ELP 1993: Extensions of Logic Programming pp 333-347 | Cite as
Definitional reflection and the completion
Conference paper
First Online:
Abstract
The logic of definitional reflection is extended with a theory of free equality. Based on this equality theory a sequent-style notion of the completion of a definition is motivated. Definitional reflection with free equality turns out to be equivalent to the completion in this sense.
Keywords
Logic Programming Intuitionistic Logic Equality Theory Substructural Logic Free Equality
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Download
to read the full conference paper text
References
- 1.Aronsson, M., GCLA: The Design, Use, and Implementation of a Program Development System. Ph.D. thesis, University of Stockholm 1993.Google Scholar
- 2.Aronsson, M., Eriksson, L.-H., Gäredal, A., Hallnäs, L. & Olin, P. The programming language GCLA: A definitional approach to logic programming. New Generation Computing, 4 (1990), 381–404.Google Scholar
- 3.Clark, K. L. Negation as failure. In: Gallaire, H. & Minker, J. (Eds.), Logic and Data Bases, New York 1978, 293–322.Google Scholar
- 4.Coquand, T. Pattern matching with dependent types. In: Workshop on Logical Frameworks, Båstad 1992, Proceedings, available by ftp from ftp.cs.chalmers.se as /pub/cs/reports/baastad.92/procSS.Google Scholar
- 5.Eriksson, L.-H. A finitary version of the calculus of partial inductive definitions. In: Eriksson, L.-H., Hallnäs, L. & Schroeder-Heister, P. (Eds.), Extensions of Logic Programming. Second International Workshop, ELP-91, Stockholm, January 1991, Proceedings. Springer LNCS, Vol. 596, Berlin 1992, 89–134.Google Scholar
- 6.Eriksson, L.-H. Finitary Partial Inductive Definitions and General Logic. Ph.D. thesis, Royal Institute of Technology, Stockholm 1993.Google Scholar
- 7.Girard, J.-Y. Linear logic. Theoretical Computer Science, 50 (1987), 1–102.Google Scholar
- 8.Girard, J.-Y. A fixpoint theorem for linear logic. In: P. Lincoln (Ed.), Linear Logic Mailing List, linear@cs.stanford.edu, 5 February 1992 (Reply: ibid., 19 February 1992).Google Scholar
- 9.Hallnäs, L. & Schroeder-Heister, P. A proof-theoretic approach to logic programming. I. Clauses as rules. Journal of Logic and Computation, 1 (1990), 261–283; II. Programs as definitions, ibid. 1 (1991), 635–660. Originally published as SICS Research Report 88005, 1988.Google Scholar
- 10.Jäger, G. & Stärk, R. F. A proof-theoretic framework for logic programming. In: S. Buss (Ed.), Handbook of Proof Theory (forthcoming).Google Scholar
- 11.Kanger, S. A simplified proof method for elementary logic. In: Braffort, P. & Hirschberg, D. (Eds.), Computer Programming and Formal Systems, Amsterdam 1963, 87–94.Google Scholar
- 12.Kreuger, P. Axioms in definitional calculi. This volume.Google Scholar
- 13.Lifshits, V.A. Normal form for deductions in predicate calculus with equality and functional symbols. In: Slisenko, A.O. (Ed.), Studies in Constructive Mathematics and Mathematical Logic I, New York 1969, 21–23.Google Scholar
- 14.Martelli, A. & Montanari, U. An efficient unification algorithm. ACM Transactions on Programming Languages and Systems, 4 (1982), 259–282.Google Scholar
- 15.Richter, M.M. Logikkalküle. Teubner, Stuttgart 1978.Google Scholar
- 16.Sahlin, D., Franzén, T. & Haridi, S. An intuitionistic predicate logic theorem prover. Journal of Logic and Computation 2 (1992), 619–656.Google Scholar
- 17.Schroeder-Heister, P. Cut-elimination in logics with definitional reflection. In: D. Pearce & H. Wansing (Eds.), Nonclassical Logics and Information Processing. International Workshop, Berlin 1990, Proceedings. Springer LNCS, Vol. 619, Berlin 1992, 146–171.Google Scholar
- 18.Schroeder-Heister, P. Rules of definitional reflection. In: 8th Annual IEEE Symposium on Logic in Computer Science (Montreal 1993). IEEE Computer Society Press, Los Alamitos 1993, 222–232.Google Scholar
- 19.Schroeder-Heister, P. Cut elimination for logics with definitional reflection and restricted initial sequents. Manuscript, available by ftp as /pub/LS/resini from gopher.informatik.uni-tuebingen.de.Google Scholar
- 20.Snyder, W. A Proof Theory for General Unification. Birkhäuser, Basel 1991.Google Scholar
- 21.Stärk, R. F. Cut-property and negation as failure. Technical report, Institut für Informatik und angewandte Mathematik, Universität Bern, 1992 (available by ftp as /pub/staerk/cut from ftp.cis.uni-muenchen.de).Google Scholar
Copyright information
© Springer-Verlag Berlin Heidelberg 1994