## Dealing with Incomplete Knowledge on CLP(FD) Variable Domains (2003)

Venue: | ACM Transactions on Programming Languages and Systems |

Citations: | 5 - 2 self |

### BibTeX

@ARTICLE{Gavanelli03dealingwith,

author = {Marco Gavanelli and Evelina Lamma and Paola Mello and Michela Milano},

title = {Dealing with Incomplete Knowledge on CLP(FD) Variable Domains},

journal = {ACM Transactions on Programming Languages and Systems},

year = {2003},

volume = {27},

pages = {2005}

}

### OpenURL

### Abstract

Constraint Logic Programming languages on Finite Domains, CLP(FD), provide a declarative framework for Artificial Intelligence problems. However, in many real life cases, domains are not known and must be acquired or computed.

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Citation Context ...t two different CLP systems (Conjunto and {log}) can be effectively used. We provide motivating examples and describe promising applications. 1. Introduction The Constraint Satisfaction Problem (CSP) =-=[26]-=- is a powerful framework for dealing with many problems in Artificial Intelligence. A CSP consists of a set of variables that range over some given domains, and are subject to a set of constraints. Co... |

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Citation Context ...ariables. The domain of a variable X will be indicated with DX. When considering a variable with an index, Xi, we will sometimes call Di its domain, instead of DXi. Constraint Logic Programming (CLP) =-=[21]-=- is a class of declarative languages. Each CLP language can be seen as an instance of a general CLP(X ) scheme where each instance can be specified by instantiating the parameter X [22]. The parameter... |

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Citation Context ...the Holy Grail of programming: the user states the problem, the computer solves it.” [17]. A natural mapping of CSP can be given in terms of Constraint Logic Programming over Finite Domains, CLP(F D=-=) [13]-=-. In CLP(F D) programs, variables range over finite domains, and are constrained each other. Constraint propagation algorithms, like Arc-Consistency [26] and its evolutions, are often embedded in CLP(... |

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Citation Context ...rcing arc-consistency means translating a given problem P into a different but equivalent problem P ′ in which the constraint network is arc-consistent. Many algorithms have been given [34] [26] [29=-=] [19]-=- [4] [5] for computing arc-consistency; the algorithms have different performance, but all detect inconsistency in the same problem instances (when a domain becomes empty). In the same way, there are ... |

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Citation Context ...btain a more expressive framework, like {log}; thus if more expressive power is necessary, another instance of the CLP(F D+PF D) framework, the CLP(F D)+{log} instance, can be used. Codognet and Diaz =-=[6]-=- described a method for compiling constraints in CLP(F D). In their language, clp(FD), there is only one primitive constraint X in R, used to implement all the other constraints. R represents a collec... |

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Citation Context ...eness of such an approach is shown. In our language, implementation of delayed evaluation is quite natural and simple. 20sOur framework can be somehow related to Dynamic Constraint Satisfaction (DCS) =-=[11]-=-. DCS is a field of AI taking into account dynamic changes of the constraint store such as the addition, deletion of values and constraints. The difference between DCS and our approach concerns the wa... |

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Citation Context ... arc-consistency means translating a given problem P into a different but equivalent problem P ′ in which the constraint network is arc-consistent. Many algorithms have been given [34] [26] [29] [19=-=] [4]-=- [5] for computing arc-consistency; the algorithms have different performance, but all detect inconsistency in the same problem instances (when a domain becomes empty). In the same way, there are many... |

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Citation Context ...tead, domain elements that are unknown can be requested and inserted in the domain. DCS solvers record the dependencies between constraints and the corresponding propagation in proper data structures =-=[31]-=- so as to tackle modifications of the constraint store as soon as new data changes. In this perspective, we also cope with changes since the acquisition of new variable values can be seen as a modific... |

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Citation Context ...ets, the same algorithms could be used in conjunction with other CLP languages. For this reason, we generalize the framework to exploit other CLP(PF D) (the powerset of F D) systems, such as Conjunto =-=[18]-=- or {log} [14]. We also define which features CLP(F D + PF D) requires from the employed CLP(PF D) system. The rest of the paper is organized as follows. In section 2 we provide the preliminaries and ... |

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Citation Context ...-consistency means translating a given problem P into a different but equivalent problem P ′ in which the constraint network is arc-consistent. Many algorithms have been given [34] [26] [29] [19] [4=-=] [5]-=- for computing arc-consistency; the algorithms have different performance, but all detect inconsistency in the same problem instances (when a domain becomes empty). In the same way, there are many alg... |

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Citation Context ...anagement. The planner instead of retrieving all the resources in the systems before starting the plan construction, collects them only when needed thus saving a significant amount of time. Mailharro =-=[27] sho-=-ws a system that considers unbound domains. A domain can contain a “wildcard” element that can be linked to any possible element. Operationally, this idea has some similarities to the ICSP, howeve... |

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Citation Context ...algorithms could be used in conjunction with other CLP languages. For this reason, we generalize the framework to exploit other CLP(PF D) (the powerset of F D) systems, such as Conjunto [18] or {log} =-=[14]-=-. We also define which features CLP(F D + PF D) requires from the employed CLP(PF D) system. The rest of the paper is organized as follows. In section 2 we provide the preliminaries and basic notation... |

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Citation Context ...different domain formalizations, thus achieving different expressive power and efficiency levels. Besides I-Sets, we could build a two-sorted CLP system on top of a CLP dealing with lists [7] or sets =-=[16, 18]-=-. Of course, the obtained system inherits advantages and drawbacks from the host language. For example, sets are managed in a wide variety of ways, so, if we have a combinatorial problem and need a ve... |

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Citation Context ...tion domains can be cast. Examples of such solution domains are rational trees, hereditarily finite well-founded and non-well-founded sets, hereditarily finite well-founded and non-well-founded lists =-=[1]. Given a -=-set Γ of equations between (Σ1 ∪ Σ2)-terms, their combination algorithm executes four basic steps: 1. Decomposition: Using variable abstraction, compute an equivalent system Γ1 ∪ Γ2, with Γ1... |

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Citation Context ...ted work Many systems consider set objects, because sets have powerful description capabilities. In particular, some have been described as instances of the general CLP(X ) framework [23], like {log} =-=[14, 15], CL-=-PS [25], or Conjunto [18]. In {log} [14, 15], a set can be either the empty set ∅, or defined by a constructor with that, given a set S and an element e, returns the set composed of S ∪{e}. This l... |

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Citation Context ...collection of objects and can also be a user function. Thus, in clp(FD) domains are managed as first-class objects; our framework can be fruitfully implemented in systems exploiting this idea. Sergot =-=[32]-=- proposes a framework to deal with interaction with the user in a logic programming environment. In particular, he suggests that the user should not provide all the possible values at the beginning of... |

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Citation Context ...idely used for communication purposes in concurrent logic programming [33]. Zweben and Eskey [35] describe a forward checking algorithm in which the domains of the variables are viewed as streams. In =-=[12]-=-, the effectiveness of such an approach is shown. In our language, implementation of delayed evaluation is quite natural and simple. 20sOur framework can be somehow related to Dynamic Constraint Satis... |

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Citation Context ...application which could be promising for our language could be the acquisition of domain values from the web: “The interactive behaviour of our constraint reasoner also can be seen as a form of ICSP=-=” [24]-=-. 8. Conclusions and Future Work In this work, we presented a language that performs a constraint computation on variables with finite domains when information about domains is not fully known. Domain... |

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Citation Context ...t CSP which is Arc Consistent. Intuitively, one would like to get to a network where variables’ domains are smaller, but no solution is removed. More precisely, let us define the concept of subdomai=-=n [30]: Definition 5. Gi-=-ven a CSP=〈X, D, C〉 where D = (D1, . . . , Dn) is the domain of the CSP, we say that D ′ = (D ′ 1, . . . , D ′ n) is a subdomain of D iff ∀n i=1D′ i ⊆ Di. 5sprocedure AC Q ← {c(Xi, X... |

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Citation Context ...ystems consider set objects, because sets have powerful description capabilities. In particular, some have been described as instances of the general CLP(X ) framework [23], like {log} [14, 15], CLPS =-=[25], or-=- Conjunto [18]. In {log} [14, 15], a set can be either the empty set ∅, or defined by a constructor with that, given a set S and an element e, returns the set composed of S ∪{e}. This language is ... |

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Citation Context ...set semantics (i.e., in an I-Set there are no repeated elements and elements are not sorted). Streams are widely used for communication purposes in concurrent logic programming [33]. Zweben and Eskey =-=[35]-=- describe a forward checking algorithm in which the domains of the variables are viewed as streams. In [12], the effectiveness of such an approach is shown. In our language, implementation of delayed ... |

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Citation Context ...values are acquired or computed during the solution process only when needed, and then inserted into domains. The ICSP model has been successfully applied to visual recognition tasks [9] and planning =-=[3]-=-. Experiments on randomly-generated problems [10] show that in many instances, ICSP solving algorithms can avoid domain element acquisition steps, achieving good performance in problems where informat... |

6 |
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Citation Context ...ficient method would exploit the imposed constraints to prune the search space even on the computation providing domain values. An effective solution to this issue is the Interactive CSP (ICSP) model =-=[8]-=-. In this model, domains need not to be ground (i.e., fully known), their values are acquired or computed during the solution process only when needed, and then inserted into domains. The ICSP model h... |

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(Show Context)
Citation Context ...ly known), their values are acquired or computed during the solution process only when needed, and then inserted into domains. The ICSP model has been successfully applied to visual recognition tasks =-=[9]-=- and planning [3]. Experiments on randomly-generated problems [10] show that in many instances, ICSP solving algorithms can avoid domain element acquisition steps, achieving good performance in proble... |

5 | Combining constraint solving
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(Show Context)
Citation Context ...ding a solution where only some of the variables are assigned a value, while the others are inactive. However, the set of domain values is given at the specification of the problem. Baader and Schulz =-=[2]-=- propose a general and elegant framework for integration of constraint solvers. They first address the problem of combining solvers based on equational theories on free algebras, then they generalize ... |

4 |
M.: From eager to lazy constrained data acquisition: A general framework
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(Show Context)
Citation Context ...ion process only when needed, and then inserted into domains. The ICSP model has been successfully applied to visual recognition tasks [9] and planning [3]. Experiments on randomly-generated problems =-=[10]-=- show that in many instances, ICSP solving algorithms can avoid domain element acquisition steps, achieving good performance in problems where information is partially specified. In this paper, we pro... |

3 |
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(Show Context)
Citation Context ...ealing with different domain formalizations, thus achieving different expressive power and efficiency levels. Besides I-Sets, we could build a two-sorted CLP system on top of a CLP dealing with lists =-=[7]-=- or sets [16, 18]. Of course, the obtained system inherits advantages and drawbacks from the host language. For example, sets are managed in a wide variety of ways, so, if we have a combinatorial prob... |

3 |
pursuit of the holy grail
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(Show Context)
Citation Context ...ution algorithm. “Constraint programming represents one of the closest approaches computer science has yet made to the Holy Grail of programming: the user states the problem, the computer solves it.=-=” [17]-=-. A natural mapping of CSP can be given in terms of Constraint Logic Programming over Finite Domains, CLP(F D) [13]. In CLP(F D) programs, variables range over finite domains, and are constrained each... |

1 |
i PS e User Manual, Release 5.2
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(Show Context)
Citation Context ... more elements belong to the I-Set. These primitives will not generate repeated elements in an I-Set, even if they are allowed by the syntax. In the code in Figure 3, we use the syntax of ECL i P S e =-=[20]-=- for declaring that the goal get(S,E) should be delayed whenever S is a variable. insert(S,E) :- nonground(E), !, raise_exception. insert(S,E) :- var(S), !, S={E|_}. insert({},E) :- !, fail. insert({E... |