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Constraint Propagation for First-Order Logic and Inductive Definitions

Constraint Propagation for First-Order Logic and Inductive Definitions 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

Constraint Propagation for First-Order Logic and Inductive Definitions

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References (103)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2013 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/2499937.2499938
Publisher site
See Article on Publisher Site

Abstract

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

Journal

ACM Transactions on Computational Logic (TOCL)Association for Computing Machinery

Published: Aug 1, 2013

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