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H. Ebbinghaus, J. Flum, W. Thomas (1985)
Mathematical logic
T. Janhunen (2004)
Representing Normal Programs with Clauses
Francesco Calimeri, Giovambattista Ianni, F. Ricca, Mario Alviano, Annamaria Bria, Gelsomina Catalano, Susanna Cozza, Wolfgang Faber, Onofrio Febbraro, N. Leone, M. Manna, Alessandra Martello, Claudio Panetta, S. Perri, Kristian Reale, M. Santoro, M. Sirianni, G. Terracina, P. Veltri (2011)
The Third Answer Set Programming Competition: Preliminary Report of the System Competition Track
P. Hill, D. Warren (2009)
Logic programming : 25th International Conference, ICLP 2009, Pasadena, CA, USA, July 14-17, 2009 : proceedings
H. Vlaeminck, Johan Wittocx, Joost Vennekens, M. Denecker, M. Bruynooghe (2010)
An Approximative Inference Method for Solving THERE EXISTS FOR ALL SO Satisfiability Problems
A. Freiburg (2012)
Principles of Knowledge Representation and Reasoning
K. Apt (1998)
The Essence of Constraint PropagationTheor. Comput. Sci., 221
M. Gebser, M. Ostrowski, Torsten Schaub (2009)
Constraint Answer Set Solving
M. Denecker, E. Ternovska (2008)
A logic of nonmonotone inductive definitionsACM Trans. Comput. Log., 9
Nick Calus, Joost Vennekens (2011)
A Java API for a knowledge base system
H. Vlaeminck, Joost Vennekens, M. Denecker, M. Bruynooghe (2012)
An approximative inference method for solving ∃∀SO satisfiability problemsJ. Artif. Intell. Res., 45
S. Kleene, M. Beeson (1952)
Introduction to Metamathematics
N. Leone, G. Pfeifer, Wolfgang Faber, Thomas Eiter, G. Gottlob, S. Perri, Francesco Scarcello (2002)
The DLV system for knowledge representation and reasoningACM Trans. Comput. Log., 7
M. Bruynooghe (1991)
A Practical Framework for the Abstract Interpretation of Logic ProgramsJ. Log. Program., 10
Jeffrey Uuman (1989)
Principles of database and knowledge- base systems
Paul Bell (2007)
A Note on the Emptiness of Semigroup IntersectionsFundam. Informaticae, 79
K. Marriott, N. Nethercote, R. Rafeh, Peter Stuckey, M. Banda, M. Wallace (2008)
The Design of the Zinc Modelling LanguageConstraints, 13
K. Apt, V. Marek, M. Truszczynski, D. Warren (2011)
The Logic Programming Paradigm: A 25-Year Perspective
M. Mariën, R. Mitra, M. Denecker, M. Bruynooghe (2005)
Satisfiability Checking for PC(ID)
K. Apt (1999)
Some Remarks on Boolean Constraint PropagationArXiv, cs.AI/0003080
G. Tseitin (1983)
On the Complexity of Derivation in Propositional Calculus
N. Belnap (1977)
A Useful Four-Valued Logic
(1990)
8th National Conference on Artificial Intelligence Proceedings. AAAI
Ronald Fagin (1974)
Generalized first-order spectra, and polynomial. time recognizable sets
Artif. Intell
Alan Frisch, Warwick Harvey, Christopher Jefferson, B. Hernández, Ian Miguel (2007)
Essence: A constraint language for specifying combinatorial problemsConstraints, 13
J. Goubault-Larrecq (1995)
A BDD-Based Simplification and Skolemization ProcedureLog. J. IGPL, 3
C. Forgy (1979)
On the efficient implementation of production systems.
Johan Wittocx, M. Denecker, M. Bruynooghe (2010)
Constraint Propagation for Extended First-Order LogicArXiv, abs/1008.2121
M. Stickel (1986)
A prolog technology theorem prover: Implementation by an extended prolog compilerJournal of Automated Reasoning, 4
H. Vlaeminck, Joost Vennekens, M. Denecker (2009)
A logical framework for configuration software
D. Jackson (2002)
Alloy: a lightweight object modelling notationACM Trans. Softw. Eng. Methodol., 11
M. Leuschel (1997)
Advanced Techniques for Logic Program SpecialisationAI Commun., 10
(2009)
Model generation for ID-logic
P. Weert (2010)
Efficient Lazy Evaluation of Rule-Based ProgramsIEEE Transactions on Knowledge and Data Engineering, 22
S. Feferman (1984)
Toward useful type-free theories. IJournal of Symbolic Logic, 49
V. Mellarkod, M. Gelfond, Yuanlin Zhang (2008)
Integrating answer set programming and constraint logic programmingAnnals of Mathematics and Artificial Intelligence, 53
Alvaro Cortés-Calabuig, M. Denecker, O. Arieli, M. Bruynooghe (2008)
Accuracy and Efficiency of Fixpoint Methods for Approximate Query Answering in Locally Complete Databases
Daniel Miranker, D. Brant, Bernie Lofaso, D. Gadbois (1990)
On the Performance of Lazy Matching in Production Systems
Amir Aavani, Xiongnan Wu, S. Tasharrofi, E. Ternovska, D. Mitchell (2012)
Enfragmo: A System for Modelling and Solving Search Problems with Logic
Johan Wittocx, M. Mariën, M. Denecker (2008)
The IDP system: A model expansion system for an extension of classical logic
M. Denecker, Joost Vennekens, Stephen Bond, M. Gebser, M. Truszczynski (2009)
The Second Answer Set Programming Competition
E. Torlak, D. Jackson (2007)
Kodkod: A Relational Model Finder
P. Simons, I. Niemelä, T. Soininen (2000)
Extending and implementing the stable model semanticsArtif. Intell., 138
G. Grahne, A. Mendelzon (1999)
Tableau Techniques for Querying Information Sources through Global Schemas
H. Enderton (1972)
A mathematical introduction to logic
Johan Wittocx, M. Mariën, M. Denecker (2008)
Grounding with Bounds
Alvaro Cortés-Calabuig, M. Denecker, O. Arieli, M. Bruynooghe (2006)
Representation of Partial Knowledge and Query Answering in Locally Complete Databases
L. Libkin (2004)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Wolfgang Faber, G. Pfeifer, N. Leone, Tina Dell'Armi, Giuseppe Ielpa (2008)
Design and implementation of aggregate functions in the DLV system*Theory and Practice of Logic Programming, 8
E. Gurari (1989)
Introduction to the theory of computation
M. Denecker (1998)
The Well-Founded Semantics Is the Principle of Inductive Definition
J. Ullman (1988)
Principles of database and knowledge-base systems, Vol. I, 14
A. Silva, V. Costa (2006)
The Design of the YAP Compiler: An Optimizing Compiler for Logic Programming LanguagesJ. Univers. Comput. Sci., 12
A. Gelder, K. Ross, J. Schlipf (1991)
The well-founded semantics for general logic programsJ. ACM, 38
Pashootan Vaezipoor, D. Mitchell, M. Mariën (2011)
Lifted Unit Propagation for Effective GroundingArXiv, abs/1109.1317
A. Morales, P. Tu, Tran Son (2007)
An Extension to Conformant Planning Using Logic Programming
Article 17, Publication date: August 2013
(2013)
ACM Transactions on Computational Logic
E. Grädel, Phokion Kolaitis, L. Libkin, maarten marx, J. Spencer, Moshe Vardi, Y. Venema, S. Weinstein (2007)
Finite Model Theory and Its Applications
Johan Wittocx, M. Mariën, M. Denecker (2010)
Grounding FO and FO(ID) with BoundsJ. Artif. Intell. Res., 38
M. Denecker, Joost Vennekens (2007)
Well-Founded Semantics and the Algebraic Theory of Non-monotone Inductive Definitions
David McAllester (1990)
Truth Maintenance
E. Ternovska, D. Mitchell (2009)
Declarative Programming of Search Problems with Built-in Arithmetic
R. Nieuwenhuis, Albert Oliveras, C. Tinelli (2006)
Solving SAT and SAT Modulo Theories: From an abstract Davis--Putnam--Logemann--Loveland procedure to DPLL(T)J. ACM, 53
Alvaro Cortés-Calabuig, M. Denecker, O. Arieli, M. Bruynooghe (2007)
Approximate Query Answering in Locally Closed Databases
I. Niemelä, P. Simons, T. Syrjänen (2000)
Smodels: A System for Answer Set ProgrammingArXiv, cs.AI/0003033
A. Pettorossi, M. Proietti (1994)
Transformation of Logic Programs
D. Mitchell, E. Ternovska (2005)
A Framework for Representing and Solving NP Search Problems
M. Gelfond, V. Lifschitz (1991)
Classical negation in logic programs and disjunctive databasesNew Generation Computing, 9
Chitta Baral (2003)
Knowledge Representation, Reasoning and Declarative Problem Solving
Wolfgang Faber, G. Pfeifer, Nicola Leone (2011)
Semantics and complexity of recursive aggregates in answer set programmingArtif. Intell., 175
I. Niemelä (1999)
Logic programs with stable model semantics as a constraint programming paradigmAnnals of Mathematics and Artificial Intelligence, 25
T. Swift (2009)
An Engine for Computing Well-Founded Models
Nikolay Pelov, E. Ternovska (2005)
Reducing Inductive Definitions to Propositional Satisfiability
Pascal Hentenryck (1999)
The OPL optimization programming language
S. Perri, Francesco Scarcello, Gelsomina Catalano, N. Leone (2007)
Enhancing DLV instantiator by backjumping techniquesAnnals of Mathematics and Artificial Intelligence, 51
P. Hou, Broes Cat, M. Denecker (2010)
FO(FD): Extending classical logic with rule-based fixpoint definitionsTheory and Practice of Logic Programming, 10
G. Brewka, J. Lang (2008)
Principles of Knowledge Representation and Reasoning: Proceedings of the 11th International Conference (KR 2008)
ACKNOWLEDGMENTS This research was supported by projects G.0357.06 and G.0489.10 of Research Foundation -Flanders (FWO-Vlaanderen) and by GOA/08/008
A. Doctoral (2010)
TECHNIQUES FOR REASONING IN FO(ID) AND FIXPOINT LOGIC
Johan Wittocx, M. Mariën, M. Denecker (2008)
Approximate Reasoning in First-Order Logic Theories
L. Libkin (2004)
Elements of Finite Model Theory
M. Denecker (2000)
Extending Classical Logic with Inductive DefinitionsArXiv, cs.LO/0003019
Nikolay Pelov, M. Denecker, M. Bruynooghe (2005)
Well-founded and stable semantics of logic programs with aggregatesTheory and Practice of Logic Programming, 7
Johan Wittocx, H. Vlaeminck, M. Denecker (2009)
Debugging for Model Expansion
(1990)
8th National Conference on Artificial Intelligence, Boston, Massachusetts, July 29 - August 3, 1990, Proceedings
V. Marek, M. Truszczynski (1998)
Stable models and an alternative logic programming paradigm
Jesús Aranda, G. Assayag, C. Olarte, Jorge Pérez, C. Rueda, Mauricio Toro, F. Valencia (2009)
An Overview of FORCES: An INRIA Project on Declarative Formalisms for Emergent Systems
D. Mitchell, E. Ternovska (2008)
Expressive power and abstraction in EssenceConstraints, 13
The case where ϕ is of the form ∀x∀z (P (x, z) ⇔ z ≤ f({y | L[x, y]})) is analo- gous
D. East, M. Truszczynski (2001)
Propositional Satisfiability in Answer-Set Programming
M. Gebser, B. Kaufmann, A. Neumann, Torsten Schaub (2007)
clasp : A Conflict-Driven Answer Set Solver
Chitta Baral, G. Brewka, J. Schlipf (2007)
Logic programming and nonmonotonic reasoning : 9th International Conference, LPNMR 2007, Tempe, AZ, USA, May 15-17, 2007 : proceedings
E. Grädel, Phokion Kolaitis, L. Libkin, M. Marx, J. Spencer, Moshe Vardi, Y. Venema, S. Weinstein (2005)
Finite Model Theory and Its Applications (Texts in Theoretical Computer Science. An EATCS Series)
K. Apt (2003)
Principles of constraint programming
M. Denecker, Alvaro Cortés-Calabuig, M. Bruynooghe, O. Arieli (2010)
Towards a logical reconstruction of a theory for locally closed databasesACM Trans. Database Syst., 35
M. Denecker, Joost Vennekens (2008)
Building a Knowledge Base System for an Integration of Logic Programming and Classical Logic
S. Abiteboul, V. Vianu (1991)
Datalog Extensions for Database Queries and UpdatesJ. Comput. Syst. Sci., 43
C. Forgy (1982)
Rete: A Fast Algorithm for the Many Patterns/Many Objects Match ProblemArtif. Intell., 19
Joost Vennekens, Johan Wittocx, M. Mariën, M. Denecker (2007)
Predicate Introduction for Logics with a Fixpoint Semantics. Part I: Logic ProgrammingFundam. Informaticae, 79
M. Denecker, E. Ternovska (2004)
Inductive situation calculusArtif. Intell., 171
Johan Wittocx (2010)
Finite domain and symbolic inference methods for extensions of first-order logicAI Commun., 24
17 Constraint Propagation for First-Order Logic and Inductive Definitions JOHAN WITTOCX, MARC DENECKER, and MAURICE BRUYNOOGHE, KU Leuven In Constraint Programming, constraint propagation is a basic component of constraint satisfaction solvers. Here we study constraint propagation as a basic form of inference in the context of first-order logic (FO) and extensions with inductive definitions (FO(ID)) and aggregates (FO(AGG)). In a first, semantic approach, a theory of propagators and constraint propagation is developed for theories in the context of three-valued interpretations. We present an algorithm with polynomial-time data complexity. We show that constraint propagation in this manner can be represented by a datalog program. In a second, symbolic approach, the semantic algorithm is lifted to a constraint propagation algorithm in symbolic structures, symbolic representations of classes of structures. The third part of the article is an overview of existing and potential applications of constraint propagation for model generation, grounding, interactive search problems, approximate methods for SO problems, and approximate query answering in incomplete databases. Categories and Subject Descriptors: I.2.4 [Artificial Intelligence]: Knowledge Representation Formalisms and Methods--Predicate Logic; F.4.1 [Mathematical Logic and Formal Languages]: Mathematical Logic--Logic and Constraint Programming General Terms: Algorithms, Theory Additional Key Words and Phrases: Aggregates, constraint
ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery
Published: Aug 1, 2013
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