Extending classical logic with inductive definitions

Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science)

Volumn 1861, Issue , 2000, Pages 703-717

  Denecker, Marc ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

CLASSICAL LOGIC; DEDUCTIVE DATABASE; INDUCTIVE DEFINITIONS; NON-MONOTONIC REASONING;

LOGIC PROGRAMMING;

KNOWLEDGE REPRESENTATION;

EID: 84867778292     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/3-540-44957-4_47     Document Type: Conference Paper

References (32)

1. P. Aczel. An Introduction to Inductive De-nitions. In J. Barwise, editor, Handbook of Mathematical Logic, pages 739-782. North-Holland Publishing Company, 1977.
2. Gianni Amati, Luigia Carlucci Aiello, and Fiora Pirri. De-nability and common-sense reasoning. Artificial Intelligence Journal, 93:1-30, 1997. Abstract of this paper appeared also in Third Symposium on Logical Formalization of Common-sense Reaso ning, Stanford, USA, 96.
3. K.R. Apt and M. Bezem. Acyclic programs. In Proc. of the International Conference on Logic Programming, pages 579-597. MIT press, 1990.
4. R. J. Brachman and H.J. Levesque. Competence in Knowledge Representation. In Proc. of the National Conference on Artificial Intelligence, pages 189-192, 1982.
5. W. Buchholz, S. Feferman, and W. Pohlers W. S ieg. Iterated Inductive De-nitions and Subsystems of Analysis: Recent Proof-Theoretical Studies. Springer-Verlag, Lecture Notes in Mathematics 897, 1981.
6. K.L. Clark. Negation as failure. In H. Gallaire and J. Minker, editors, Logic and Databases, pages 293-322. Plenum Press, 1978.
7. M. Denecker. A Terminological Interpretation of (Abductive) Logic Programming. In V.W. Marek, A. Nerode, and M. Truszczynski, ed itors, International Conference on Logic Programming and Nonmonotonic Reasoning, Lecture notes in Artificial Intelligence 928, pages 15-29. Springer, 1995.
8. M. Denecker, D. Theseider Dupr-e, and K. Van Belleg hem. An inductive de-nition approach to rami-cations. Linköping Electronic Articles in Computer and Information Science, 3(7):1-43, 1998. URL: http://www.ep.liu.se/ea/cis/1998/007/.
9. Marc Deneck er. The well-founded semantics is the principle of inductive de-nition. In J. Dix, L. Fari nas del Cerro, and U. Furbach, editors, Logics in Artificial Intelligence, pages 1-16, Schloss Daghstull, October 12-15 1998. Springer-Verlag, Lecture notes in Artificial Intelligence 1489.
10. Marc Denecker and Bert Van Nu-elen. Experiments for integration CLP and ab-duction. In Krysztof R. Apt, Antonios C. Kakas, Eric Monfroy, and Francesca Ross i, editors, Workshop on Constraints, pages 1-15. ERCIM/COMPULOG, Oc-tober 25-27 1999.
11. S. Feferman. Formal theories for transfinite iterations of generalised inductive de-nitions and some subsystems of analysis. In A. Kino, J. Myhill, and R.E. Vesley, editors, Intuitionism and Proof theory, pages 303-326. North Holland, 1970.
12. M. Fitting. A Kripke-Kleene Semantics for Logic Programs. Journal of Logic Programming, 2(4):295-312, 1985.
13. A. Van Gelder. The Alternating Fixpoint of Logic Programs with Negation. Journal of computer and system sciences, 47:185-221, 1993.
14. M. Gelfond and V. Lifschitz. The stable model semantics for logic programming. In Proc. of the International Joint Conference and Symposium on Logic Programming, pages 1070-1080. IEEE, 1988.
15. M. Gelfond and V. Lifschitz. Classical negation in logic programs and disjunctive databases. New Generation Computing, pages 365-387, 1991.
16. A. C. Kakas, R.A. Kowalski, and F. Toni. Abductive Logic Programming. Journal of Logic and Computation, 2(6):719-770, 1993.
17. V.W. Marek and M. Truszczy-nski. Nonmonotonic Logic Context-Dependent Reasoning . Springer-Verlag, 1993.
18. J. McCarthy Circumscription-A form of nonmonotonic reasoning Artifical Intelligence 13, 27-39, 1980.
19. John McCarthy. Elaboration tolerance. In COMMON SENSE 98, Symposium On Logical Formalizations Of Commonsense Reasoning, January 1998.
20. Y. N. Moschovakis. Elementary Induction on Abstract Structures. North-Holland Publishing Company, Amsterdam-New York, 1974.
21. T.C. Przymusinski. On the semantics of Strati-ed Databases. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming. Morgan Kaufman, 1988.
22. T.C. Przymusinski. Extended Stable Semantics for Normal and Disjunctive Pro-grams. In D.H.D.Warren and P. Szeredi, editors, Proc. of the seventh international conference on logic programming, pages 459-477. MIT press, 1990.
23. T.C. Przymusinski. Well founded semantics coincides with three valued Stable Models. Fundamenta Informaticae, 13:445-463, 1990.
24. H. Reichgelt. Knowledge Representation: an AI Perspecitive. Ablex Publishing Corporation, 1991.
25. R. Reiter. Equality and domain closure in first-order databases. JACM, 27:235-249, 1980.
26. R. Reiter. The Frame Problem in the Situation Calculus: A simple Solution (Some-times) and a Completeness Result for Goal Regression. In V. Lifschitz, editor, Arti-cial Intelligence and Mathematical Theory of Computation: Papers in Honour of John McCarthy, pages 359-380. Academic Press, 1991.
27. R. Reiter. Nonmonotonic Reasoning: Compiled vs Interpreted Theories. Dis-tributed at the conference of Nonmonotonic Reasoning NMR96 as considerations for the panel discussion, 1996.
28. A. Tarski. Lattice-theoretic-xpoint theorem and its applications. Paci-c journal of Mathematics, 5:285-309, 1955.
29. E. Ternovskaia. Inductive De-nability and the Situation Calculus. In Burkhard Freitag, Hendrik Decker, Michael Kifer, and Andrei Voronkov, editors, Transactions and Change in Logic Databases, volume 1472 of LNCS. Springer-Verlag, Berlin, 1998.
30. M. Van Emden and R.A Kowalski. The semantics of Predicate Logic as a Program-ming Language. Journal of the ACM, 4(4):733-742, 1976.
31. A . Van Gelder, K.A. Ross, and J.S. Schlipf. The Well-Founded Semantics for General Logic Programs. Journal of the ACM, 38(3):620-650, 1991.
32. S. Verbaeten, M. Denecker, and D. De S chreye. Compositionality of normal open logic programs. Journal of Logic Programming, 41(3):151-183, March 2000.