Unification in the data structure sets

Büttner, Wolfram

doi:10.1007/3-540-16780-3_112

Cited by 9 publications

(7 citation statements)

References 6 publications

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“…This work mostly deals with AC unification -by reducing it to the solution of Diophantine equations -and only in the end it suggests a solution of the ACI problem, by replacing arithmetic equations with Boolean equations. Direct solutions of the ACI problem have been proposed by Büttner (1986) and Baader and Büttner (1988). More recently, Baader and Schulz (1996) provided a general methodology allowing the unification with constants algorithms proposed for ACI to be extended to general ACI1 unification algorithms.…”

Section: Unification Algorithmsmentioning

confidence: 99%

Section: Unification Algorithmsmentioning

confidence: 99%

“…The union-based representation, on the contrary, has been often used when dealing with the problem of set unification on its own (Büttner 1986;Livesey and Siekmann 1976), where set unification is dealt with as an Associative-Commutative-Idempotent (ACI ) unification problem-i.e., unification in presence of operators satisfying the Associativity, Commutativity, and Idempotence properties. In (Legeard and Legros 1991) sets are represented using the union-based approach; however, since set operations are evaluated only when applied to ground sets, set unification is not required at all.…”

Section: Introductionmentioning

confidence: 99%

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Set unification

Dovier¹,

Pontelli²,

Rossi³

2006

Theory and Practice of Logic Programming

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The unification problem in algebras capable of describing sets has been tackled, directly or indirectly, by many researchers and it finds important applications in various research areas-e.g., deductive databases, theorem proving, static analysis, rapid software prototyping. The various solutions proposed are spread across a large literature. In this paper we provide a uniform presentation of unification of sets, formalizing it at the level of set theory. We address the problem of deciding existence of solutions at an abstract level. This provides also the ability to classify different types of set unification problems. Unification algorithms are uniformly proposed to solve the unification problem in each of such classes.The algorithms presented are partly drawn from the literature-and properly revisited and analyzed-and partly novel proposals. In particular, we present a new goal-driven algorithm for general ACI 1 unification and a new simpler algorithm for general (Ab)(C ℓ) unification.

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Section: Unification Algorithmsmentioning

confidence: 99%

Section: Unification Algorithmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Set unification

Dovier¹,

Pontelli²,

Rossi³

2006

Theory and Practice of Logic Programming

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“…Alternative methods for representing sets have been considered in the literature. In particular, one of the most popular approaches relies on the use of the binary union symbol as the set constructor 7,11,44].…”

Section: Alternative Representations Of Setsmentioning

confidence: 99%

“…When F is composed by , ;, and by an arbitrary number of constant symbols, the uni cation problem belongs to the class of ACI1-uni cation problems with constants. Various solutions to this problem have been studied in the literature 7,11,44]. ACI1-uni cation with constants does not distinguish explicitly between sets and elements of sets.…”

Section: Alternative Representations Of Setsmentioning

confidence: 99%

Sets and constraint logic programming

Dovier

Piazza

Pontelli

et al. 2000

ACM Trans. Program. Lang. Syst.

125

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In this paper we present a study of the problem of handling constraints made by conjunctions of positive and negative literals based on the predicate symbols =, ∈,∪ and || (i.e., disjointness of two sets) in a (hybrid) universe of finite sets . We also review and compare the main techniques considered to represent finite sets in the context of logic languages. The resulting contraint algorithms are embedded in a Constraint Logic Programming (CLP) language which provides finite sets—along with basic set-theoretic operations—as first-class objects of the language. The language—called CLP( SET )—is an instance of the general CLP framework, and as such it inherits all the general features and theoretical results of this scheme. We provide, through programming examples, a taste of the expressive power offered by programming in CLP( SET ).

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Unification in monoidal theories

Nutt

1990

10th International Conference on Automated Deduction

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Unification in the data structure sets

Cited by 9 publications

References 6 publications

Set unification

Set unification

Sets and constraint logic programming

Unification in monoidal theories

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