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First-order Answer Set Programming as Constructive Proof Search

Published online by Cambridge University Press:  10 August 2018

ALEKSY SCHUBERT  and
PAWEŁ URZYCZYN
ALEKSY SCHUBERT
Affiliation:
University of Warsaw, Poland (e-mail: alx@mimuw.edu.pl, urzy@mimuw.edu.pl)
PAWEŁ URZYCZYN
Affiliation:
University of Warsaw, Poland (e-mail: alx@mimuw.edu.pl, urzy@mimuw.edu.pl)
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Abstract

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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

Keywords

Answer set programmingintuitionistic logicproof termslambda calculus

Information

Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 18 , Special Issue 3-4: 34th International Conference on Logic Programming , July 2018 , pp. 673 - 690
Copyright
Copyright © Cambridge University Press 2018 

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