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Abstract: The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of non-monotonic reasoning, logic programming and deductive databases, and to show its application for knowledge representation by giving a typology of definitional knowledge. (Update)
Context of citations to this paper: More
...1995) the problem of logic programming under the definition view is that a logic program contains definitions for all predicates. For this reason, one should extend the formalismwith the possibility of leaving certain predicates open. This view is further explored in ##CITE##(Denecker...
...evolutions, using set theory and logic [3] 3 Logical Theories 3. 1 The Language and its Semantics Inductive Definition Logic (ID Logic [7, 8]) is an integration of first order logic and Logic Programming 3, interpreting the logic program as a non monotone inductive definition....
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BibTeX entry: (Update)
Marc Denecker. Extending classical logic with inductive definitions. In J. et al. Lloyd, editor, First International Conference on Computational Logic (CL2000), volume 1861 of Lecture Notes in Artificial Intelligence, pages 703--717, London, July 2000. Springer. http://citeseer.ist.psu.edu/article/denecker00extending.html More
@article{ denecker00extending,
author = "Marc Denecker",
title = "Extending Classical Logic with Inductive Definitions",
journal = "Lecture Notes in Computer Science",
volume = "1861",
pages = "703--??",
year = "2000",
url = "citeseer.ist.psu.edu/article/denecker00extending.html" }
Citations (may not include all citations):858 The stable model semantics for logic programming - Gelfond, Lifschitz - 1988 DBLP
775 Foundations of Databases (context) - Abiteboul, Hull et al. - 1995
759 Negation as failure (context) - Clark - 1978 ACM DBLP
663 Some philosophical problems from the standpoint of artificia.. (context) - McCarthy, Hayes - 1969 ACM
451 Circumscription - a form of nonmonotonic reasoning (context) - McCarthy - 1980
388 The Frame Problem in the Situation Calculus: A simple Soluti.. (context) - Reiter - 1991
234 The Well-Founded Semantics for General Logic Programs - Van Gelder, Ross et al. - 1991 ACM DBLP
212 Abductive Logic Programming - Kakas, Kowalski et al. - 1993 DBLP
174 A Kripke-Kleene Semantics for Logic Programs (context) - Fitting - 1985 DBLP
125 Well founded semantics coincides with three valued Stable Mo.. - Przymusinski
120 Elementary Induction on Abstract Structures (context) - Moschovakis - 1974
115 The Alternating Fixpoint of Logic Programs with Negation (context) - Gelder - 1993 ACM DBLP
98 Extended Stable Semantics for Normal and Disjunctive Program.. (context) - Przymusinski ACM DBLP
97 An Introduction to Inductive Definitions (context) - Aczel - 1977
95 Fixed-point Extensions of First-Order Logic (context) - Gurevich, Shelah - 1986 DBLP
78 Acyclic programs (context) - Apt, Bezem - 1990 ACM DBLP
77 Representing Incomplete Knowledge in Abductive Logic Program.. - Denecker, De Schreye - 1995 ACM DBLP
40 Iterated Inductive Definitions and Subsystems of Analysis: R.. (context) - Buchholz, Feferman et al. - 1981
36 Equality and domain closure in first-order databases (context) - Reiter - 1980 ACM DBLP
26 A Terminological Interpretation (context) - Denecker - 1995
24 Elaboration tolerance - McCarthy - 1998
19 Formal theories for transfinite iterations of generalised in.. (context) - Feferman - 1970
18 The well-founded semantics is the principle of inductive def.. - Denecker - 1998 ACM DBLP
17 Competence in Knowledge Representation (context) - Brachman, Levesque - 1982 DBLP
13 Compositionality of normal open logic programs - Verbaeten, Denecker et al. - 2000 ACM DBLP
6 An inductive definition approach to ramifications - Denecker, Theseider et al. - 1998
5 the semantics of Stratified Databases (context) - Przymusinski - 1988
4 Inductive Definability and the Situation Calculus - Ternovskaia - 1998 ACM DBLP
3 Knowledge Representation: an AI Perspecitive (context) - Reichgelt - 1991
3 Nonmonotonic Reasoning: Compiled vs Interpreted Theories (context) - Reiter - 1996
3 A strong correspondence between description logics and open .. - Van Belleghem, Denecker et al. - 1997 DBLP
2 Definability and commonsense reasoning - Amati, Carlucci et al. - 1997 ACM DBLP
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