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Constraint Logic Programming: A Survey
"... Constraint Logic Programming (CLP) is a merger of two declarative paradigms: constraint solving and logic programming. Although a relatively new field, CLP has progressed in several quite different directions. In particular, the early fundamental concepts have been adapted to better serve in differe ..."
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Cited by 771 (23 self)
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Constraint Logic Programming (CLP) is a merger of two declarative paradigms: constraint solving and logic programming. Although a relatively new field, CLP has progressed in several quite different directions. In particular, the early fundamental concepts have been adapted to better serve in different areas of applications. In this survey of CLP, a primary goal is to give a systematic description of the major trends in terms of common fundamental concepts. The three main parts cover the theory, implementation issues, and programming for applications.
A Terminological Knowledge Representation System with Complete Inference Algorithms
 In Proceedings of the First International Workshop on Processing Declarative Knowledge
, 1991
"... The knowledge representation system klone rst appeared in 1977. Since then many systems based on the idea of klone have been built. The formal modeltheoretic semantics which has been introduced for klone languages [BL84] provides means for investigating soundness and completeness of inference al ..."
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Cited by 96 (19 self)
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The knowledge representation system klone rst appeared in 1977. Since then many systems based on the idea of klone have been built. The formal modeltheoretic semantics which has been introduced for klone languages [BL84] provides means for investigating soundness and completeness of inference algorithms. It turned out that almost all implemented klone systems such as back, kltwo, loom, nikl, sbone use sound but incomplete algorithms.
The Substitutional Framework for Sorted Deduction: Fundamental Results on Hybrid Reasoning
 Artificial Intelligence
, 1990
"... Researchers in artificial intelligence have recently been taking great interest in hybrid representations, among them sorted logicslogics that link a traditional logical representation to a taxonomic (or sort) representation such as those prevalent in semantic networks. This paper introduces a ge ..."
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Cited by 50 (9 self)
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Researchers in artificial intelligence have recently been taking great interest in hybrid representations, among them sorted logicslogics that link a traditional logical representation to a taxonomic (or sort) representation such as those prevalent in semantic networks. This paper introduces a general frameworkthe substitutional frameworkfor integrating logical deduction and sortal deduction to form a deductive system for sorted logic. This paper also presents results that provide the theoretical underpinnings of the framework. A distinguishing characteristic of a deductive system that is structured according to the substitutional framework is that the sort subsystem is invoked only when the logic subsystem performs unification, and thus sort information is used only in determining what substitutions to make for variables. Unlike every other known approach to sorted deduction, the substitutional framework provides for a systematic transformation of unsorted deductive systems ...
A Logic Programming View of CLP
 International Conference on Logic Programming
, 1993
"... We address the problem of lifting definitions, results, and even proofs for the theory of logic programming, so that they apply to constraint logic programming (CLP). We attempt to systematize this lifting, where it is possible, and delineate where it is not possible. We show that the Independence o ..."
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Cited by 47 (9 self)
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We address the problem of lifting definitions, results, and even proofs for the theory of logic programming, so that they apply to constraint logic programming (CLP). We attempt to systematize this lifting, where it is possible, and delineate where it is not possible. We show that the Independence of Negated Constraints property of constraint domains is fundamental to several different aspects of constraint logic programming. This is a principal cause for the inability to lift some traditional logic programming results to constraint logic programming. 1 Introduction We address the problem of lifting definitions, results, and even proofs for the theory of logic programming, so that they apply to constraint logic programming (CLP). (In viewing the theory of constraint logic programming as lifted from the theory of logic programming, we are taking a logic programming view of CLP.) Several papers have dealt with this problem for specific results, mostly inspired by the CLP Scheme [10, 11...
Combination Techniques and Decision Problems for Disunification
 Theoretical Computer Science
"... Previous work on combination techniques considered the question of how to combine unification algorithms for disjoint equational theories E 1 ; : : : ; E n in order to obtain a unification algorithm for the union E 1 [ : : : [ E n of the theories. Here we want to show that variants of this method m ..."
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Cited by 22 (7 self)
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Previous work on combination techniques considered the question of how to combine unification algorithms for disjoint equational theories E 1 ; : : : ; E n in order to obtain a unification algorithm for the union E 1 [ : : : [ E n of the theories. Here we want to show that variants of this method may be used to decide solvability and ground solvability of disunification problems in E 1 [ : : : [E n . Our first result says that solvability of disunification problems in the free algebra of the combined theory E 1 [ : : : [E n is decidable if solvability of disunification problems with linear constant restrictions in the free algebras of the theories E i (i = 1; : : : ; n) is decidable. In order to decide ground solvability (i.e., solvability in the initial algebra) of disunification problems in E 1 [ : : : [ E n we have to consider a new kind of subproblem for the particular theories E i , namely solvability (in the free algebra) of disunification problems with linear constant restricti...
Sorted Unification Using Set Constraints
, 1992
"... . This paper describes a new representation for sortal constraints and a unification algorithm for the corresponding constrained terms. Variables range over sets of terms described by systems of set constraints that can express limited intervariable dependencies. These sets of terms are more genera ..."
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Cited by 10 (0 self)
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. This paper describes a new representation for sortal constraints and a unification algorithm for the corresponding constrained terms. Variables range over sets of terms described by systems of set constraints that can express limited intervariable dependencies. These sets of terms are more general than regular tree languages, but are still closed under intersection. The new unification algorithm shows sorted unification to be decidable for a broad class of sorted signatures, which we call semilinear , and, more generally, for sort theories with a least Herbrand model that can be represented using the new constraints. A finite representation of a complete set of wellsorted unifiers can always be found, even in those cases where this set is infinite. 1 Introduction Sorts are widely used to add more "structure" to first order logic, improving the efficiency of deductive systems [ Cohn, 1989 ] . Increasingly, sorted logic is being viewed as an instance of constraint logic [ Comon and ...
Theorem Proving in Cancellative Abelian Monoids
, 1996
"... We describe a refined superposition calculus for cancellative abelian monoids. They encompass not only abelian groups, but also such ubiquitous structures as the natural numbers or multisets. Both the AC axioms and the cancellation law are difficult for a general purpose superposition theorem prover ..."
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Cited by 8 (1 self)
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We describe a refined superposition calculus for cancellative abelian monoids. They encompass not only abelian groups, but also such ubiquitous structures as the natural numbers or multisets. Both the AC axioms and the cancellation law are difficult for a general purpose superposition theorem prover, as they create many variants of clauses which contain sums. Our calculus requires neither explicit inferences with the theory clauses for cancellative abelian monoids nor extended equations or clauses. Improved ordering constraints allow us to restrict to inferences that involve the maximal term of the maximal sum in the maximal literal. Furthermore, the search space is reduced drastically by certain variable elimination techniques. Keywords Automated Theorem Proving, FirstOrder Logic, Superposition, Cancellative Abelian Monoids, Associativity, Commutativity, Variable Elimination, Term Rewriting. 1 Introduction To be useful in applications such as program verification and synthesis, a...
General A and AXUnification via Optimized Combination Procedures
, 1991
"... In a recent paper [BS91] we introduced a new unification algorithm for the combination of disjoint equational theories. Among other consequences we mentioned (1) that the algorithm provides us with a decision procedure for the solvability of general A and AIunification problems and (2) that Kapur ..."
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Cited by 6 (3 self)
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In a recent paper [BS91] we introduced a new unification algorithm for the combination of disjoint equational theories. Among other consequences we mentioned (1) that the algorithm provides us with a decision procedure for the solvability of general A and AIunification problems and (2) that Kapur and Narendran's result about the NPdecidability of the solvability of general AC and ACIunification problems (see [KN91]) may be obtained from our results. In [BS91] we did not give detailled proofs for these two consequences. In the present paper we will treat these problems in more detail. Moreover, we will use the two examples of general A and AIunification for a case study of possible optimizations of the basic combination procedure.
A Unified Approach to Theory Reasoning
, 1992
"... Theory reasoning is a kind of twolevel reasoning in automated theorem proving, where the knowledge of a given domain or theory is separated and treated by special purpose inference rules. We define a classification for the various approaches for theory reasoning which is based on the syntactic con ..."
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Cited by 6 (1 self)
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Theory reasoning is a kind of twolevel reasoning in automated theorem proving, where the knowledge of a given domain or theory is separated and treated by special purpose inference rules. We define a classification for the various approaches for theory reasoning which is based on the syntactic concepts of literal level  term level  variable level. The main part is a review of theory extensions of common calculi (resolution, model elimination and a connection method). In order to see the relationships among these calculi, we define a supercalculus called theory consolution. Completeness of the various theory calculi is proven. Finally, due to its relevance in automated reasoning, we describe current ways of equality handling.