First-order Answer Set Programming as Constructive Proof Search. Issue 3 (10th August 2018)

• Record Type: Journal Article
• Authors: SCHUBERT, ALEKSY; URZYCZYN, PAWEŁ
• Editors: Dal Palu, Alessandro; Tarau, Paul
• Is Part Of: Theory and practice of logic programming. Volume 18:Issue 3/4(2018)
• Page Start: 673
• Page End: 690
• Publication Date: 2018-08-10
• Subjects: Answer set programming, -- intuitionistic logic, -- proof terms, -- lambda calculus; Logic programming -- Periodicals; Artificial intelligence -- Computer programs -- Periodicals; Constraint programming (Computer science) -- Periodicals; 005.115
• DOI: 10.1017/S147106841800008X
• Languages: English
• ISSNs: 1471-0684

Abstract

Abstract: 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