First-order Answer Set Programming as Constructive Proof Search

We propose an interpretation of the first-order answer set programming (FOASP) in terms of intuitionistic proof theory. It is obtained by two polynomial translations between FOASP and the bounded-arity fragment of the Σ1 level of the Mints hierarchy in first-order intuitionistic logic. It follows th...

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Vydáno v:Theory and practice of logic programming Ročník 18; číslo 3-4; s. 673 - 690
Hlavní autoři: SCHUBERT, ALEKSY, URZYCZYN, PAWEŁ
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cambridge, UK Cambridge University Press 01.07.2018
Témata:
Logic programming
Mathematical programming
Original Article
Translations
intuitionistic logic
proof terms
lambda calculus
Answer set programming
ISSN:1471-0684, 1475-3081
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Shrnutí:We propose an interpretation of the first-order answer set programming (FOASP) in terms of intuitionistic proof theory. It is obtained by two polynomial translations between FOASP and the bounded-arity fragment of the Σ1 level of the Mints hierarchy in first-order intuitionistic logic. It follows that Σ1 formulas using predicates of fixed arity (in particular unary) is of the same strength as FOASP. Our construction reveals a close similarity between constructive provability and stable entailment, or equivalently, between the construction of an answer set and an intuitionistic refutation. This paper is under consideration for publication in Theory and Practice of Logic Programming
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1471-0684
1475-3081
DOI:10.1017/S147106841800008X