External Behavior of a Logic Program and Verification of Refactoring

FANDINNO, JORGE; HANSEN, ZACHARY; LIERLER, YULIYA; LIFSCHITZ, VLADIMIR; TEMPLE, NATHAN

doi:10.1017/s1471068423000200

Cited by 4 publications

References 15 publications

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Synthesizing Strongly Equivalent Logic Programs: Beth Definability for Answer Set Programs via Craig Interpolation in First-Order Logic

Heuer,

Wernhard

2024

Lecture Notes in Computer Science

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We show a projective Beth definability theorem for logic programs under the stable model semantics: For given programs P and Q and vocabulary V (set of predicates) the existence of a program R in V such that $$P \cup R$$ P ∪ R and $$P \cup Q$$ P ∪ Q are strongly equivalent can be expressed as a first-order entailment. Moreover, our result is effective: A program R can be constructed from a Craig interpolant for this entailment, using a known first-order encoding for testing strong equivalence, which we apply in reverse to extract programs from formulas. As a further perspective, this allows transforming logic programs via transforming their first-order encodings. In a prototypical implementation, the Craig interpolation is performed by first-order provers based on clausal tableaux or resolution calculi. Our work shows how definability and interpolation, which underlie modern logic-based approaches to advanced tasks in knowledge representation, transfer to answer set programming.

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Synthesizing Strongly Equivalent Logic Programs: Beth Definability for Answer Set Programs via Craig Interpolation in First-Order Logic

Heuer,

Wernhard

2024

Lecture Notes in Computer Science

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Deductive Systems for Logic Programs with Counting: Preliminary Report

Fandinno,

Lifschitz

2024

Lecture Notes in Computer Science

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Locally Tight Programs

FANDINNO,

LIFSCHITZ,

TEMPLE

2024

Theory and Practice of Logic Programming

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Program completion is a translation from the language of logic programs into the language of first-order theories. Its original definition has been extended to programs that include integer arithmetic, accept input, and distinguish between output predicates and auxiliary predicates. For tight programs, that generalization of completion is known to match the stable model semantics, which is the basis of answer set programming. We show that the tightness condition in this theorem can be replaced by a less restrictive “local tightness” requirement. From this fact we conclude that the proof assistant anthem-p2p can be used to verify equivalence between locally tight programs.

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External Behavior of a Logic Program and Verification of Refactoring

Cited by 4 publications

References 15 publications

Synthesizing Strongly Equivalent Logic Programs: Beth Definability for Answer Set Programs via Craig Interpolation in First-Order Logic

Synthesizing Strongly Equivalent Logic Programs: Beth Definability for Answer Set Programs via Craig Interpolation in First-Order Logic

Deductive Systems for Logic Programs with Counting: Preliminary Report

Locally Tight Programs

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