M. Wilson and A. Borning. Hierarchical constraint logic programming. Journal of Logic Programming, 16(3):277--318, July 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....is called a comparator and its main feature is respecting the hierarchy, i.e. the comparator prefers the valuations satisfying the stronger constraints. It is possible to define various comparators like locally better or globally better comparators, for details and precise definitions see [4,6,16]. An important aspect of constraint hierarchies is the existence of efficient satisfaction algorithms constraint hierarchy solvers. In this paper, we are interested in two groups of these solvers: algorithms based on refining method and local propagation algorithms. The refining algorithms ....

....for HCLP (Hierarchical 1 Charles University, Faculty of Mathematics and Physics, Malostransk nmest 2 25, Praha, Czech Republic. bartak kti.mff.cuni.cz. Supported by GACR grant 201 99 D057. Constraint Logic Programming) programs [6] and it is also employed in the DeltaStar algorithm [16] and in the HCLP language CHAL [14] The refining method is general it can be applied to any constraint hierarchy using any comparator. However, this method requires the solution to be recomputed from scratch after every change (e.g. after adding or removing a constraint) The local propagation ....

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Wilson, M., Borning, A., Hierarchical Constraint Logic Programming, in: The Journal of Logic Programming, special issue on Constraint Logic Programming, Vol. 16 No. 3 & 4, pp. 227-318, 1993.

....they force in literals contrapositively. An interesting issue for future work is to investigate the relationship between the courteous approach and the representational methods based on abnormalities given by Baral Gelfond and Pereira et al. . Hierarchical Constraint Logic Programming (HCLP) [ 38 ] has a notion somewhat similar to defaults with priorities: soft constraints, which are used in an abductive flavor manner. In details of concept, inferencing, and application, HCLP differs markedly from courteous logic programs. Contemporaneously and independently of this paper, the following ....

Molly Wilson and Alan Borning. Hierarchical constraint logic programming. Journal of Logic Programming, 16:277--318, 1993.

....all constraints can be fulfilled. Unfortunately this is often not the case, because of disturbances in the image like occlusions, noise and segmentation errors. Thus the problem often is over constrained. In recent years different methods for solving over constrained systems have been developed [7, 19, 30]. Although several frameworks were proposed which have these methods as special cases [8, 15] the specific techniques concentrate either on the relaxation of constraints or on the elimination of variables. Unobservability of objects in aerial images occurs rather often, and sometimes it can even ....

....one CSP, they have to be rated by an evaluation function, allowing the definition of an ordering on them. In literature several methods with specific evaluation functions for solving OCS have been proposed. They can be basically classified into two categories: 1. Relaxation of constraints (HCLP [30], MaxCSP [8] 2. Elimination of variables (Dynamic CSP [19] Above, different frameworks (PCSP [8] GOCS [15] have been suggested. These frameworks abstract from concrete evaluation functions and the way of weakening the original problem. As we will explain below, they have HCLP and or MaxCSP ....

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M. A. Wilson. Hierarchical Constraint Logic Programming. PhD thesis, Dept. of Computer Science, University of Washington, May 1993.

....Value Selection. This chapter ends with a simple example illustrating the use of the value selection heuristic proposed. CHAPTER 3. FINITE DOMAIN CONSTRAINT PROGRAMMING 21 3. 2 TRANSFORMING CONSTRAINT HIERARCHIES INTO ORDINARY CONSTRAINT SYSTEM Previous work on solving constraint hierarchies [27, 5, 28, 15, 20] concentrates on speci c solvers for constraint hierarchies either in general or for speci c constraint systems. However, such preferential constraints are not available in most ordinary constraint systems and solvers. In this section, we present a general framework for transforming a constraint ....

M. Wilson and A. Borning. Hierarchical constraint logic programming. Journal of Logic Programming, 16(3/4):277-319, 1993.

....and hence by de nition it is not possible to satisfy all given constraints. 2 Henz, Lim, Lua, Shi, Walser, Yap Solving Hierarchical Constraints over Finite Domains with Local Search There are two general approaches to dealing with over constrained problems. Constraint hierarchies [2] HCLP [14] exempli es this approach) addresses the over constrainedness by resolving the con ict using preferences on the importance of some constraints and particular solutions. The other approach exempli ed by PCSP (Partial CSP) 4] is to relax the problem de nition so that it is consistent. Some even ....

Molly Wilson and A. Borning. Hierarchical constraint logic programming. Journal of Logic Programming, 16(3/4):277-319, 1993.

....is to admit constraints which are not required to be satisfied by a solution, but express a preference for solutions which do satisfy them. Such constraints are sometimes called soft constraints. The most developed use of this approach is in hierarchical constraint logic programming (HCLP) [33, 263]. In HCLP, soft constraints have different strengths and the constraints accumulated during a derivation form a constraint hierarchy based on these strengths. There are many possible ways to compare solutions using these constraint hierarchies [33, 178, 263] different methods being suitable for ....

....constraint logic programming (HCLP) 33, 263] In HCLP, soft constraints have different strengths and the constraints accumulated during a derivation form a constraint hierarchy based on these strengths. There are many possible ways to compare solutions using these constraint hierarchies [33, 178, 263], different methods being suitable for different problems. The hierarchy dictates that any number of weak constraints can be over ruled by a stronger constraint. Thus, for example, default behavior can be expressed in a program by weak constraints, which will be over ruled by stronger constraints ....

M. Wilson & A. Borning, Hierarchical Constraint Logic Programming, Journal of Logic Programming, 16, 277--318, 1993.

....of a CLP deduction. For an over constrained system to produce a solution, some of the conflicting constraints have to be (automatically) relaxed. This can, for example, be achieved by extending the CLP paradigm with hierarchical constraints such as in the HCLP framework (Borning et al. 1989; Wilson Borning 1993). As yet we have not investigated methods to support over constrained specifications in our framework. A good overview of recent research into over constrained systems can be found in (Jampel, Freuder, Maher 1996) Under constrained systems, on the other hand, are of no harm to the derivation, ....

Wilson, M., and Borning, A. 1993. Hierarchical constraint logic programming. Journal of Logic Programming 16(3 & 4):277 -- 318.

....in defining the problem constraints precisely. Problems with such features are typically over constrained, and hence by definition it is not possible to satisfy all given constraints. There are two general approaches to dealing with over constrained problems. Constraint hierarchies [2] HCLP [10] exemplifies this approach) addresses the over constrainedness by resolving the conflict with preferences on the importance of constraints and solutions. The other approach exemplified by PCSP (Partial CSP) 4] is to relax the problem definition so that it is consistent. Some even more general ....

M. Wilson and A. Borning. Hierarchical constraint logic programming. Journal of Logic Programming, 16(3/4):277--319, 1993. 8

....problem solution scenario. The manager has generated a solution which is quite good except some details. e.g. he could desire to shift some (sub)processes from actor a 1 to actor a 5 because actor a 1 was overburdened in the last days. Following the model of constraint hierarchies (cf. [10, 11]) he can formulate the new constraints as hard (have to be fulfilled in each case) and the remaining elements of the existing solution as weak (have to be fulfilled if possible) The integration of a constraint hierarchie solver (cf. 8] which is realized in a CLPlanguage guarantees finding best ....

M.A. Wilson. Hierarchical Constraint Logic Programming. PhD Thesis. Dep. of Computer Science and Engineering. University of Washington. 1993.

....scheme which removes precisely those BCH solutions which are unacceptable to HCLP. Thus we separate HCLP into two parts, one compositional and one non compositional. 1 Background 1. 1 Introduction The Hierarchical Constraint Logic Programming (HCLP) scheme of Borning, Wilson, and others [ 2; 10; 12 ] greatly extends the expressibility of the general CLP scheme [ 5 ] There is also related work by Satoh [ 9 ] A semantics has been defined for HCLP [ 10; 11 ] and some instances of it have been implemented [ 8; 10 ] However, the semantics is not as natural as one might hope, and the ....

....a solution oe if it satisfies every constraint that oe does in levels 1 : k Gamma 1, and at level k it satisfies a strict superset of the constraints satisfied by oe. If and oe satisfy different constraints then they are incomparable and both will appear in the solution set. See [ 10; 12 ] The disorderly property of HCLP Wilson discusses a very simple but powerful example in her PhD thesis [ 10 ] which shows the nonmonotonic, hence non compositional, nature of any variant of HCLP which respects the hierarchy. Wilson defines the orderly property as follows: let P and Q be ....

Molly Wilson and Alan Borning. Hierarchical Constraint Logic Programming. Journal of Logic Programming, 16(3):277--318, July 1993.

....CLP (HCLP) is not compositional, and so incremental implementations have to make assumptions which may then need to be retracted [ 8 ] But before we can demonstrate this non compositionality, it is necessary to provide an overview of HCLP. 1 For example, X 4 over the finite domain 0. 10 will give rise to 6 solutions. 1.3 Hierarchical Constraint Logic Programming A good introduction to HCLP can be found in Molly Wilson s PhD thesis [ 10, chapter 4 ] or in the early reference [ 2 ] here is a brief overview. Just as Logic Programming can be extended to CLP, so CLP can be ....

....3 . Weights can be used within a particular level of the hierarchy in order to influence the solution, but a heavily weighted constraint in a given level is completely dominated by the lightest constraint in any more important level. Wilson calls this property respecting the hierarchy [ 10 ] In this paper, we shall only consider the unsatisfiedcount better (UCB) comparator, which is quite simple to understand and which can be defined over any domain. Basically, one valuation is better than another if it leaves fewer constraints unsatisfied (or equivalently, if it satisfies more ....

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Molly Wilson. Hierarchical Constraint Logic Programming. Technical Report 93-05-01, University of Washington, Seattle, May 1993. (PhD Dissertation) .

....approach is to use an overconstrained specification, including both hard constraints and soft constraints (that merely specify preferences) and have a system to compute the solutions that satisfy in the best possible way a subset of these preference constraints. This was the approach taken by [2, 16], that proposed an HCLP scheme that allows non required (or soft) constraints to be specified with some preference level and rely on a constraint solver that explores this hierarchy of constraints to detect the best solutions. Although the scheme is quite general, little details were published on ....

Wilson M., Borning A.: Hierarchical Constraint Logic Programming. J. Logic Programming, 1993:16.

....be satisfied and levels of preferential constraints which need not be satisfied. Various comparators can be used to specify the preference of particular solutions over other solutions. There are two general approaches to dealing with over constrained problems. Constraint hierarchies [2] HCLP [18] exemplifies this approach) addresses the over constrainedness by resolving the conflict with preferences on the importance of constraints and solutions. The other approach exemplified by PCSP (Partial CSP) 5] is to relax the problem definition so that it is consistent. Some even more general ....

....g for constraint weights is defined as: g( C i ) j X c2C i w c e(c ) In this paper, we concentrate on the use of global comparators and more specifically weighted sum better. 2. 2 Transforming Hierarchies into Non hierarchical Systems Previous work on solving constraint hierarchies [18, 4, 19, 9, 12] concentrates on specific solvers for constraint hierarchies either in general or for specific constraint systems. However, such preferential constraints are not available in practical constraint systems and solvers. In this section, we present a general framework for transforming a constraint ....

M. Wilson and A. Borning. Hierarchical constraint logic programming. Journal of Logic Programming, 16(3/4):277--319, 1993.

....Stuckey [65] provided a declarative semantics for minimization predicates based on a translation into subgoals with negation. They propose an operational semantics in which the current optimal solution is used to prune sub optimal solutions. Hierarchical Constraint Logic Programming: Borning et al. [10, 100] introduced the framework of Hierarchical Constraint Logic Programming (HCLP) which extends the paradigm of CLP [36, 38] by allowing the programmer to specify soft constraints in addition to the required or hard constraints. A HCLP scheme is parametrized by both the domain of the constraints and ....

....where a space of problems and a metric on that space is associated with the constraint satisfaction problem under question. The best partial solutions are the solutions to the partial problem in the space that is closest to the original problem according to the metric. 2. Borning, Wilson et al. [10, 100] discuss the paradigm of hierarchical constraint logic programming where strengths are associated with constraint and a comparator is used to decide which partial solution to a set of constraints is the best. HCLP has proven useful in modelling problems that involve constraint relaxation. Examples ....

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M. Wilson and A. Borning. Hierarchical Constraint Logic Programming. Journal of Logic Programming, 16:277--318, 1993.

....desirable property of associating a unique intended preference model with every preference logic program something that is not necessarily guaranteed by the negation based approaches. The idea of hard and soft requirements has also been explored in HCLP (hierarchic constraint logic programming) [26] wherein a constraint may be optionally tagged with a weight, such as strong, weak, etc. This tag indicates the relative importance of a constraint and serves to organize all constraints into a linear hierarchy. The notion of a comparator is introduced in order to compare and order alternative ....

M. Wilson and A. Borning. Hierarchical Constraint Logic Programming. Journal of Logic Programming, 16:277--318, 1993.

....into two extensions, one with p and one with :p, when a locale has unrefuted candidate(s) for each. A major practical difficulty with each of these variants is that there are, in the worst case, an exponential number of extensions to consider. Hierarchical Constraint Logic Programming (HCLP) Wilson and Borning, 1993 ] has a notion somewhat similar to defaults with priorities: soft constraints, which are used in an abductive flavor manner. In details of concept, inferencing, and application, HCLP differs markedly from courteous logic programs. 12 Current Work In current work, we are implementing courteous ....

Molly Wilson and Alan Borning. Hierarchical constraint logic programming. Journal of Logic Programming, 16:277--318, 1993.

....This is the main topic of the present paper. While there has been considerable research on partial constraint satisfaction [3] not much has been done within the framework of logic programming. Two notable efforts are Relaxable Horn Clauses [2, 7] and Hierarchical Constraint Logic Programming [1, 9]. Mantha et al. introduced Relaxable Horn Clauses, where a relaxable clause is a definite clause with a partial order over the goals in the body; the partial order dictates the order in which the goals are to be relaxed if all the goals in the body are not satisfiable. However, stating the ....

....which the goals are to be relaxed if all the goals in the body are not satisfiable. However, stating the relaxation criteria in this way, i.e. in terms of goals local to a clause, provides only limited expressiveness for our intended applications. Hierarchical Constraint Logic Programming (HCLP) [1, 9] is a paradigm that has proven useful for performing constraint relaxation in applications such as interactive graphics, document formatting, and scheduling. HCLP extends CLP by supporting required as well as relaxable constraints. It allows (numeric) strengths to be associated with relaxable ....

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M. Wilson and A. Borning. Hierarchical Constraint Logic Programming. Journal of Logic Programming, 16:277--318, 1993.

....problem, we introduce composite constraints into (PO )HCLP. We present the formal syntax and semantics of PO HCLP, and establish its soundness and completeness results. A prototype of PO HCLP(R,WSPB) is constructed using CLP(R) 1 Introduction Hierarchical Constraint Logic Programming (HCLP) [15, 16] extends the CLP scheme [8] by including non required constraints (or soft constraints) so that overconstrained problems can be modeled more declaratively in this extended framework. HCLP, however, suffers from two limitations. First, constraints are classified into different levels according to ....

....possibility of introducing partially ordered hierarchies is also briefly discussed. They suggest the set of solutions of a partially ordered constraint hierarchy to be the union of solutions from all totally ordered hierarchies that are consistent with the partially ordered one. Wilson and Borning [16] adopt the constraint hierarchy theory to extend the CLP scheme [8] for non required constraint processing. Jampel and Hunt [10] propose a weakening of the HCLP semantics, in which the incrementality and compositionality properties are preserved. Govindarajan et al. [6] propose preference logic ....

M.A. Wilson and A. Borning. Hierarchical constraint logic programming. Journal of Logic Programming, 16(3):277--318, 1993.

....and unsound. Stuckey [Stu95] proposes a constructive form of negation for CLP which, he claims, offers a clean and flexible (though expensive) alternative to existing methods. In most CLP implementations, the user is only allowed to specify constraints that must hold. Wilson and Borning [WB93] claim, however, that in many applications one needs to express preferences of constraints as well as strict requirements. They accordingly extend the CLP scheme to incorporate the notion of constraint hierarchies, and provide operational, model theoretic and fixed point semantics of the ....

M. Wilson and A. Borning. Hierarchical constraint logic programming. Journal of Logic Programming, 16:277--318, 1993.

....formalism [32] with grammatical arbiter clauses for this purpose. The resulting grammar is called a preference logic grammar, and its translation to a preference logic program is straightforward (see [16] for details) We also show how the concept of constraint hierarchies described by Borning [40] is subsumed by preference logic programs. Our paradigm goes further in providing a more flexible notion of relaxation, called preference relaxation, as illustrated by the example given earlier. We formalize the declarative semantics of optimization and relaxation using simple semantic concepts ....

....of relaxation, while there has been interest in partial constraint satisfaction [9] and heuristic approaches to over constrained systems [10] not much has been done within the framework of logic programming. The most notable work is the paradigm of Hierarchical Constraint Logic Programming (HCLP) [4, 40]. HCLP has proven useful for specifying constraint relaxation regimes that arise in applications such as interactive graphics, document formatting, and scheduling. HCLP extends CLP by supporting required as well as relaxable constraints, i.e. constraints that are tagged with a weight (such as ....

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M. Wilson and A. Borning. Hierarchical Constraint Logic Programming. Journal of Logic Programming, 16:277--318, 1993.

.... predicates such as minimum and maximum predicates can be efficiently computed; Par89, JOM93] discuss partial order programming over lattice domains in which the notion of maximizing (minimizing) is incorporated directly into the semantics by taking least upper bounds (greatest lower bounds) [BMMW89, WB93] discuss Hierarchical CLP (HCLP) which is an extension to CLP where (numeric) strengths are associated with constraints, and the desired behavior of the system is captured by trying to satisfy the constraints in the best possible way. Such an approach was shown to be natural for describing the ....

M. Wilson and A. Borning. Hierarchical Constraint Logic Programming. Journal of Logic Programming, 16:277--318, 1993.

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M. Wilson and A. Borning. Hierarchical constraint logic programming. Journal of Logic Programming, 16(3):277--318, July 1993.

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M. Wilson and A. Borning, "Hierarchical constraint logic programming," Journal of Logic Programming, Vol. 16, pp. 277--318, 1993.

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M. Wilson and A. Borning. Hierarchical constraint logic programming. Journal of Logic Programming, 16:277--318, 1993.

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Molly Wilson, `Hierarchical constraint logic programming', Ph.D. Thesis, Department of Computer Science and Engineering, University of Washington, 1992.

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