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Tableau Calculi for Logic Programs under Answer Set Semantics

Tableau Calculi for Logic Programs under Answer Set Semantics Tableau Calculi for Logic Programs under Answer Set Semantics ¨ MARTIN GEBSER and TORSTEN SCHAUB, Universitat Potsdam We introduce formal proof systems based on tableau methods for analyzing computations in Answer Set Programming (ASP). Our approach furnishes fine-grained instruments for characterizing operations as well as strategies of ASP solvers. The granularity is detailed enough to capture a variety of propagation and choice methods of algorithms used for ASP solving, also incorporating SAT-based and conflict-driven learning approaches to some extent. This provides us with a uniform setting for identifying and comparing fundamental properties of ASP solving approaches. In particular, we investigate their proof complexities and show that the run-times of best-case computations can vary exponentially between different existing ASP solvers. Apart from providing a framework for comparing ASP solving approaches, our characterizations also contribute to their understanding by pinning down the constitutive atomic operations. Furthermore, our framework is flexible enough to integrate new inference patterns, and so to study their relation to existing ones. To this end, we generalize our approach and provide an extensible basis aiming at a modular incorporation of additional language constructs. This is exemplified by augmenting our basic tableau methods with cardinality constraints and disjunctions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

Tableau Calculi for Logic Programs under Answer Set Semantics

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References (109)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2013 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/2480759.2480767
Publisher site
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Abstract

Tableau Calculi for Logic Programs under Answer Set Semantics ¨ MARTIN GEBSER and TORSTEN SCHAUB, Universitat Potsdam We introduce formal proof systems based on tableau methods for analyzing computations in Answer Set Programming (ASP). Our approach furnishes fine-grained instruments for characterizing operations as well as strategies of ASP solvers. The granularity is detailed enough to capture a variety of propagation and choice methods of algorithms used for ASP solving, also incorporating SAT-based and conflict-driven learning approaches to some extent. This provides us with a uniform setting for identifying and comparing fundamental properties of ASP solving approaches. In particular, we investigate their proof complexities and show that the run-times of best-case computations can vary exponentially between different existing ASP solvers. Apart from providing a framework for comparing ASP solving approaches, our characterizations also contribute to their understanding by pinning down the constitutive atomic operations. Furthermore, our framework is flexible enough to integrate new inference patterns, and so to study their relation to existing ones. To this end, we generalize our approach and provide an extensible basis aiming at a modular incorporation of additional language constructs. This is exemplified by augmenting our basic tableau methods with cardinality constraints and disjunctions.

Journal

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

Published: Jun 1, 2013

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