsylvania
Petr Hájek
Affiliation:
Academy of Sciences of the Czech Republic, Prague
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Gödel '96
Logical Foundations of Mathematics, Computer Science and Physics - Kurt Gödel's Legacy
, pp. 267 - 290
Publisher: Cambridge University Press
Print publication year: 2017

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References

Apt, K. R. and Pedreschi, D.. Reasoning about termination of pure Prolog programs. Information and Computation, 106(1):109–157, 1993.Google Scholar
Blair, H. A.. The recursion-theoretic complexity of the semantics of predicate logic as a programming language. Information and Control, 54:25–47, 1982.Google Scholar
Blair, H. A. and Brown, A. L.. Definite clause programs are canonical (over a suitable domain). Annals of Mathematics and Artificial Intelligence, 1:1–19, 1990.Google Scholar
Blankertz, B. and Weiermann, A.. How to characterize provably total functions by the Buchholz operator method. This volume.
Buchholz, W.. A simplified version of local predicativity. In Aczel, P., Simmons, H., and Wainer, S. S., editors, Proof Theory. A selection of papers from the Leeds Proof Theory Programme 1990, pages 115–147. Cambridge University Press, 1992.
Buchholz, W., Cichon, A., and Weiermann, A.. A uniform approach to fundamental sequences and hierarchies. Mathematical Logic Quarterly, 40:273–286, 1994.Google Scholar
Buchholz, W., Feferman, S., Pohlers, W., and Sieg, W.. Iterated Inductive Definitions and Subsystems of Analysis: Recent Proof-Theoretical Studies, volume 897 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1981.
Cantini, A.. Levels of implication and type free theories of classifications with approximation operator. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 38:107–141, 1992.Google Scholar
Cantini, A.. Proof-theoretic aspects of self-referential truth. Technical report, Department of Philosophy, Università degli Studi di Firenze, 1995.
Clark, K. L.. Negation as failure. In Gallaire, H. and Minker, J., editors, Logic and Data Bases, pages 293–322. Plenum Press, New York, 1978.
Fitting, M.. A Kripke-Kleene semantics for logic programs. J. of Logic Programming, 2:295–312, 1985.Google Scholar
Jäger, G.. Fixed points in Peano arithmetic with ordinals. Annals of Pure and Applied Logic, 60:119–132, 1993.Google Scholar
Jäger, G. and Stärk, R. F.. A proof-theoretic framework for logic programming. In Buss, S. R., editor, Handbook of Proof Theory. To appear.
Kunen, K.. Negation in logic programming. J. of Logic Programming, 4(4):289–308, 1987.Google Scholar
Kunen, K.. Signed data dependencies in logic programs. J. of Logic Programming, 7(3):231–245, 1989.Google Scholar
Mal'cev, A. I.. Axiomatizable classes of locally free algebras of various types. In The Metamathematics of Algebraic Systems, Collected Papers, chapter 23, pages 262–281. North-Holland, Amsterdam, 1971.
Moschovakis, Y. N.. Elementary Induction on Abstract Structures. North-Holland, Amsterdam, 1974.
Pohlers, W.. Proof theory: an introduction, volume 1407 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1989.
Pohlers, W.. A short course in ordinal analysis. In Aczel, P., Simmons, H., and Wainer, S. S., editors, Proof Theory. A selection of papers from the Leeds Proof Theory Programme 1990, pages 26–78. Cambridge University Press, 1992.
Shepherdson, J. C.. Language and equality theory in logic programming. Technical Report PM-88–08, University of Bristol, 1988.
Stärk, R. F.. Input/output dependencies of normal logic programs. J. of Logic and Computation, 4(3):249–262, 1994.Google Scholar
Stärk, R. F.. First-order theories for pure Prolog programs with negation. Archive for Mathematical Logic, 34(2): 113–144, 1995.Google Scholar
Stärk, R. F.. Formal methods for logic programming systems. Technical report, Department of Mathematics, Stanford University, 1995.
Stärk, R. F.. Total correctness of pure Prolog programs: A formal approach. In Dyckhoff, R., Herre, H., and Schroeder-Heister, P., editors, Proceedings of the 5th International Workshop on Extensions of Logic Programming, ELP '96, pages 237–254, Leipzig, Germany, 1996. Springer-Verlag, Lecture Notes in Artificial Intelligence 1050.
van Emden, M. H. and Kowalski, R. A.. The semantics of predicate logic as a programming language. J. of the Association for Computing Machinery, 4(23):733–742, 1976.Google Scholar
Weiermann, A.. How to characterize provably total functions by local predicativity. J. of Symbolic Logic. To appear.

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