Finite-Choice Logic Programming
Logic programming, as exemplified by datalog, defines the meaning of a program as its unique smallest model: the deductive closure of its inference rules. However, many problems call for an enumeration of models that vary along some set of choices while maintaining structural and logical constraints...
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| Published in | Proceedings of ACM on programming languages Vol. 9; no. POPL; pp. 362 - 390 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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New York, NY, USA
ACM
07.01.2025
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| ISSN | 2475-1421 2475-1421 |
| DOI | 10.1145/3704849 |
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| Abstract | Logic programming, as exemplified by datalog, defines the meaning of a program as its unique smallest model: the deductive closure of its inference rules. However, many problems call for an enumeration of models that vary along some set of choices while maintaining structural and logical constraints—there is no single canonical model. The notion of stable models for logic programs with negation has successfully captured programmer intuition about the set of valid solutions for such problems, giving rise to a family of programming languages and associated solvers known as answer set programming. Unfortunately, the definition of a stable model is frustratingly indirect, especially in the presence of rules containing free variables. We propose a new formalism, finite-choice logic programming, that uses choice, not negation, to admit multiple solutions. Finite-choice logic programming contains all the expressive power of the stable model semantics, gives meaning to a new and useful class of programs, and enjoys a least-fixed-point interpretation over a novel domain. We present an algorithm for exploring the solution space and prove it correct with respect to our semantics. Our implementation, the Dusa logic programming language, has performance that compares favorably with state-of-the-art answer set solvers and exhibits more predictable scaling with problem size. |
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| AbstractList | Logic programming, as exemplified by datalog, defines the meaning of a program as its unique smallest model: the deductive closure of its inference rules. However, many problems call for an enumeration of models that vary along some set of choices while maintaining structural and logical constraints—there is no single canonical model. The notion of stable models for logic programs with negation has successfully captured programmer intuition about the set of valid solutions for such problems, giving rise to a family of programming languages and associated solvers known as answer set programming. Unfortunately, the definition of a stable model is frustratingly indirect, especially in the presence of rules containing free variables. We propose a new formalism, finite-choice logic programming, that uses choice, not negation, to admit multiple solutions. Finite-choice logic programming contains all the expressive power of the stable model semantics, gives meaning to a new and useful class of programs, and enjoys a least-fixed-point interpretation over a novel domain. We present an algorithm for exploring the solution space and prove it correct with respect to our semantics. Our implementation, the Dusa logic programming language, has performance that compares favorably with state-of-the-art answer set solvers and exhibits more predictable scaling with problem size. |
| ArticleNumber | 13 |
| Author | Martens, Chris Arntzenius, Michael Simmons, Robert J. |
| Author_xml | – sequence: 1 givenname: Chris orcidid: 0000-0002-7026-0348 surname: Martens fullname: Martens, Chris email: c.martens@northeastern.edu organization: Northeastern University, Boston, USA – sequence: 2 givenname: Robert J. orcidid: 0000-0003-2420-3067 surname: Simmons fullname: Simmons, Robert J. email: robsimmons@gmail.com organization: Unaffiliated, Boston, USA – sequence: 3 givenname: Michael orcidid: 0009-0002-0417-5636 surname: Arntzenius fullname: Arntzenius, Michael email: daekharel@gmail.com organization: Unaffiliated, Hamilton Township, USA |
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| SubjectTerms | Computing methodologies Constraint and logic languages Constraint and logic programming Control structures Database query languages (principles) Denotational semantics Logic and databases Logic programming and answer set programming Nonmonotonic, default reasoning and belief revision Software and its engineering Theory of computation |
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| Title | Finite-Choice Logic Programming |
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