TY - CHAP

T1 - An equational approach to logic programming

AU - Gabbay, Dov M.

PY - 2012

Y1 - 2012

N2 - In this paper we follow ideas from our Equational approach to argumentation, [3,4], and develop the Equational approach to Logic programs. We regard a logic program P as a template for generating a system of equations Eq(P), where the literals are considered variables ranging over the unit interval [0, 1], and where the solutions to the equations give us the logical meaning of the logic program. We show soundness of the equational approach with respect to traditional Prolog computation and with respect to answer set programming. We prove completeness of answer sets for P with respect to {0,1} solutions of Eq(P) for programs with only negated atoms in the body of clauses. We offer equational semantics for logic programs with negation as failure in the spirit of Clark's completion.

AB - In this paper we follow ideas from our Equational approach to argumentation, [3,4], and develop the Equational approach to Logic programs. We regard a logic program P as a template for generating a system of equations Eq(P), where the literals are considered variables ranging over the unit interval [0, 1], and where the solutions to the equations give us the logical meaning of the logic program. We show soundness of the equational approach with respect to traditional Prolog computation and with respect to answer set programming. We prove completeness of answer sets for P with respect to {0,1} solutions of Eq(P) for programs with only negated atoms in the body of clauses. We offer equational semantics for logic programs with negation as failure in the spirit of Clark's completion.

UR - http://www.scopus.com/inward/record.url?scp=84864257719&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-30743-0_19

DO - 10.1007/978-3-642-30743-0_19

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AN - SCOPUS:84864257719

SN - 9783642307423

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 279

EP - 295

BT - Correct Reasoning

A2 - Esra, Erdem

A2 - Joohyung, Lee

A2 - Yuliya, Lierler

A2 - David, Pearce

ER -