Quasi-Metrics and the Semantics of Logic Programs

Seda, Anthony Karel

doi:10.3233/fi-1997-291205

Cited by 38 publications

(17 citation statements)

References 13 publications

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“…Other questions can be posed, and indeed all are under investigation and will be considered elsewhere. Thus, we regard this paper as a continuation of a programme of work, begun in [17,18], in which semantical questions within declarative programming are investigated using the tools of domain theory.…”

Section: Discussionmentioning

confidence: 99%

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Multivalued Mappings, Fixed-Point Theorems and Disjunctive Databases

Hitzler

Seda

1999

Electronic Workshops in Computing

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In this paper, we discuss the semantics of disjunctive programs and databases and show how multivalued mappings and their fixed points arise naturally within this context. A number of fixed-point theorems for multivalued mappings are considered, some of which are already known and some of which are new. The notion of a normal derivative of a disjunctive program is introduced. Normal derivatives are normal logic programs which are determined by the disjunctive program. Thus, the well-known single-step operator associated with a normal derivative is single-valued, and its fixed points can be found by well-established means. It is shown how fixed points of the multivalued mapping determined by a disjunctive program relate to the fixed points of the single-step operators coming from its normal derivatives. This procedure has potential for simplifying the construction of models of disjunctive databases, and this point is discussed.Most of the results for multivalued mappings rest on corresponding, known results concerning fixed points of single-valued mappings. Since the latter results are frequently referred to, they have been collected together for convenience in a survey which should be of independent interest as well as being preparatory for the later results. Finally, a number of problems and issues raised by this work are discussed. * The first named author acknowledges financial support under grant SC/98/621 from Enterprise Ireland.3rd Irish Workshop on Formal Methods (IWFM-99).

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Section: Discussionmentioning

confidence: 99%

“…the partial order approach and the metric approach. The same thing was done in [18] for logic programs, again using Theorem 2.15.…”

Section: Theorem (Rutten-smyth)mentioning

confidence: 99%

Multivalued Mappings, Fixed-Point Theorems and Disjunctive Databases

Hitzler

Seda

1999

Electronic Workshops in Computing

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“…This cone has n facets L ii , 2 n 2 facets M ij,i and 3 n 3 facets T r ij,k . Partial metrics were introduced by Matthews in [Ma92] for treatment of partially defined objects in Computer Science; see also [Ma08,Hi01,Se97]. The cone PMET n was considered in [DeDe10].…”

Section: Convex Cones Under Considerationmentioning

confidence: 99%

Cones of Weighted and Partial Metrics

Deza

Deza²,

Vidali

2011

Proceedings of the International Conference on Algebra 2010

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A partial semimetric on V n = {1, . . . , n} is a function f = ((f ij )) :We describe the cones of weak and strong partial semimetrics via corresponding weighted semimetrics and list their 0, 1-valued elements, identifying when they belong to extreme rays. We consider also related cones, including those of partial hypermetrics, weighted hypermetrics, 1 -quasi semimetrics and weighted/partial cuts.

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“…The application of metric techniques is being extended in several directions. Seda, by using quasi-metric spaces, shows how both the lattice-theoretic and the metric approaches can be combined into a single treatment [35]. Khamsi, Kreinovich and Misane [21] have shown that more powerful metric fixed point theorems also have natural applications here.…”

Section: Definition 33mentioning

confidence: 99%

Fixpoint semantics for logic programming a survey

Fitting

2002

Theoretical Computer Science

174

168

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The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and many-valued logic, lattice theory, game theory, and topology. One source of this richness is the inherent non-monotonicity of its negation, something that does not have close parallels with the machinery of other programming paradigms. Nonetheless, much of the work on logic programming semantics seems to exist side by side with similar work done for imperative and functional programming, with relatively minimal contact between communities. In this paper we summarize one variety of approaches to the semantics of logic programs: that based on fixpoint theory. We do not attempt to cover much beyond this single area, which is already remarkably fruitful. We hope readers will see parallels with, and the divergences from the better known fixpoint treatments developed for other programming methodologies.

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Quasi-Metrics and the Semantics of Logic Programs

Cited by 38 publications

References 13 publications

Multivalued Mappings, Fixed-Point Theorems and Disjunctive Databases

Multivalued Mappings, Fixed-Point Theorems and Disjunctive Databases

Cones of Weighted and Partial Metrics

Fixpoint semantics for logic programming a survey

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