Signed data dependencies in logic programs

Kunen, Kenneth

doi:10.1016/0743-1066(89)90022-8

Cited by 148 publications

(50 citation statements)

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“…The notion of a "signing" of a program is due to Kunen (1989). A program P is signed if there is a set S of atoms such that, for every rule r ∈ P ,…”

Section: Signed Programs Are Cautiously Monotonicmentioning

confidence: 99%

Order-consistent programs are cautiously monotonic

Turner

2001

Theory and Practice of Logic Programming

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Some normal logic programs under the answer set (or stable model) semantics lack the appealing property of "cautious monotonicity." That is, augmenting a program with one of its consequences may cause it to lose another of its consequences. The syntactic condition of "order-consistency" was shown by Fages to guarantee existence of an answer set. This note establishes that order-consistent programs are not only consistent, but cautiously monotonic. From this it follows that they are also "cumulative." That is, augmenting an order-consistent program with some of its consequences does not alter its consequences. In fact, as we show, its answer sets remain unchanged.

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“…The notion of a "signing" of a program is due to Kunen (1989). A program P is signed if there is a set S of atoms such that, for every rule r ∈ P ,…”

Section: Signed Programs Are Cautiously Monotonicmentioning

confidence: 99%

Order-consistent programs are cautiously monotonic

Turner

2001

Theory and Practice of Logic Programming

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“…Then, as it is done in [19] to extend [13] to the general constraint case, we consider the Fitting's ordering on Dom Σ interpreted in the following sense: For all partial interpretations A,B ∈ Dom Σ , for each Σ X -constraint c(x) and each Σ-literal (x):…”

Section: Fixpoint Semanticsmentioning

confidence: 99%

A Functorial Framework for Constraint Normal Logic Programming

Lucio

Orejas

Pasarella

et al. 2006

Algebra, Meaning, and Computation

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Abstract. The semantic constructions and results for definite programs do not extend when dealing with negation. The main problem is related to a well-known problem in the area of algebraic specification: if we fix a constraint domain as a given model, its free extension by means of a set of Horn clauses defining a set of new predicates is semicomputable. However, if the language of the extension is richer than Horn clauses its free extension (if it exists) is not necessarily semicomputable. In this paper we present a framework that allows us to deal with these problems in a novel way. This framework is based on two main ideas: a reformulation of the notion of constraint domain and a functorial presentation of our semantics. In particular, the semantics of a logic program P is defined in terms of three functors: (OP P , ALG P , LOG P ) that apply to constraint domains and provide the operational, the least fixpoint and the logical semantics of P, respectively. To be more concrete, the idea is that the application of OP P to a specific constraint solver, provides the operational semantics of P that uses this solver; the application of ALG P to a specific domain, provides the least fixpoint of P over this domain; and, the application of LOG P to a theory of constraints, provides the logic theory associated to P. In this context, we prove that these three functors are in some sense equivalent.

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“…are equivalent [Kunen, 1989]) Table 1 gives an overview of the different completeness results. Note that the query ¢ is always considered to be allowed.…”

Section: Prog P Semantics Completenessmentioning

confidence: 99%