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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 768 (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.
Tractable Disjunctions of Linear Constraints: Basic Results and Applications to Temporal Reasoning
 Theoretical Computer Science
, 1996
"... We study the problems of deciding consistency and performing variable elimination for disjunctions of linear inequalities and disequations with at most one inequality per disjunction. This new class of constraints extends the class of generalized linear constraints originally studied by Lassez an ..."
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Cited by 49 (2 self)
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We study the problems of deciding consistency and performing variable elimination for disjunctions of linear inequalities and disequations with at most one inequality per disjunction. This new class of constraints extends the class of generalized linear constraints originally studied by Lassez and McAloon. We show that deciding consistency of a set of constraints in this class can be done in polynomial time. We also present a variable elimination algorithm which is similar to Fourier's algorithm for linear inequalities. Finally, we use these results to provide new temporal reasoning algorithms for the OrdHorn subclass of Allen's interval formalism. We also show that there is no low level of local consistency that can guarantee global consistency for the OrdHorn subclass. This property distinguishes the OrdHorn subclass from the pointizable subclass (for which strong 5consistency is sufficient to guarantee global consistency), and the continuous endpoint subclass (for whi...
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...
An Incremental Algorithm for Satisfying Hierarchies of Multiway, Dataflow Constraints
 ACM Transactions on Programming Languages and Systems
, 1995
"... Oneway dataflow constraints have gained popularity in many types of interactive systems because of their simplicity, efficiency, and manageability. Although it is widely acknowledged that multiway dataflow constraints could make it easier to specify certain relationships in these applications, con ..."
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Cited by 46 (1 self)
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Oneway dataflow constraints have gained popularity in many types of interactive systems because of their simplicity, efficiency, and manageability. Although it is widely acknowledged that multiway dataflow constraints could make it easier to specify certain relationships in these applications, concerns about their predictability and efficiency have impeded their acceptance. Constraint hierarchies have been developed to address the predictability problem and incremental algorithms have been developed to address the efficiency problem. However, existing incremental algorithms for satisfying constraint hierarchies encounter two difficulties: (1) they are incapable of guaranteeing an acyclic solution if a constraint hierarchy has one or more cyclic solutions, and (2) they require worstcase exponential time to satisfy systems of multioutput constraints. This paper surmounts these difficulties by presenting an 2 incremental algorithm called QuickPlan that satisfies in worst case O(N ) ...
Modeling answer constraints in Constraint Logic Programs
 Proc. Eighth Int'l Conf. on Logic Programming
, 1991
"... The constraint logic programming paradigm CLP(X) (CLP for short) has been proposed by Jaffar and Lassez in order to integrate a generic computational mechanism based on constraints with the logic programming framework. This paradigm retains the semantic properties of logic languages, namely the exis ..."
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Cited by 36 (11 self)
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The constraint logic programming paradigm CLP(X) (CLP for short) has been proposed by Jaffar and Lassez in order to integrate a generic computational mechanism based on constraints with the logic programming framework. This paradigm retains the semantic properties of logic languages, namely the existence of equivalent operational, model theoretic and fixpoint semantics. Moreover, since computation is performed over the particular domain of computation X , CLP(X) programs have an equivalent "algebraic" semantics, i.e. a semantics which is defined directly on the algebraic structure of the domain X . In this paper we propose an extension of such a semantics, for the success set case, in order to fully characterize the operational behaviour of programs. We introduce a framework for defining various notions of models, each corresponding to a specific operationally observable property. The construction is based on a new notion of interpretation (set of constrained atoms), on a natural exten...
A Unifying Framework for Integer and Finite Domain Constraint Programming
, 1997
"... We present a unifying framework for integer linear programming and finite domain constraint programming, which is based on a distinction of primitive and nonprimitive constraints and a general notion of branchandinfer. We compare the two approaches with respect to their modeling and solving capab ..."
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Cited by 32 (2 self)
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We present a unifying framework for integer linear programming and finite domain constraint programming, which is based on a distinction of primitive and nonprimitive constraints and a general notion of branchandinfer. We compare the two approaches with respect to their modeling and solving capabilities. We introduce symbolic constraint abstractions into integer programming. Finally, we discuss possible combinations of the two approaches.
A Unifying Approach to Temporal Constraint Reasoning
 Artificial Intelligence
"... We present a formalism, Disjunctive Linear Relations (DLRs), for reasoning about temporal constraints. DLRs subsume most of the formalisms for temporal constraint reasoning proposed in the literature and is therefore computationally expensive. We also present a restricted type of DLRs, Horn DLRs ..."
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Cited by 31 (9 self)
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We present a formalism, Disjunctive Linear Relations (DLRs), for reasoning about temporal constraints. DLRs subsume most of the formalisms for temporal constraint reasoning proposed in the literature and is therefore computationally expensive. We also present a restricted type of DLRs, Horn DLRs, which have a polynomialtime satisfiability problem. We prove that most approaches to tractable temporal constraint reasoning can be encoded as Horn DLRs, including the ORDHorn algebra by Nebel and Burckert and the simple temporal constraints by Dechter et al. Thus, DLRs is a suitable unifying formalism for reasoning about temporal constraints. 1 Introduction Reasoning about temporal knowledge abounds in artificial intelligence applications and other areas, such as planning [4], natural language understanding [25] and molecular biology [6, 13]. In most applications, knowledge of temporal constraints is expressed in terms of collections of relations between time intervals or time po...
Observable Semantics for Constraint Logic Programs
 Journal of Logic and Computation
, 1995
"... We consider the Constraint Logic Programming paradigm CLP(X ), as defined by Jaffar and Lassez [29, 28]. CLP(X ) integrates a generic computational mechanism based on constraints within the logic programming framework. The paradigm retains the semantic properties of pure logic programs, namely the e ..."
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Cited by 28 (2 self)
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We consider the Constraint Logic Programming paradigm CLP(X ), as defined by Jaffar and Lassez [29, 28]. CLP(X ) integrates a generic computational mechanism based on constraints within the logic programming framework. The paradigm retains the semantic properties of pure logic programs, namely the existence of equivalent operational, modeltheoretic and fixpoint semantics. We introduce a framework for defining various semantics, each corresponding to a specific observable property of CLP computations. Each semantics can be defined either operationally (i.e. topdown) or declaratively (i.e. bottomup). The construction is based on a new notion of interpretation, on a natural extension of the standard notion of model and on the definition of various immediate consequences operators, whose least fixpoints on the lattice of interpretations are models corresponding to various observable properties. We first consider some semantics defined in [29] and their relations, in terms of correctne...
On Fourier's Algorithm for Linear Arithmetic
 Journal of Automated Reasoning
, 1992
"... In the 1820's Fourier provided the first algorithm for solving linear arithmetic constraints. In other words, this algorithm determines whether or not the polyhedral set associated with the constraints is empty. We show here that Fourier's algorithm has an important hidden property: in effect it ..."
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Cited by 27 (4 self)
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In the 1820's Fourier provided the first algorithm for solving linear arithmetic constraints. In other words, this algorithm determines whether or not the polyhedral set associated with the constraints is empty. We show here that Fourier's algorithm has an important hidden property: in effect it also computes the affine hull of the polyhedral set. This result is established by making use of a recent theorem on the independence of negative constraints.