Sets and negation in a logic data base language (LDL1)

Abstract

first two ancedor rules and the parent base rel&on and a second layer conslstmg of the ezcl-ancestor rule The second layer may be computed once the first one has been computed The followmg 19 an madmlssrble LDL program smce it csnnot be strtified, the reason bemg that even must be m a layer below even (&Q denotes the successor of Xj m 0 in 91 s X)) <--in(X) even 0 even 11 s X)) <--int(X), 7 even(X) Set terms as arguments of LDL predicates can be used for two different purposes s&enumemtwn and set-groupmg Set enumeration 15 the process of constructing a set from ib elements as in the followmg example t-We4 Qc, Y, Z)) <--bd(X, I+), took(Y, Py), book(Z, Pz), Px+Py+Pz<lOO The example derives a reltion on sets of book htles from the boolc base rel&on such that their total price does not exceed 100 Dollars 'Ihe cardmabty of the sets m the denved relatron ls bounded by 3, duplicate elements are ehmmsted durmg the set con&u&on process so that books unth the ssme t&e but a different price e g , paperbacks and hardcovers sre ehmmated Observe that book-deal may yield singleton and doublet se$ 'Xhe followmg example IS of sebgroupmg m which $1 of the parts supplied by a supplier are grouped with the supplier number part-sets(S#, <P#>) <-supplier(S#, P#) Unhke sebenumerataon, where the set B constructed by hstmg its elements, m grouping the set K+ constructed by definmg lla elements by a properly (I e , a coqunctaon of predicates) that they satrsfy It follows that the cardma& of the grouped set m a derived relataon B unbounded (but finite) 'Ihe la& dlustr&ve example of an admissible LDL program 19 Included to demon&&?

Correspondence and translation for heterogeneous data

“…This is in the style of rule-based languages for objects, e.g., IQL [7], LDL [8], F-logic [20] and more precisely, of MedMaker [25]. The language we present in this section is tailored to correspondence derivation, and thus in some sense more limited.…”

“…Similar correspondences could be easily derived using more powerful languages previously proposed (e.g., LDL [8] or IQL [7]). But in these languages it would be much more di cult (sometimes impossible) to derive translation rules from given correspondence rules.…”

Une procédure de décision pour un problème de satisfiabilité dans un univers ensembliste héréditairement fini

“…Ainsi, en programmation en logique, plusieurs propositions d'extensions ensemblistes sont apparues récemment (le. LPS [22], LDL1 [4], {Log} [10] ou [32]). Ces approches se présentent comme une extension des signatures des langages de type Prolog par l'introduction des constructeurs de termes ensemblistes, et donc l'introduction d'expressions ensemblistes dans les clauses de Horn.…”

Embedding finite sets in a logic programming language

“…Other properties for which a number of extended unification algorithms 3 have been developed in the past, such as associativity, commutativity, distributivity and their combinations, are unfortunately not satisfied by the with operator. In particular, ACI-unification cannot be directly applied in our case.…”

“…In particular, logic programming languages have been advocated by many as a suitable setting for declarative programming with sets. Among them, the proposals of the logic database languages LDL [3] and LPS [11]. Also the recent work by Legeard and Legros [13] introduces sets in a Prolog-like language dealing with set expressions as constraints, while [23] analyzes the problem of logic programming with sets in its generality (including infinite sets).…”