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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Published in:Theory and practice of logic programming Vol. 18; no. 3-4; pp. 673 - 690
Main Authors: SCHUBERT, ALEKSY, URZYCZYN, PAWEŁ
Format: Journal Article
Language:English
Published: Cambridge, UK Cambridge University Press 01.07.2018
Subjects:
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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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
AbstractList 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
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 Σ 1 level of the Mints hierarchy in first-order intuitionistic logic. It follows that Σ 1 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
Author SCHUBERT, ALEKSY
URZYCZYN, PAWEŁ
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10.1145/502807.502810
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10.1145/308386.308446
10.1145/2043174.2043195
10.1007/s00165-016-0403-1
10.1007/s10472-006-9028-z
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Original Article
Translations
Title First-order Answer Set Programming as Constructive Proof Search
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