Maher, M.J., A Logic Programming View of CLP, Proc. 10th International Conference on Logic Programming, pp.737-753, MIT Press, 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... satisfies 1. OE j= 9x ) Delta j= 9x (provided no variable in x occurs in OE) Note that our definition of independence involves existential quantification, which is not the case for the conventional definition [16] Our notion of independence agrees however with the definitions in [33, 20]. 16 2. OE j=j Delta ) A complete relative simplification procedure together with a test Delta j= 9xOE is the basic operational machinery one has to provide for the underlying constraint system in order to decide whether a reduction rule is applicable. Relative simplification ....

Michael J. Maher. A logic programming view of CLP. In David S. Warren, editor, Proceedings of the 10th DInternational Conference on Logic Programming, pages 737--753, Budapest, Hungary, June 1993. The MIT Press.

....RULE SETS 249 The constraint theory consists of only one single model for the finite domain case. This is an important property, because it simplifies our proof procedure. Every constraint theory consisting of only one model enjoys the socalled independence of negated constraints property (Maher, 1993). Because of this, it suffices to consider only one derivation (refutation) for computing answers. This means, the completeness result for CME has a simple structure in this restricted case (see section 3.3) Since we assume that all variables have only finite domains, the only model is even ....

Maher, M. J.: 1993, `A Logic Programming View of CLP'. In: D. S. Warren (ed.): Proceedings of the 10th International Conference on Logic Programming. Budapest, pp. 737--753, MIT Press, Cambridge, MA, London.

....ning a clean semantics for functional evaluations was a challenging problem in Logic Programming until the full framework of constraint logic programming was settled ( 6] This section recalls these works and is subdivided into 2 parts : the syntax and the semantics parts. We advise to report to [6, 9] for an extensive presentation. 2.1 Constraint language and constraint programs : syntax Given an in nite set of variables V , a nite set of function symbols , a nite set of constraint predicate symbols c supposed to contain a binary symbol = these are the built in or interpreted ....

....that B is the full set of constraint atoms and is necessarily denumerable as a product of denumerable sets : the set of formula and the set of atoms. As claimed in the beginning of section 2, constraints atoms are a more natural choice of observables than the standard success set as de ned in [9]. That is why the very meaning of a constraint logic program is actually a non ground meaning. So what about a distance over non ground semantics i.e. over the set I 2 B 2 B (to follow the notation of section 2) Starting from our level issued distance d, we induce a real valued mapping ....

M.J. Maher. A Logic Programming View of CLP. In MIT Press, editor, Proceedings of 10th ICLP, pages 737-753, 1993.

....E j= 9(R :R 1 Delta Delta Delta :R k ) E j= 9(R :R i ) for 1 i k This is equivalent to the very strong completeness property, i.e. we can restrict to only one derivation while answering any query, provided that we do not have any inequalities. For details, the reader is referred to [Mah93]. If we assume the set of function symbols F to be finite, then we need the weak domain closure axiom in order to make our theory complete [Mah88] 8x f2F 9z x = f(z) This case is mainly considered in [CL89] But this point of view is restricted to Herbrand models only and increases the ....

Michael J. Maher. A logic programming view of CLP. In David S. Warren, editor, Proceedings of the 10th International Conference on Logic Programming, pages 737--753. MIT Press, Cambridge, MA, London, England, 1993. Budapest, 1993.

....for constraint systems that is of further reaching interest. Colmerauer has introduced it for the manipulation of inequations in the context of constraint logic programming (CLP) 20] The property also characterizes (and is characterized by) the semantics of bottom up and top down computations [44]. 1 For comparison, any class of set constraints over the domain of possibly empty sets of trees does not have the independence property. As an example take the constraint = f(x; y) 0 x 6 0 y 6 0. Then the conjuncts x 6 0 and y 6 0 are not independent from each other: is not ....

M. J. Maher. A logic programming view of CLP. In D. S. Warren, editor, Proceedings of the 10th International Conference on Logic Programming, pages 737--753, Budapest, Hungary, June 1993. The MIT Press.

....properties. Some of the semantics we consider are the generalization to the CLP case of the non ground semantics for (positive) logic programs in [17] and of the compositional semantics in [7] Indeed, most semantic constructions and results lift directly from logic programming to CLP (see [37] for a detailed discussion of this lifting) Moving to a non ground semantics is even more natural in the case of CLP, since the computation structure may not even include constants so that there might be no ground objects. As a matter of fact, most of the success set and fixpoint semantics ....

M. J. Maher. A Logic Programming view of CLP. In D. S. Warren, editor, Proc. Tenth Int'l Conf. on Logic Programming, pages 737--753. The MIT Press, Cambridge, Mass., 1993.

....Thus u 62 susp(s) Note that, as a consequence of this lemma, an approximation s of a d complete skeleton s 0 with s 6= s 0 cannot be d complete. 12 4 SLD Resolution with delay Motivated by SLD derivations and SLD trees ( 15, 1] we recall the abstract framework : transition system (as [23, 18]) in which the notion of derivation and search tree can be defined. A transition system T is a triple (S; F; T ) where S is a set, F S and T a binary relation (S Gamma F ) Theta S. The members of S are called states of T , the member of F are the final states. T is the transition ....

M.J. Maher. A Logic Programming view of CLP. ICLP'93 , pages 737-753, Warren ed., 1993.

....problems of test pattern generation and car sequencing. Many of the definitions, results, and proofs for the theory of logic programming applies to constraint logic programming as well. The problems of lifting from logic programming to constraint logic programming are addressed in the paper [30]. The main difference is that the unification in logic programming is replaced by checking the satisfiability of constraints. The equations that are implicit in the use of unification are treated as primitive constraints. It is the operational interpretation of constraints, rather than the ....

M.J. Maher. A logic programming view of CLP. In International Conference on Logic Programming, pages 737--753, 1993.

....reasons, none of the various operational semantics [7,11,26] neither the different model theoretic approaches (see e.g. 2] nor the completion semantics [6,17] seem to be adequate to be the basis for defining a compositional semantics for normal logic program units. To our knowledge, only [8, 14, 19] provide some compositional semantic constructs for normal logic programs. Below we compare the results presented in this paper and these approaches. In [21] it is presented a methodology for the semantic definition of modular logic programs ensuring compositionality and full abstraction, and we ....

.... compositional and fully abstract (categorical) semantics for a number of program units [4,15] The kind of compositionality results that can be achieved, using our semantics as the basis for defining the corresponding specification frame, are quite more powerful than the results presented in [8, 14, 19]. In these papers different semantic definitions are provided for certain kinds of modular units which are shown to be compositional. However, they all impose (at least) the restriction that when putting together (through the corresponding composition operation) two units then the sets of ....

M. Maher, A logic programming view of CLP, in Proc. 10th Int. Conf. on Logic Programing, D.S. Warren, ed. (1993), 737-753

....of values requires addition of new operations on the corresponding algebras. In logic query languages, stemming from logic programming, there seems to be a uniform viewpoint on how complex values should be treated. There are two major approaches. 1. In constraint logic programming (Maher 1992, Maher 1993) and constraint databases (Kanellakis, Kuper Revesz 1995) any value is identified by the set of constraints true on this value. The addition of a new type of values requires the addition of new constraint predicates. A similar approach to relational query languages was also considered in ....

Maher, M. (1993), A logic programming view of CLP, in `International Conference on Logic Programming', pp. 737--753.

....[62] In: Proceedings of the Seventeenth ACM SIGACTSIGMOD SIGART Symposium on Principles of Database Systems (PODS 98) June 1 3, 1998, Seattle, WA. Jan Paredaens, Latha Colby, editors. c flACM, 1998 values should be treated. There are two major approaches. 1. In constraint logic programming [41, 42] and constraint databases [33] any value is identified by the set of constraints true on this value. The addition of a new type of values requires the addition of new constraint predicates. A similar approach to relational query languages was also considered in [10] 2. Another approach to adding ....

M.J. Maher. A logic programming view of CLP. In International Conference on Logic Programming, pages 737--753, 1993.

....goes into a looping computation. It illustrates that, thanks to the simplification rule, our mechanism is loop avoiding. Our paper is now organized as follows : in section 2, we recall the basic concepts of rewriting necessary to understand our works and we briefly review the CLP scheme as in [7]. Section 3 is the main part where we define the new mechanism. We adapt linear completion mechanism to take into account constraint handling and we get the Constraint Linear Completion (CLC) In section 4, we propose a declarative semantics for constraint rewrite programs. Then, we compare the ....

....the termination of the rewrite system. A more complete presentation of rewrite techniques will be out of the scope of this paper. For more details, see [4] 6] 2. 2 Constraint Logic Programming With the Constraint Logic Programming scheme, new basis for logic programming are established ( 5] [7]) Here, the basic definitions and the main theoretical results are recalled as in [7] Given an infinite set of variables V, a finite set of function symbols Sigma, a finite set of constraint predicate symbols Pi c supposed to contain a binary symbol = and a finite set of program predicate ....

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M.J. Maher. A logic programming view of CLP. In MIT Press, editor, Proceedings of 10th ICLP, pages 737--753, 1993.

....Also, we observe that techniques for improving the termination of bottom up evaluation of logic programs can be easily incorporated into our operational semantics without affecting its correctness and completeness. The following is an example that illustrates the need for subsumption tests [25, 23, 42, 29]. Consider the following program. p(X) T : T=0, X=a. p(X) T : T =0, p(X) T. It is obvious that the meaning of this program is the singleton set consisting of the fact p(X) T : T=0, X=a. It is easy to verify that each iteration of the operational semantics will generate the above fact and ....

....It is easy to verify that each iteration of the operational semantics will generate the above fact and leave the program unchanged. That is, the program does not terminate. Simple checking for duplicate solutions will solve this case but in general more powerful subsumption tests are necessary [29]. This raises complex issues of the tradeoff between computational efficiency and the set of programs on which the operational semantics will terminate. a) Intial Configuration: Timer: t = 0 Current Program: even T : T=0. even T : T=S 1,S =0, not(even S) Generated Facts: b) ....

M. Maher. A logic programming view of CLP. In Warren [48], pages 737--753.

....reasons, none of the various operational semantics [13, 11, 32] neither the di erent modeltheoretic approaches (see e.g. 3] nor the completion semantics [12, 25] seems to be adequate to be the basis for de ning a compositional semantics for normal logic program units. To our knowledge, only [17, 19, 27, 35, 9] provide some compositional semantic constructs for normal logic programs. In section 6 we compare the results presented in this paper and these approaches. It must be noted that compositionality is a very important property for de ning the semantics of a modular unit. In particular, if the ....

....program fragments which is compositional and fully abstract with respect to standard program union. Actually, other kind of units and composition operations can be seen just as a special case. The kind of compositionality results obtained are quite more powerful than the results presented in [17, 19, 27, 35, 9]. In [17, 19, 27] di erent semantic de nitions are provided for certain kinds of modular units which are shown to be compositional. However, they all impose (at least) the restriction (not needed in our work) that, for putting together (through the corresponding composition operation) two units, ....

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Maher, M., A logic programming view of CLP, in: Warren, D. S. (ed) Proc. 10th Int. Conf. on Logic Programming, 1993.

....holds D ) We will now define a counterpart to SLD derivations for CLP goals. In our context of partial deduction, the initial and final programs are just ordinary logic programs (i.e. they can be seen as CLP programs using just equality constraints over the structure of feature terms FT , see [44]) In order for our constraint manipulations to be correct wrt the initial ordinary logic program, we have to ensure that equality is not handled in an unsound manner in the intermediate CLP program. For instance, something like a = b should not succeed in the CLP program. In other words, if there ....

M. Maher. A logic programming view of CLP. In D. S. Warren, editor, Proceedings of the 10th International Conference on Logic Programming, pages 737--753. The MIT Press, 1993. 44

....of all languages referred to as constraint logic programming languages. For instance, it does not take into account disjunctive constraints. However, it describes one common framework for CLP operational semantics, and is also the one considered in much of the standard literature on CLP, e.g. [Mah93]. This section studies the theory of such satisfiability functions , which will be defined as partial recursive functions from finite sets of constraints to results including true and false . The motivation for doing so is to build a homogeneous theory of CLP systems, whether they use ....

....of L and S is a set of constraints of L; C. In basing an operational semantics on a satisfiability function sat, we may want to give a definition that takes into account the various truth values which can act as results of sat. We must make the following minimum requirements, following Maher [Mah93]. Definition 2.4 Given a satisfiability function sat whose range is the truth values in T , a binary relation between states is an operational transition relation for sat with program P if: 1. The relation includes the transition hG [ H ; Si hG [ B ; S [ S 0 i if the program P contains ....

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Michael J. Maher. A logic programming view of CLP. In Proceedings of the Tenth International Conference on Logic Programming, pages 737--753, Budapest, July 1993. MIT Press.

.... : V A which extends by 4 Constructive negation by pruning morphism to terms and primitive constraints. Logical connectives and quantifiers are interpreted as usual, a constraint c is A solvable iff A j= 9c. It is not necessary for our purpose to suppose that A is solution compact [13] [19], we suppose only that the constraints are decidable in A, so that A can be presented by a decidable first order theory th(A) i.e. satisfying: 1. soundness) A j= th(A) 2. satisfaction completeness) either th(A) j= 9c or th(A) j= 9c, for any constraint c. As a constraint is any Sigma; V ....

....are closed by disjunction on false atoms (proposition 5.6) Example 4.3. Let us consider an example over the Herbrand domain formed with a constant 0 and an unary function symbols s. Clark s equational theory CET augmented with the domain closure axiom DCA is a complete theory for that structure [19], in particular we have CET DCA j= 8y x 6= s(y) x = 0. The following program is a classical example that shows that Fitting s operator Phi A P is not continuous: p(x) x = s(y)jp(y) q p(x) No atom is true in the powers of Phi A P and TP . At ordinal , all ground instances of ....

M.J. Maher, "A logic programming view of CLP", Proc. 10th International Conference on Logic Programming, pp.737-753, MIT Press, 1993.

....UPC Department LSI, Campus Nord, C Jordi Girona Salgado, 1 3, 08034 Barcelona, SPAIN. Tel: 34 3 4017018, Fax: 34 3 4017014, e mail: orejas lsi.upc.es [13, 27] seems to be adequate to be the basis for defining a compositional semantics for normal logic programs units. To our knowledge, only [18, 20, 29, 40, 9] provide some compositional semantic constructs for normal logic programs. In section 6 we compare the results presented in this paper and these approaches. It must be noted that compositionality is a very important property for defining the semantics of a modular unit. In particular, if the ....

....program fragments which is compositional and fully abstract with respect to standard program union. Actually, other kind of units and composition operations can be seen just as a special case. The kind of compositionality results obtained are quite more powerful than the results presented in [18, 20, 29, 40, 9]. In [18, 20, 29] different semantic definitions are provided for certain kinds of modular units which are shown to be compositional. However, they all impose (at least) the restriction (not needed in our work) that, for putting together (through the corresponding composition operation) two units, ....

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Maher, M., A logic programming view of CLP, in: Warren, D. S. (ed) Proc. 10th Int. Conf. on Logic Programming, 1993.

....de reformuler les s emantiques classiques dans un cadre homog ene et clair. Cette reformulation etend la vision grammaticale [5] aux programmes logiques avec contraintes. Elle permet de rendre compte des s emantiques classiques bas ees sur une interpr etation ou une th eorie des contraintes [9, 13, 10, 15, 7, 6, 3] ou bas ees sur des relations abstraites d ecrivant les solveurs de contraintes [10, 8, 14, 2, 3] Mais cette comparaison d epasse la cadre de cet article. Nous mettons en avant les squelettes qui sont intrins eques au programme. C est la structure id eale qui rassemblent toute l information ....

Michael J. Maher. A Logic Programming view of CLP. In Warren, editor, International Conference on Logic Programming, pages 737--753. MIT Press, 1993.

....language L, we will distinguish a class of quantifier free formulas called L constraints. The atomic formulas of L will be included in the class of L constraints. There will also be two distinguished L constraints true and false with obvious semantics. Similar assumptions have been made in [Mah93] in the contex of the CLP scheme. A set of L constraints will be the algebraic counterpart of the logical conjunction of its members. Thus we will freely mix the terms set of L constraints and conjunction of L constraints . We will assume that the reader is familiar with the notions of ....

....will be the algebraic counterpart of the logical conjunction of its members. Thus we will freely mix the terms set of L constraints and conjunction of L constraints . We will assume that the reader is familiar with the notions of solution, consistency and equivalence of sets of constraints [Mah93]. Let us now give some examples of constraint languages. Example 1. The language ECL (Equality Constraint Language) with predicate symbols = 6= and an infinite number of constants has been defined in [KKR90] The intended structure for this language interprets = as equality, 6= as nonequality ....

M. Maher. A Logic Programming View of CLP. In Proceedings of the 10th International Conference on Logic Programming, pages 737--753, 1993.

....are not finitely expressible in the program language (e.g. in CLP(R) 10] In fact, they are only handled through constraints. In LP, each answer, which is a logical consequence of the program, is covered by a single more general computed answer. the Herbrand s domain has the INC property [15]) In CLP, there is no single cover any more. For example, let us consider the CLP(R) program: fp(x) x 0; p(x) x 0g. Assume we expect the answer true to the goal p(x) It is not because true does not occur (in the less general sense) in fx 0; x 0g that an answer is lacking. We must ....

....[11] based on a constraint theory or interpretation. Our program semantics abstract the constraint semantics: a constraint interpretation D or a (non satisfaction complete) constraint theory T or an (incomplete) constraint solver A are particular cases. We show that classical program semantics [11, 8, 15, 12, 19] are instance of our own. We can remark that the three previous possible constraint semantics have not the same behaviours: T or D vs. A : For example, the constraint solver of CLP(R) provides three kinds of answers: yes (satisfiable constraint) no (unsatisfiable constraint) maybe (it cannot ....

M. J. Maher. A Logic Programming view of CLP. In Warren, editor, International Conference on Logic Programming, pages 737--753. MIT Press, 1993.

....cover, negative interpolation) Let F be a formula built over the constraint language. If FI(P ) j= D p(X 0 ) F then for each S 2 Z Gamma (p) the positive cover S 9 GammaX 0 F is valid in D. 11 Reduced to a singleton when the domain has the Independence of Negated Constraints [12] (see the example of the Introduction) Proof. Use the greatest D model of FI(P ) and lemma 1. 2 Again, Z Gamma (p) is halfway (interpolation formula) between p(X 0 ) and 9 GammaX 0 F . Corollary 10 Negative completeness and compactness. Let F be a formula built over the constraint ....

Michael J. Maher. A Logic Programming view of CLP. In Warren, editor, International Conference on Logic Programming, pages 737--753. MIT Press, 1993.

.... considerations, we develop the model of indefinite constraint databases by integrating the constraint database model of [KKR90] and the conditional table model of [IL84, Gra89] Our contributions to the theory of constraint databases is the following: ffl Following the approach of [JL87, Mah93] we develop three database schemes: ML relational databases, L constraint databases and indefinite L constraint databases (chapters 4 and 5) The language L defines the constraint vocabulary and ML is the structure over which L constraints will be interpreted. The last two schemes are ....

....The atomic formulas of L will be included in the class of L constraints. There will also be two distinguished L constraints true and false with obvious semantics. In the rest of this dissertation these assumptions will always be made implicitly. Similar assumptions have been made in [Mah93] in the context of the CLP scheme. A set of L constraints will be the algebraic counterpart of the logical conjunction of its members. Thus we will freely mix the terms set of L constraints and conjunction of L constraints . Definition 3.1.1 Let C be a set of L constraints in variables x 1 ; ....

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M. Maher. A Logic Programming View of CLP. In Proceedings of the 10th International Conference on Logic Programming, pages 737--753, 1993.

....extending the work of M.P Bonacina and J. Hsiang to CLP . 1 Introduction Constraint Logic Programming (CLP ) is a general framework providing formal foundations for a lot of languages based on the logic programming paradigm. A complete introduction of CLP is developed in [5] and more recently in [8]. In this framework, we point out two significant features : firstly, the semantic model can be founded on a specific domain of discourse, secondly the basic operational step in program execution is mainly based on determinating constraint solvability with regards to this domain. Despite its great ....

....P and a query Q, the mechanism produces a new set of constrained rewrite rules, containing only the Ans predicate, which is a synthetic description of the set of answers given by P for the query Q. Our paper is organized as follows : in section 2, we briefly review the CLP scheme as in [8] and we sum up the basic theoretical results. Section 3 is the declarative part where we define our transformation function and a declarative semantics for constraint rewrite programs. Section 4 is the operational part : we adapt linear completion mechanism to take into account constraint handling ....

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M.J. Maher. A logic programming view of clp. In MIT Press, editor, Proceedings of 10th ICLP, pages 737--753, 1993.

....notions. That is to say that we have to split the notion of result in two notions. A goal being given, there is a first notion of result which is a computed answer constraint, the computation being a success derivation. This is a first level of computation. In the formal logical semantics for CLP ([11, 12, 16, 10]) the relation between the goal G and the computed answer constraint c is formalized by using the implication c G. Even from a purely operational viewpoint we can consider that c G is computed. But there is a second level of computation that is to say another notion of finite computation ....

....for each store c 0 such that 8(c 0 c a) is expected (i.e. 8(c 0 c) is valid in D and 8(a c 0 ) is valid in I) 8(a c 0 ) is covered. Note that the previous definition is more intricate that in pure logic programming because there is no more independence of negated constraints [16]. But, if each valuation v is the unique solution of a store c v then 8(p( x) c v ) in some sense v(p( x) is covered if there exists a clause 8(p( x) b) of the definition of p such that v is a solution of the body b of the clause in I. c a is completely covered if for each valuation v ....

M. J. Maher. A Logic Programming view of CLP. In Warren, editor, International Conference on Logic Programming, pages 737--753. MIT Press, 1993.

....for an object oriented logic language. Recent works extend declarative diagnosis to constraint logic programming. The main difficulties is that Herbrand interpretations do not represent program semantics any more. Moreover, few constraint domains have the Independence of Negated Constraints [27]. Naish announce in [32] a prototype implemented for CLP(R) based on its scheme. 41] provide a formal inductive framework based on the grammatical view [12] in order to extend declarative diagnosis to CLP. 22] wrong answers) abstracts the constraint interpretation by a reject criterion in ....

M. J. Maher. A Logic Programming view of CLP. In Warren, editor, International Conference on Logic Programming, pages 737--753. MIT Press, 1993.

.... 0 satisfies 1. OE j= 9x ) Delta j= 9x 0 (provided no variable in x occurs in OE) 4 Note that our definition of independence involves existential quantification, which is not the case for the conventional definition [16] Our notion of independence agrees however with the definitions in [33, 20]. 2. OE j=j Delta ) 0 = A complete relative simplification procedure together with a test Delta j= 9xOE is the basic operational machinery one has to provide for the underlying constraint system in order to decide whether a reduction rule is applicable. Relative simplification ....

Michael J. Maher. A logic programming view of CLP. In David S. Warren, editor, Proceedings of the 10th DInternational Conference on Logic Programming, pages 737--753, Budapest, Hungary, June 1993. The MIT Press.

....of some domain values In fact, elements of the domain are only manipulated through constraints. ffl In LP, each answer, which is a logical consequence of the program, is covered by a single more general computed answer (the Herbrand s domain has the Independence of Negated Constraint property [17]) In CLP, there is no single cover any more. For example, in CLP(R) let us consider the program: fp(x) x 0 ; p(x) x 0g. Assume we expect the answer true to the goal p(x) Must we consider true as an insufficiency symptom and the previous program as wrong In fact, the IR theory has for ....

....frameworks [14] based on a theory or a domain. Our semantics abstract the constraint interpretation. Then, the constraint interpretation by a domain D or a (non satisfaction complete) theory T or an (incomplete) constraint solver A becomes particular case. We show that classical semantics [14, 11, 17, 15, 21] are instance of our own. We can remark that the three previous possible constraint interpretations have not the same behaviours: ffl T (or D) vs. A. For example, the constraint solver of CLP(R) provides three kinds of answers: yes (satisfiable constraint) no (unsatisfiable constraint) maybe ....

M. J. Maher. A Logic Programming view of CLP. In Warren, editor, International Conference on Logic Programming, pages 737--753. MIT Press, 1993.

....proposition stated above. In the CLP context, this means that we can restrict to only one derivation while answering any query, provided that we do not have any inequalities. In our context, it means that in certain cases we can do it without the MERGE rule. For details, the reader is referred to [Mah93] ffl If we assume the set of function symbols F to be finite, then we need the weak domain closure axiom in order to make our theory complete [Mah88] 8x f2F 9z x = f(z) This case is mainly considered in [CL89] But this point of view is restricted to Herbrand models only and increases the ....

Michael J. Maher. A logic programming view of CLP. In David S. Warren, editor, Proceedings of the 10th International Conference on Logic Programming, pages 737--753, Budapest, 1993. MIT Press, Cambridge, MA, London.

....interpretations do not represent program semantics. Moreover, in LP each answer which is a logical consequence of the program is covered by a more general computed answer. This is not true in CLP (although a sufficient condition for this covering property is the Independence of Negated Constraints [16]) So, new theoretical foundations are necessary. Other work were concerned with declarative debugging for constraint programs, but in different frameworks. 9] considers concurrent constraint (cc) programs and is based on the concept of observable and specified behaviours of cc processes. 3] ....

....whose free variables are y, such that hhead body; 9 Gamma y C(S)i is an incorrectness of P wrt I. Remark 31 Particular case of logic programs. In the domain H of the herbrand terms, the constraints which represent the substitutions have the Independence of Negated Constraints property [16]. A consequence of the second part of the lemma 24 and the Independence of Negated Constraints is : if P j= H c g then j= H c r, where r is an answer constraint for the goal g. This result is known in Logic Programming [15] as : if P j= g then there is a computed answer oe for g which is ....

M. J. Maher, A Logic Programming view of CLP, ICLP'93, pp 737-753, Warren Ed., 1993.

....P et la formule vrai X = a X = b est vraie dans le domaine de Herbrand. Si au contraire il y a d autres constantes alors il y a moins de contraintes c telles que c p(X) est vrai dans le plus petit mod ele de Herbrand de P . De plus, a cause de propri et es particuli eres a ce domaine (INC [19]) pour chacune de ces contraintes c, l une des formules c X = a ou c X = b est vraie dans le domaine de Herbrand. En termes de substitutions on retrouve que les seuls termes t pour lesquels p(t) est cons equence de P sont les termes a et b. 1 Rappelons que Prolog est un cas particulier de ....

.... p(X 0 ) est toujours vrai et sans int eret car ind ependant du programme P . Pour formaliser le solveur de contraintes nous introduisons, dans la section suivante, le crit ere de rejet. 9 R eduite a un singleton quand le domaine a la propri et e d Ind ependance des Contraintes N egatives [19], comme dans l exemple donn e en introduction. 5 Correction et compl etude (de la s emantique op erationnelle) Cette section etudie la correction et la compl etude de la s emantique op erationnelle th eorique classique des syst emes de PLC. 5.1 Crit ere de rejet Un crit ere de rejet est un ....

Michael J. Maher. A Logic Programming view of CLP. In Warren, editor, International Conference on Logic Programming, pages 737--753. MIT Press, 1993.

....extended in [3] and for CLP programs in [11] Compositionality vs. non monotonicity. However, in the development of semantics for normal logic programs, which employ the negation operator) compositionality has been widely disregarded. Notable exception to this are the papers by Maher [21] and Ferrand and Lallouet [9] comparison between these papers and this one is deferred to the concluding section) The reason of this disattention is that, because of the presence of the negation as failure mechanism, the semantics of normal logic programs is typically non monotonic. Now, ....

....a generic computational mechanism based on constraints with the logic programming framework. Such an integration results in a framework which for programs without negation preserves the existence of equivalent operational, model theoretic and fixpoint semantics. Indeed, as discussed in [21], most of the results which hold for definite (i.e. negation free) constraint logic programs can be lifted to CLP in a quite straightforward way. We refer to the recent survey [15] by Jaffar and Maher for the notation and the necessary background material about CLP. A CLP clause is a formula of ....

[Article contains additional citation context not shown here]

M. J. Maher. A Logic Programming view of CLP. In D. S. Warren, editor, Proc. Tenth Int'l Conf. on Logic Programming, pages 737--753. MIT Press, 1993.

....every language L, we will distinguish a class of quantifier free formulas called L constraints. The atomic formulas of L will be included in the class of L constraints. There will also be two distinguished L constraints true and false with obvious semantics. Similar assumptions have been made in [37] in the contex of the CLP scheme. A set of L constraints will be the algebraic counterpart of the logical conjunction of its members. Thus we will freely mix the terms set of L constraints and conjunction of L constraints . We will assume that the reader is familiar with the notions of ....

....will be the algebraic counterpart of the logical conjunction of its members. Thus we will freely mix the terms set of L constraints and conjunction of L constraints . We will assume that the reader is familiar with the notions of solution, consistency and equivalence of sets of constraints [37]. Let us now give some examples of constraint languages. The language ECL. The language ECL (Equality Constraint Language) with predicate symbols = 6= and an infinite number of constants has been defined in [26] The intended structure for this language interprets = as equality, 6= as ....

M. Maher. A Logic Programming View of CLP. In Proceedings of the 10th International Conference on Logic Programming, pages 737--753, 1993.

.... follow the point of view developed in [16] Since what we observe about a goal G is a set of constraints produced by its computations with regard to a program P , namely the computed answers constraints, these constraints are a more natural choice of observables than the success set as defined in [28]. Following theses ideas, we emphasize a declarative semantics based over sets of constrained atoms. 4.1 Semantics A constrained atom is a couple (c; A) where c is a satisfiable constraint such that V ar(c) V ar(A) The set of constrained atoms is denoted B and a subset I of B is a ....

M.J. Maher. A Logic Programming View of CLP. In MIT Press, editor, Proceedings of 10th ICLP, pages 737--753, 1993.

....for each store c 0 such that 8(c 0 c a) is expected (i.e. 8(c 0 c) is valid in D and 8(a c 0 ) is valid in I) 8(a c 0 ) is covered. Note that the previous definition is more intricate that in pure logic programming because there is no more independence of negated constraints [9]. But, if each valuation v is the unique solution of a store c v then 8(p( x) c v ) in some sense v(p( x) is covered if there exists a clause 8(p( x) b) of the definition of p such that v is a solution of the body b of the clause in I. c a is completely covered if for each valuation v ....

Michael J. Maher. A Logic Programming view of CLP. In Warren, editor, International Conference on Logic Programming, pages 737--753. MIT Press, 1993.

....over the domain of possibly empty sets of trees does not have the independence property: In the constraint f(x; y) 0 x 6 0 y 6 0, the conjuncts x 6 0 and y 6 0 are not independent from each other. izes (and is characterized by) the semantics of bottomup and top down computations [32]. A general study of the property shows its importance in various symbolic computation areas [31] In constraint data bases, the property allows the efficient containment test between constraint relations [26] The property is necessary for the inference of constrained functional dependencies in ....

M. J. Maher. A logic programming view of CLP. In D. S. Warren, editor, Proceedings of the 10th International Conference on Logic Programming, pages 737-- 753, Budapest, Hungary, June 1993. The MIT Press.

....rules for this. A constraint simplification rule is called globally preserving iff several instances of the same rule can be combined to preserve the set of solutions. P Expressibility of Proper Disjunctions: Not all constraint theories enjoy the independence of negated constraints property [Mah93] For satisfaction complete theories this means, it is not possible to express proper disjunctions, i.e. for all constraint formulae R, R 1 ; Delta Delta Delta ; R n it holds: T j= 8(R ) R 1 Delta Delta Delta R n ) T j= 8(R ) R k ) for some k (1 k n) For our example (finite ....

Michael J. Maher. A logic programming view of CLP. In David S. Warren, editor, Proceedings of the 10th International Conference on Logic Programming, pages 737--753. MIT Press, Cambridge, MA, London, England, 1993. Budapest, 1993.

....through constraints. ffl In LP, each answer, which is a logical consequence of the program, is covered by a single more general computed answer. In CLP, there is no single cover any more. A sufficient condition for the single cover property is the Independence of Negated Constraint (INC) [23] which is, unfortunately, verified by few interesting constraint domains. For example, in CLP(R) let us consider the program: p(x) x 0 p(x) x 0 Assume that for the goal p(x) we expect the answer true. Must we consider true as an insufficiency symptom and the previous program as ....

....framework [18] based on a theory or a domain. Our semantics abstract the constraint interpretation. Then, the constraint interpretation by a domain D or a (non satisfaction complete) theory T or an (incomplete) constraint solver A becomes particular case. We show that classical semantics [18, 14, 23, 19, 29, 19] are instance of our own. We can remark that the three previous possible constraint interpretations have not the same behaviours: ffl T (or D) vs. A. For example, the constraint solver of CLP(R) provides three kinds of answers: yes (satisfiable constraint) no (unsatisfiable constraint) maybe ....

[Article contains additional citation context not shown here]

Michael J. Maher. A Logic Programming view of CLP. In Warren, editor, International Conference on Logic Programming, pages 737--753. MIT Press, 1993.

....every language L, we will distinguish a class of quantifier free formulas called L constraints. The atomic formulas of L will be included in the class of L constraints. There will also be two distinguished L constraints true and false with obvious semantics. Similar assumptions have been made in [Mah93] in the contex of the CLP scheme. A set of L constraints will be the algebraic counterpart of the logical conjunction of its members. Thus we will freely mix the terms set of L constraints and conjunction of L constraints . We will assume that the reader is familiar with the notions of ....

....will be the algebraic counterpart of the logical conjunction of its members. Thus we will freely mix the terms set of L constraints and conjunction of L constraints . We will assume that the reader is familiar with the notions of solution, consistency and equivalence of sets of constraints [Mah93]. The following are some examples of a constraint language which will be our focus in this paper: 1. ECL (Equality Constraint Language) this language allows us to make statements about atomic data values [KKR90] ECL has predicate symbols = 6= and an infinite number of constants (the atomic ....

M. Maher. A Logic Programming View of CLP. In Proceedings of the 10th International Conference on Logic Programming, pages 737--753, 1993.

....notions. That is to say that we have to split the notion of result in two notions. A goal being given, there is a first notion of result which is a computed answer constraint, the computation being a success derivation. This is a first level of computation. In the formal logical semantics for CLP ([8, 9, 13, 7]) the relation between the goal G and the computed answer constraint c is formalized by using the implication c G. Even from a purely operational viewpoint we can consider that c G is computed. But there is a second level of computation that is to say another notion of finite computation ....

....c 0 such that c 0 c 2 a is expected (i.e. c 0 c is true in the constraint interpretation and a c 0 is expected) a c 0 is covered. Note that the previous definition is more intricate that in pure logic programming because there is no more independence of negated constraints [13]. But, if each valuation v is the unique solution of a store c v then v(a) is covered if there exists a clause of the definition of a such that v is a solution of the body of the clause in I. And c 2 a is completely covered if for each valuation v solution of c 2 a in I, v(a) is covered. Now, we ....

M. J. Maher. A Logic Programming view of CLP. In Warren, editor, International Conference on Logic Programming, pages 737--753. MIT Press, 1993.

....to Q 2 respectively. We will use empty query to refer to any query whose answer set is empty for any database instance. Clearly, a GCQ is empty if and only if its constraint is unsatisfiable. The following lemma relates GCQ containment to the existence of some particular containment mappings [Mah93]. Lemma 2.1 Let Q i (i = 1, 2) be GCQs. Let C i be the constraints in Q i . 1) If there are containment mappings # 1 , # k from Q 2 to Q 1 such that C 1 i=1 # i (C 2 ) then Q 1 Q 2 . Note that the constraint of a GCQ refers to built in predicates, rather than integrity ....

M. J. Maher. A logic programming view of CLP. In Proc. 10th International Conference on Logic Programming, pages 737--753, 1993.

....mapping from a GCQ Q 2 to another GCQ Q 1 is a mapping from Var(Q 2 ) to Arg(Q 1 ) such that it maps the output of Q 2 to the output of Q 1 , and maps each subgoal of Q 2 to a subgoal of Q 1 . The following lemma relates query containment to the existence of some particular containment mappings [13]. Lemma 1. Let Q i (i = 0, s) be GCQs. Let C i be the constraints in Q i . 1) If there are containment mappings # i,1 , # i,k i from Q i to Q 0 such that C 0 # # s i=1 # k i j=1 # i,j (C i ) then Q 0 # # s i=1 Q i . 2) If Q 1 , Q s are in normal form, C 0 is ....

M. J. Maher. A logic programming view of CLP. In Proc. 10th International Conference on Logic Programming, pages 737--753, 1993.

....to Q 2 respectively. We will use empty query to refer to any query whose answer set is empty for any database instance. Clearly, a GCQ is empty if and only if its constraint is unsatisfiable. The following lemma relates GCQ containment to the existence of some particular containment mappings [Mah93]. Lemma 2.1 Let Q i (i = 1, 2) be GCQs. Let C i be the constraints in Q i . 1) If there are containment mappings # 1 , # k from Q 2 to Q 1 such that C 1 # # k i=1 # i (C 2 ) then Q 1 # Q 2 . 1 Note that the constraint of a GCQ refers to built in predicates, rather than integrity ....

M. J. Maher. A logic programming view of CLP. In Proc. 10th International Conference on Logic Programming, pages 737--753, 1993.

....DCTGD. If is an CM from f to Q, then Q is equivalent under f to the union of Q 0 = fV : R; D (C)g and Q i = fV : R; P 0 i ) D (C C 0 i )g (i = 1; k) where the variables Y i are renamed to distinct variables not in V [ Var(R) The next lemma is slightly generalized from [8]. It can be used as a basic tool for detecting GCQ containment and equivalence. Lemma 2. Let Q i fV i : R i ; D i g (i = 0; 1; 2; n) be GCQs. Suppose Q 0 6= and Q 1 ; Qn are in NF. Then Q 0 v S n i=1 Q i i there are CMs i;1 ; i;k i from Q i to Q 0 such that D 0 n ....

....set as in Example 3. Let g be p(x) 9y q(x; y) As shown in Example 3, Ctest can detect that fx : p(x)g v= 4fx : p(x) q(x; y)g, thus we know 4 j= g. But Chase2 will not terminate and thus can not detect this. Chase1 can not detect this either, because the constraints do not have the INC property[8]. 6 Comparison with related work We have shown in the previous section that Ctest is strictly more powerful than the chase algorithms in [1] Two other most closely related papers are [6] and [4] The former studies conjunctive query containment under implication constraints and referential ....

M. J. Maher. A logic programming view of CLP. In Proc. 10th International Conference on Logic Programming, pages 737-753, Budapest, Hungary, 1993.

....our work is an extension of the notion of constraint independence (which is usually considered as a property of the query language) so that it is a property of speci c situations. Independence, when it holds, greatly improves computational performance on problems such as uniform query containment [Mah93] since disjunctive reasoning can be avoided. Thus the extended independence permits us to achieve a more ecient optimization process, based on the speci c elements of the application and the query. Many of the issues enumerated above apply also to distributed data (where remote data is ....

M. J. Maher. A logic programming view of CLP. In Proc. 10th International Conference on Logic Programming, pages 737-753, Budapest, Hungary, 1993.

....as with most of the other formalisms we will discuss, there is already a constraint domain involved the Herbrand domain. This simplifies the addition of constraints because we are simply replacing the Herbrand domain with another constraint domain. This replacement is discussed in detail in [38]. Briefly, unification problems become equational constraints; accumulated substitutions become accumulated constraints; unification is replaced by testing for unsatisfiability in D; Clark s equality theory is replaced by TD ; Herbrand models are replaced by D models; and groundedness of variables ....

....by existing facts p( x) c i , i = 1; n exactly when D j= c W n i=1 c i . In cases where D has INC this test reduces to a collection of tests D j= c c i , i = 1; n. When testing whether a conjunctive query Q 1 uniformly contains another Q 2 a similar disjunctive problem arises [25,24,38], which similarly simplifies when INC holds. For both these operations, the comparatively simpler definitions in the original formalism are special cases of the general definitions in which INC is exploited. On the other hand, uniform containment of positive recursive queries is equivalent to D ....

[Article contains additional citation context not shown here]

M.J. Maher, A Logic Programming View of CLP, Proc. 10th International Conference on Logic Programming, 737--753, MIT Press, 1993.

....is denoted by BOOL1 . An important property of constraint domains is generally phrased as a form of independence. This property has been investigated in some generality in [25] The significance of the property for the optimization of bottom up execution of CDBs and CLP programs is discussed in [26]. Definition 2.2 A constraint domain (D; L) has the independence of negative constraints property if, for all constraints c; c 1 ; c n 2 L, D j= 9 c :c 1 Delta Delta Delta :cn iff D j= 9 c :c i for i = 1; n. The following alternative formulation of independence of ....

M.J. Maher, A Logic Programming View of CLP, Proc. 10th International Conference on Logic Programming, MIT Press, 1993, 737--753.

No context found.

Maher, M.J., A Logic Programming View of CLP, Proc. 10th International Conference on Logic Programming, pp.737-753, MIT Press, 1993.

No context found.

M. Maher. A logic programmingview of CLP. In D. S. Warren, editor, Proceedings of the 10th International Conference on Logic Programming, pages 737-753. The MIT Press, 1993.

No context found.

Maher, M.J., "A Logic Programming View of CLP". Proc. 10th Intl. Conf. on Logic Programming, Budapest, 1993, pp. 737-753.

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