article

Predicate-calculus-based logics for modeling and solving search problems

Authors:

Miroslaw TruszczyńskiAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 7, Issue 1

Pages 38 - 83

https://doi.org/10.1145/1119439.1119441

Published: 01 January 2006 Publication History

Abstract

The answer-set programming (ASP) paradigm is a way of using logic to solve search problems. Given a search problem, to solve it one designs a logic theory so that models of this theory represent problem solutions. To compute a solution to the problem, one computes a model of the theory. Several answer-set programming formalisms have been developed on the basis of logic programming with the semantics of answer sets. In this article we show that predicate logic also gives rise to effective implementations of the ASP paradigm, similar in spirit to logic programming with the answer-set semantics and with a similar scope of applicability. Specifically, we propose two logics based on predicate calculus as formalisms for encoding search problems. We show that the expressive power of these logics is given by the class NPMV. We demonstrate their use in programming and discuss computational approaches to model finding. To address this latter issue, we follow a two-pronged approach. On the one hand, we show that the problem can be reduced to that of computing models of propositional theories and, more generally, of collections of pseudo-Boolean constraints. Consequently, programs (solvers) developed in the areas of propositional and pseudo-Boolean satisfiability can be used to compute models of theories in our logics. On the other hand, we develop native solvers designed specifically to exploit features of our formalisms. We present experimental results demonstrating the computational effectiveness of the overall approach.

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Newton SAlemdar MGale JHernandez DEdwards DRyan MHelms MUsselman M(2023)Student-Centered Computing: Teacher Experiences in a New Introductory Computer Science CurriculumACM Transactions on Computing Education10.1145/361410123:4(1-26)Online publication date: 8-Nov-2023
De Cat BBogaerts BBruynooghe MJanssens GDenecker M(2018)Predicate logic as a modeling languageDeclarative Logic Programming10.1145/3191315.3191321(279-323)Online publication date: 1-Sep-2018
(2018)Declarative Logic ProgrammingundefinedOnline publication date: 1-Sep-2018
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Index Terms

Predicate-calculus-based logics for modeling and solving search problems
1. Theory of computation
  1. Logic
    1. Constraint and logic programming

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Published In

cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 7, Issue 1

January 2006

198 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/1119439

Issue’s Table of Contents

Copyright © 2006 ACM.

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Publication History

Published: 01 January 2006

Published in TOCL Volume 7, Issue 1

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(2018)Declarative Logic ProgrammingundefinedOnline publication date: 1-Sep-2018
Lierler Y(2017)What is answer set programming to propositional satisfiabilityConstraints10.1007/s10601-016-9257-722:3(307-337)Online publication date: 1-Jul-2017
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Janhunen TNiemelä I(2016)The Answer Set Programming ParadigmAI Magazine10.1609/aimag.v37i3.267137:3(13-24)Online publication date: 1-Sep-2016
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Mikitiuk ATruszczynski M(2013)Implementing Informal Semantics of ASPProceedings of the 12th International Conference on Logic Programming and Nonmonotonic Reasoning - Volume 814810.1007/978-3-642-40564-8_43(433-438)Online publication date: 15-Sep-2013
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