## A Logic Programming View of CLP (1993)

Venue: | International Conference on Logic Programming |

Citations: | 47 - 9 self |

### BibTeX

@INPROCEEDINGS{Maher93alogic,

author = {Michael J. Maher},

title = {A Logic Programming View of CLP},

booktitle = {International Conference on Logic Programming},

year = {1993},

pages = {737--753},

publisher = {MIT Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

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...

### Citations

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Foundations of Logic Programming
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Citation Context ...sary, in general, to consider and combine several branches and their answers to establish that c ! G holds. The corresponding result for logic programming (the completeness theorem for SLD-resolution =-=[21]-=-) requires only a single branch. The naive lifting of the statement of completeness to CLP is the following property, which will be relevant later. Very Strong Completeness: Let T be the (complete) th... |

801 | The semantics of constraint logic programs
- Jaffar, Maher, et al.
- 1998
(Show Context)
Citation Context ...ing 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]-=-. These have been on as diverse areas as general resolution [2], computed answer semantics [6], languages for concurrency [24, 30], program transformation [28], constructive negation [33]. However, of... |

347 | Constraint Query Languages
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Citation Context ...ted with a program P . In many cases, and particularly for database applications, a central condition on the constraint domain is that that bottomup evaluation terminate, for all programs and queries =-=[13]-=-. Such a condition would severely restrict possible constraint domains for use with recursive queries. Fortunately, analysis and transformation techniques can guarantee termination of queries in many ... |

237 |
Negation in logic programming
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- 1987
(Show Context)
Citation Context ...ation other than those in [21, 1] are based on ground versions of programs, and in many ways are propositional. These semantics extend easily to CLP programs. Similarly, Kunen's semantics and results =-=[15]-=- extend to CLP programs, as observed in [33]. However, as was explored in the previous section, some results do not lift readily to arbitrary constraint domains, and apply only to a limited class of C... |

222 |
Unification revisited
- Lassez, Maher, et al.
- 1988
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Citation Context ...an view the language of constraints L as generated by the equations. Although equations do not appear explicitly in most formulations of logic programming, they are implicit in the use of unification =-=[16]-=-. ffl Unifiability = Satisfiability ~ s and ~ t are unifiable iff H j= ~ 9 ~ s = ~ t. This is the central translation in lifting from logic programming to CLP [12]. ffl Most General Unifier = Solved F... |

192 |
Concurrent constraint programming languages. Doctoral Dissertation Award and Logic Programming Series
- Saraswat
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(Show Context)
Citation Context ... this problem for specific results, mostly inspired by the CLP Scheme [10, 11]. These have been on as diverse areas as general resolution [2], computed answer semantics [6], languages for concurrency =-=[24, 30], pro-=-gram transformation [28], constructive negation [33]. However, often it seems necessary to reproduce known logic programming results in the CLP setting, and these proofs are essentially direct "t... |

140 |
On conjunctive queries containing inequalities
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Citation Context ... However the link between this notion of subsumption and the ordering on functions T D P is not as direct for arbitrary constraint domains as it is for the Herbrand domain. The following example from =-=[14]-=- demonstrates the extra subtlety in other constraint domains. Example 4.9 Consider the following rules, r 1 and r 2 , over a domain with a dense linear order such as the real numbers. r 1 : p(u) / q(u... |

132 |
Logic semantics for a class of committed-choice programs
- Maher
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(Show Context)
Citation Context ... this problem for specific results, mostly inspired by the CLP Scheme [10, 11]. These have been on as diverse areas as general resolution [2], computed answer semantics [6], languages for concurrency =-=[24, 30], pro-=-gram transformation [28], constructive negation [33]. However, often it seems necessary to reproduce known logic programming results in the CLP setting, and these proofs are essentially direct "t... |

112 | Guarded horn clauses
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(Show Context)
Citation Context ...is an instance of ~ s iff H j= ~ x = ~ s ! 9~y ~ x = ~ t, where ~ y is the variables in ~ t and ~ x is new variables, not appearing in ~ s or ~ t. Consequently, concurrent logic languages such as GHC =-=[35]-=- which use matching to affect control flow can be viewed as concurrent constraint languages using validation, or ask, constraints [24, 30]. A conditional atom p(~x) / c 1 is an instance of p(~x) / c 2... |

102 |
Equations and inequations on finite and infinite trees
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Citation Context ... the clutter of substitutions. However, in some cases it is not possible to directly lift results from logic programming to CLP. In particular, there is a form of independence of negative constraints =-=[5, 19]-=- which holds for the Herbrand universe (when presented as a constraint domain) but not for many other domains. This turns out to be a major reason why some results cannot be lifted from LP to CLP. We ... |

81 |
On sentences which are true of direct unions of algebras
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Citation Context ...The class of Horn formulas contains all (unquantified) Horn clauses, and is closed under universal and existential quantification, and conjunction. This is the original class of formulas used by Horn =-=[9]-=-. Theorem 4.7 Let \Sigma be a signature and L be the language generated by the primitive constraints of \Sigma. Let D be a model of a Horn \Sigma-theory T . If T is a complete theory then (D; L) has t... |

52 |
A basis for deductive database systems
- Lloyd, Topor
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(Show Context)
Citation Context ...y element can be represented by a term, but this is not true generally. An enumeration of the function symbols provides for an enumeration of the elements of H. As a consequence, a type theory (as in =-=[22]-=-) can be used when \Sigma is finite to produce an allowed program. In general, it is not possible to produce an equivalent allowed CLP program. ffl Expressiveness of the Herbrand universe Some constra... |

51 |
The 3 Rs of optimizing constraint logic programs: Refinement, removal, and reordering
- MARRIOTT, STUCKEY
- 1992
(Show Context)
Citation Context ...n (H; L) [16], but in many constraint domains there is no most specific generalization. The existence of a most specific generalization has advantages in pushing constraints "up" through dis=-=junctions [20, 29, 31]-=-. A third case is the representation of elements of the domain; in the Herbrand universe every element can be represented by a term, but this is not true generally. An enumeration of the function symb... |

49 |
Negation as Failure, in Logic and Database (H
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Citation Context ...traints [24, 30]. A conditional atom p(~x) / c 1 is an instance of p(~x) / c 2 iff D j= 9 \Gamma ~ x c 1 ! 9 \Gamma ~ x c 2 . ffl Clark's Axioms = Satisfaction-Complete Theory Clark's equality theory =-=[4]-=- is satisfaction-complete for (H; L). The lifting here is complicated by the fact that it forms a complete theory when \Sigma is infinite, but not when \Sigma is finite. In view of the role played by ... |

48 | Model Theory, (Third edition - Chang, Keisler - 1992 |

42 |
A Transformation System for Deductive Database Modules with Perfect Model Semantics
- Maher
- 1989
(Show Context)
Citation Context ...s, mostly inspired by the CLP Scheme [10, 11]. These have been on as diverse areas as general resolution [2], computed answer semantics [6], languages for concurrency [24, 30], program transformation =-=[28], construc-=-tive negation [33]. However, often it seems necessary to reproduce known logic programming results in the CLP setting, and these proofs are essentially direct "translations" of the logic pro... |

40 |
Explicit representation of terms defined by counter examples. Journal of automated reasonning
- Lassez, Marriott
- 1987
(Show Context)
Citation Context ...till several constraint domains known to have this property, including the algebras of finite, rational and infinite trees with equational constraints, when there are infinitely many function symbols =-=[17, 25]-=-, feature trees with infinitely many sorts and features [34], linear arithmetic equations over the rational or real numbers, infinite Boolean algebras with positive constraints [8]. [19] has some othe... |

37 |
A Canonical Form for Generalized Linear Constraints
- LASSEZ, MCALOON
- 1992
(Show Context)
Citation Context ... are contained in the answers to another, as discussed in the next subsection. Because of the closure requirements on L, most works on the independence of negative constraints -- for example, [5] and =-=[18]-=- -- are not applicable. However there are still several constraint domains known to have this property, including the algebras of finite, rational and infinite trees with equational constraints, when ... |

36 | Subsumption and indexing in constraint query languages with linear arithmetic constraints
- SRIVASTAVA
- 1992
(Show Context)
Citation Context ...computationally expensive. Indeed, there may be no polynomial time algorithm for the extended test (unless P=NP) even when the subsumption of one fact by another does have a polynomial time algorithm =-=[32]-=-. Consequently, it is of great interest to identify those constraint domains for which we can employ the weaker form of subsumption without worsening termination. We say that these constraint domains ... |

29 |
Partial evaluation of a CLP language
- Smith, Hickey
- 1990
(Show Context)
Citation Context ...n (H; L) [16], but in many constraint domains there is no most specific generalization. The existence of a most specific generalization has advantages in pushing constraints "up" through dis=-=junctions [20, 29, 31]-=-. A third case is the representation of elements of the domain; in the Herbrand universe every element can be represented by a term, but this is not true generally. An enumeration of the function symb... |

27 |
A resolution principle for clauses with constraints
- BuÌˆrckert
- 1990
(Show Context)
Citation Context ...logic programming view of CLP.) Several papers have dealt with this problem for specific results, mostly inspired by the CLP Scheme [10, 11]. These have been on as diverse areas as general resolution =-=[2]-=-, computed answer semantics [6], languages for concurrency [24, 30], program transformation [28], constructive negation [33]. However, often it seems necessary to reproduce known logic programming res... |

21 |
A constraint sequent calculus
- Lassez, McAloon
- 1990
(Show Context)
Citation Context ... the clutter of substitutions. However, in some cases it is not possible to directly lift results from logic programming to CLP. In particular, there is a form of independence of negative constraints =-=[5, 19]-=- which holds for the Herbrand universe (when presented as a constraint domain) but not for many other domains. This turns out to be a major reason why some results cannot be lifted from LP to CLP. We ... |

14 | Constraint-based Query Optimization for Spatial Databases
- Helm, Marriott, et al.
- 1991
(Show Context)
Citation Context ...nction symbols [17, 25], feature trees with infinitely many sorts and features [34], linear arithmetic equations over the rational or real numbers, infinite Boolean algebras with positive constraints =-=[8]-=-. [19] has some other examples. The following result extends this list. A Horn theory is a collection of closed Horn formulas. The class of Horn formulas contains all (unquantified) Horn clauses, and ... |

10 |
From Unification to Constraints
- Jaffar, Lassez
- 1987
(Show Context)
Citation Context ...e implicit in the use of unification [16]. ffl Unifiability = Satisfiability ~ s and ~ t are unifiable iff H j= ~ 9 ~ s = ~ t. This is the central translation in lifting from logic programming to CLP =-=[12]-=-. ffl Most General Unifier = Solved Form A most general unifier is a simplified representation of all solutions in H to some equations. It is usual to assume that mgu's fx 1 / s 1 ; : : : ; x n / s n ... |

8 |
Modeling Answer Constraints
- Gabbrielli, Levi
- 1991
(Show Context)
Citation Context ... Several papers have dealt with this problem for specific results, mostly inspired by the CLP Scheme [10, 11]. These have been on as diverse areas as general resolution [2], computed answer semantics =-=[6]-=-, languages for concurrency [24, 30], program transformation [28], constructive negation [33]. However, often it seems necessary to reproduce known logic programming results in the CLP setting, and th... |

7 |
Logic Programming, in: Handbook of Theoretical
- Apt
- 1990
(Show Context)
Citation Context ... corresponds to a variable determined by a constraint in CLP. Using these relationships, most of the definitions, results and proofs in standard treatments of the theory of logic programming, such as =-=[21, 1]-=-, can be lifted to CLP. As one example, an appropriate definition of an allowed rule [21] in a CLP program requires that every variable either appear in a positive literal in the body or be determined... |

6 |
Constructive Negation for Constraint Logic
- Stuckey
- 1991
(Show Context)
Citation Context ...P Scheme [10, 11]. These have been on as diverse areas as general resolution [2], computed answer semantics [6], languages for concurrency [24, 30], program transformation [28], constructive negation =-=[33]. However,-=- often it seems necessary to reproduce known logic programming results in the CLP setting, and these proofs are essentially direct "translations" of the logic programming proofs. In this pap... |

5 |
Equivalences of Logic Programs, in: Foundations of Deductive Databases and Logic
- Maher
- 1988
(Show Context)
Citation Context ... 4.8 If every rule of P 1 is subsumed by the rules of P 2 then T D P 1sT D P 2 . For logic programs there is the stronger result: T D P 1sT D P 2 iff every rule of P 1 is subsumed by some rule of P 2 =-=[26]-=-. However the link between this notion of subsumption and the ordering on functions T D P is not as direct for arbitrary constraint domains as it is for the Herbrand domain. The following example from... |

4 |
Complete Axiomatizations of the Algebras of Finite
- Maher
- 1988
(Show Context)
Citation Context ...till several constraint domains known to have this property, including the algebras of finite, rational and infinite trees with equational constraints, when there are infinitely many function symbols =-=[17, 25]-=-, feature trees with infinitely many sorts and features [34], linear arithmetic equations over the rational or real numbers, infinite Boolean algebras with positive constraints [8]. [19] has some othe... |

2 |
A CLP View of Logic
- Maher
- 1992
(Show Context)
Citation Context ...: (SC 1 ) 8d 9fc i g i2I s:t: D j= 8x x = d $ V i2I c i (x) (SC 2 ) 8c 9fc i g i2I s:t: D j= 8~x :c(~x) $ W i2I c i (~x) The formulations of SC 2 in [10] and [11] differ. This is discussed further in =-=[27]. There is-=- no known constraint domain with a "natural" language of constraints that does not satisfy SC 2 . A sufficient condition for SC 1 is: 8d; d 0 2 D; d 6= d 0 ; 9c s:t: D j= c(d) and D j= :c(d ... |

1 |
Records for Logic
- Treinen
- 1992
(Show Context)
Citation Context ...luding the algebras of finite, rational and infinite trees with equational constraints, when there are infinitely many function symbols [17, 25], feature trees with infinitely many sorts and features =-=[34]-=-, linear arithmetic equations over the rational or real numbers, infinite Boolean algebras with positive constraints [8]. [19] has some other examples. The following result extends this list. A Horn t... |