W. Bibel. Constraint Satisfaction from a Deductive Viewpoint. Arti cial Intelligence, 35:401{ 413, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... i , i = 1; 2 [CM77] On the side of constraint satisfaction, a perusal of the literature reveals that all constraintsatisfaction problems studied can be viewed as special cases of the above homomorphism problem [FV93, FV99] see also [Jea97] It should be noted that several researchers, including [Bib88, Dec90, GJC94, PJ97], have observed that there are tight connections between constraint satisfaction problems and certain problems in relational databases. In particular, Gyssens, Jeavons and Cohen [GJC94] pointed out that the set of all solutions to a constraint satisfaction problem coincides with the join of ....

W. Bibel. Constraint satisfaction from a deductive viewpoint. Articial Intelligence, 35:401-413, 1988.

....verbatim from [ Jeavons et al. 1997 ] Many problems in Computer Science and Mathematics can be formulated as CSPs. For example, the famous problem of graph three colorability (3COL) is elegantly formulated as a CSP. Constraint Satisfiability is an NPcomplete problem. It is well known [ Bibel, 1988; Gyssens et al. 1994; Dechter, 1992 ] that the CS problem is equivalent to various database problems, e.g. to the problem of evaluating Boolean conjunctive queries over a relational database [ Maier, 1986 ] or to the equivalent problem of evaluating join dependencies on a given database. ....

W. Bibel. Constraint Satisfaction from a Deductive Viewpoint. AIJ, 35, 401--413, 1988.

....result is a dichotomy theorem which signi cantly generalises Schaefer s dichotomy for the Generalised Satis ability problem. 1 Introduction The constraint satisfaction problem provides a framework in which it is possible to express, in a natural way, a wide variety of combinatorial problems [2, 16, 18]. The aim in a constraint satisfaction problem is to nd an assignment of values to a given set of variables, subject to constraints on the values which can be assigned simultaneously to certain speci ed subsets of the variables. The mathematical framework used to describe constraint satisfaction ....

....set A, and any natural number n, the set of all n tuples of elements of A is denoted by A n . Any subset of A n is called an n ary relation on A. By RA we denote the set of all nitary relations on A. We now de ne the standard constraint satisfaction problem which has been widely studied [2, 13, 14, 15, 16, 18]. De nition 2.2 The constraint satisfaction problem (CSP) is the combinatorial decision problem with Instance: a triple (V; A; C) where 2 V is a set of variables; A is a domain of values; C is a set of constraints, fC 1 ; C q g. Each constraint C i 2 C is a pair hs i ; i i, ....

W. Bibel. Constraint satisfaction from a deductive viewpoint. Articial Intelligence, 35, 1988, 401-413.

....view every element of V as a relational attribute, every tuple of distinct elements of V as a relational scheme, and every contraint (t; R) as a relation R over the scheme t (cf. 2] It now follows from the de nition of CSP that it can be viewed as a join evaluation problem. Proposition 2. 1: [4, 32] A CSP instance (V; D; C) is solvable i 1 (t;R)2C R is nonempty. On the other hand, the homomorphism formulation is intimately related to conjunctive query evaluation. A conjunctive query Q is a query de nable by a positive existential rst order formula (X1 ; Xn ) having conjunction as ....

W. Bibel. Constraint satisfaction from a deductive viewpoint. Articial Intelligence, 35:401-413, 1988.

....in principle, straightforward backtracking techniques can be used to solve it. To improve the efficiency and eliminate redundancies exploited by a simple minded backtracking, a number of intelligent backtracking techniques was proposed, e.g. Bruynooghe and Pereira, 1984 ] Alternatively, Bibel [ 1988 ] proposes a general bottom up, lazy evaluation method which transforms a constraint satisfaction problem into the problem of evaluating a database expression. In our approach, we do not address the backtracking redundancies, but rather reduce the search by first satisfying more abstract ....

Bibel, W. Constraint satisfaction from a deductive viewpoint. Artificial Intelligence 35, pp. 401-413.

.... i , i = 1; 2 [CM77] On the side of constraint satisfaction, a perusal of the literature reveals that all constraintsatisfaction problems studied can be viewed as special cases of the above homomorphism problem [FV93, FV99] see also [Jea97] It should be noted that several researchers, including [Bib88, Dec90, GJC94, PJ97], have observed that there are tight connections between constraint satisfaction problems and certain problems in relational databases. In particular, Gyssens, Jeavons and Cohen [GJC94] pointed out that the set of all solutions to a constraint satisfaction problem coincides with the join of ....

W. Bibel. Constraint satisfaction from a deductive viewpoint. Artificial Intelligence, 35:401--413, 1988.

.... as summarized in [1] have been developed to solve constraint problems such as Predicate Calculus [2] Propositional Logic [3] Truth Maintenance [4] Integer Programming [5] Automata Theory [6] Graph Theory [7] Hill Climbing [8] Neural Networks [9] Genetic Algorithms [10] Relational Algebra [11], Constraint Synthesis [12] Disjunctive Decomposition [13] Conjunctive Decomposition [14] Constraint Logic Programming [15] and GSAT [16] We can classify these techniques into (1) problem reduction, 2) solution synthesis, and (3) searching. In problem reduction, we first identify redundant ....

W. Bibel, "Constraint satisfaction from a deductive viewpoint," Artificial Intelligence, vol. 35, pp. 401--413, July 1988.

.... homomorphism problem [FV93] see also [Jea97] Although research in conjunctive query containment and constraint satisfaction has focused on the search for tractable cases of these problems, it is fair to say that overall there has been little communication between the two communities (but see [Bib88, Dec90, GJC94, PJ97], which drew a connection between constraint satisfaction problems and satisfaction of join dependencies in relational databases) Furthermore, there does not seem to be much awareness that both communities are tackling essentially the same problem. One of our main goals in this paper is to bring ....

W. Bibel. Constraint satisfaction from a deductive viewpoint. Artificial Intelligence, 35:401-- 413, 1988.

....restricted to the case in which one of the parent clauses is a unit. Where k = 2 the same inference results in a negative 8 We do not investigate this interesting suggestion further in the present paper. See [11] for a brief account of it. 9 We are not the first to observe such things. Bibel [4] at least had a similar idea and we expect others have too. unit clause :Fax 1 which can similarly resolve with a positive clause exactly capturing the space reduction step of removing one of the possible values from S a . Where k = 1 the resolvant is the null clause, the derivation of which ....

W. Bibel, Constraint Satisfaction from a Deductive Viewpoint, Artificial Intelligence 35 (1988), pp. 401--413.

....using a given collection of explicit constraint types. The approach taken is interdisciplinary, drawing on the results of relational database theory. The close relationship between the theory of constraint satisfaction problems and relational databases has been pointed out by several authors [2, 4, 6, 15]. In this paper we present a result concerning the algebraic properties of relations which sharpens an earlier result of Paredaens [13] in database theory, and thereby allows an application to constraint satisfaction problems. The result obtained by Paredaens states that a database relation can be ....

....SPJ algebra. Most importantly of all, for our purposes, the join operator (1) 14] can be expressed in the SPJ algebra. Now, it is well known that the set of solutions to a constraint satisfaction problem (expressed as a relation) can be obtained by performing a join operation on the constraints [2, 6]. The possible derived constraints are the projections of these sets of solutions, as the following definition indicates. Definition 5. A constraint can be derived from a set of relations R if it is equal to some projection of the set of solutions to some constraint satisfaction problem with ....

W. Bibel. Constraint satisfaction from a deductive viewpoint. Artificial Intelligence, 35, 1988, pp. 401--413.

....The relational database model [5, 23, 31] has tackled this problem by storing a database as a number of projections from which the original relation may be reconstructed. The connection between constraint satisfaction problems and relational databases has been pointed out by a number of authors [4, 8, 33], and results obtained in the field of constraint satisfaction problems have been used to obtain new results on database relations [8] Here, we intend to investigate the interaction between the two fields in the opposite direction, which we believe to be very promising. In order to do this we ....

Bibel, W., "Constraint Satisfaction From a Deductive Viewpoint," Artificial Intelligence 35 (1988), pp. 401--413.

....shall denote the variables involved in C I ; the cardinality of this index set is the arity of the constraint. The maximum arity of the constraints is the highest index level: h : max C I fjIj j I f1; ngg. In the algorithms the operations semi join n and natural equi join . see also [2] and [17] may get understood as in the database field. We use the following abbreviations: CS i : entire set of constraints of arity i whose index sets are proper subsets of the index set of a specific constraint of arity i 1. See the algorithms in the following passage. jCS i j = i 1. ....

Wolfgang Bibel. Constraint Satisfaction from a Deductive Viewpoint. Artificial Intelligence, 35(3):401--413, 1988. Elsevier Science Publishers B.V., Amsterdam, The Netherlands.

....following notation. Notation 1 For any set D and any natural number n, we denote the set of all n tuples of elements of D by D n . For any tuple t 2 D n and any i in the range 1 to n, we denote the value in the ith coordinate position of t by t[i] The tuple t will be written in the form ht[1]; t[2] t[n]i. Definition 1. A subset of D n is called an n ary relation over D. Example 1 We now describe four relations which will be used as examples throughout the paper. Each of these relations is a set of tuples of elements from the set D = f0; 1; 2g, as defined below: R 1 = f ....

....operations from relational algebra [2] Definition 2. We define the following operations on relations. ffl Let R 1 be an n ary relation over a set D and let R 2 be an m ary relation over D. The Cartesian product R 1 Theta R 2 is defined to be the (n m) ary relation R 1 Theta R 2 = fht[1]; t[2] t[n m]i j (ht[1] t[2] t[n]i 2 R 1 ) ht[n 1] t[n 2] t[n m]i 2 R 2 )g: ffl Let R be an n ary relation over a set D. Let 1 i; j n. The equality selection oe i=j (R) is defined to be the n ary relation oe i=j (R) ft 2 R j t[i] t[j]g: ffl Let R be ....

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Bibel, W., "Constraint Satisfaction From a Deductive Viewpoint", Artificial Intelligence 35 , (1988), pp. 401--413.

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W. Bibel. Constraint Satisfaction from a Deductive Viewpoint. Arti cial Intelligence, 35:401{ 413, 1988.

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W. Bibel. Constraint Satisfaction from a Deductive Viewpoint. Artificial Intelligence, 35:401-- 413, 1988.

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W. Bibel. Constraint satisfaction from a deductive viewpoint. Artificial Intelligence, 35:401--413, 1988.

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