C. Beeri, S. Naqvi, R. Ramakrishnan, O. Shmueli, and S. Tsur. Sets and negation in a logic database language. In Proceedings of the Sixth ACM Symposium on Principles of Database Systems, pages 21--37. ACM Press, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the specification task and also helps in preventing inconsistencies in specifications. It should be noted that the language we use to define correspondence rules is rather 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 difficult (sometimes impossible) to derive translation rules from given correspondence rules. Nevertheless, our language is expressive enough to describe many desired correspondences translations. As will be seen, correspondence rules ....

....The correspondence predicates may have arbitrary arity, and also, because of data duplication, some n m correspondences may be introduced. 3 The Core Language In this section, we introduce the core language. 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. However, we will consider in a next section a powerful new feature. We assume the existence of three infinite sorts: a sort ....

C. Beeri, S. Naqvi, R. Ramakrishnan, O. Shmueli, and S. Tsur. Sets and negation in a logic database language (LDL1). In Proc. ACM SIGMOD/SIGACT Conf. on Princ. of Database Syst. (PODS), pages 21--37, 1987. 25

....programming languages such as SETL [43] Of interest to databases is the development of calculi, algebra and rule based languages for such structured objects which allows to naturally incorporate them in dooD systems. The introduction of the set constructor in a rule based language [16, 4, 34] leads to problems resembling those encountered when allowing negative literals in the body of rules. Indeed, consider the following rules (in COL) y 2 child(x) parent(x; y) child less person(x) person(x) child(x) which defines a function child over the set of persons and a predicate ....

C. Beeri, S. Naqvi, R. Ramakrishnan, O. Shmueli, and S. Tsur. Sets and negation in a logic database language (LDL1). In Proc. ACM Symp. on Principles of Database Systems, pages 21--37, 1987.

....the Expressive Power of Logic Programming Languages with Sets Gabriel M. Kuper IBM T. J. Watson Research Laboratory Yorktown Heights, New York 1 Introduction Several recent papers [Kup87a] Kup87b] [BNR 87] have proposed adding sets to logic programming. Their motivation was to combine recent work on extending relational database theory to more general structures, with work on using logic programming as a database query language. While the motivation was similar, the languages proposed in these ....

....over a set, which can be regarded as a logical, nonprocedural, equivalent of iteration over the elements of a set. Kup87b] shows that adding such a form of quantification preserves the minimal model, least fixpoint and procedural semantics of [vEK76] On the other hand, the LDL language of [BNR 87] uses set construction, or grouping, as the key construct. Other operations on sets can then be defined in terms of grouping. Grouping turns out to be an extremely powerful operation; in fact even negation can be defined in terms of it. Since LDL programs, in general, may not have unique minimal ....

[Article contains additional citation context not shown here]

Catriel Beeri, Shamim Naqvi, Raghu Ramakrishnan, Oded Shmueli, and Shalom Tsur. Sets and negation in a logic database language (LDL1). In Proc. Sixth Annual ACM Symposium on Principles of Database Systems, pages 21--37, ACM, 1987.

....Such languages provide a very natural way to express queries on a relational database. Furthermore, by allowing recursion, we get a language that is more powerful than the relational algebra of Codd [AU79] There has been very little work, so far, on combining these two approaches [BK86] TZ86] [BNR 87] [SN87] By this we mean both extending the data model to capture more of the semantics of the data, while at the same time using a logic programming language as the query language. In order to do this, we need to have some way to deal with complex objects in logic programs. Some types of data ....

....known values, the body can be reduced to a normal 2 Horn clause, i.e. the conjunction of the body (without the quantifiers) over all the elements of the sets. We shall see that our extension of Horn clause logic, unlike extensions that allow arbitrary quantification on the right hand side [LT84] [BNR 87], preserves the semantics of Horn clause logic. Example 1: The disj predicate could be defined by the rule disj(X; Y ) 8x 2 X) 8y 2 Y ) x 6= y) x 6= y could be defined as : x = y) negation will be discussed later on. Example 2: LPS contains the membership predicate as a primitive. ....

[Article contains additional citation context not shown here]

Catriel Beeri, Shamim Naqvi, Raghu Ramakrishnan, Oded Shmueli, and Shalom Tsur. Sets and negation in a logic database language (LDL1). In Proc. Sixth Annual ACM Symposium on Principles of Database Systems, pages 21--37, ACM, 1987.

.... hob(x) fg; hob(x) 3 tv bored(x) If John has no hobby, then hob(John) fg by the Closed World Assumption, so John is bored. Therefore, hob(john) 3 tv is deduced. The problem is very similar to the problem of recursion through negation. Indeed, the notion of stratification is extended [2, 13] in order to also prohibit such cases of recursion. Formal treatments of stratification for our context can be found in [2, 4] The notion of stratification may seem a bit obscure at first glance. However, the constraint is reasonably easy to explain syntactically. Then, all the user has to know ....

C. Beeri and al. Sets and Negation in a Logic Database Language (LDL1). In Proc. ACM PODS, 21--37, 1987.

....and the fixpoint semantics of our paper are very similar to those of [18, 19, 17] In [28, 29] it is shown how to integrate (flat) finite sets in logic programming with the idea of database applications. Sets and other collection types were also considered in the database related papers [6, 5, 34, 20, 44, 38]. Those papers study the expressive power and practical applications of languages with collection types. Bounded quantification over hereditarily finite sets is introduced in [14] In that paper sets are added to logic programming using a special set unification algorithm. In [4, 3] a limited ....

C. Beeri, Sh. Naqvi, R. Ramakrishnan, O. Shmueli, and Sh. Tsur. Sets and negation in a logic database language (LDL1). In Proc. 6th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pages 21--36. ACM Press, 1987.

....is not a commutative operation. Example 4. 2: Suppose we have two lists L 1 and L 2 with values 4 2 5 and 7 9 6 , then LIST PRODUCT(L 1 ; L 2 ) has value o 1 ; o 2 ; o 9 where o i for i = 1; 2; 9 are the oids of tuples with values [4 7] 4 9] 4 6] 2 7] 2 9] 2 6] [5 7], 5 9] and [5 6] respectively. LIST DE(list object , eq op) list object : Eliminates duplicates from lists. The first object is retained. LIST COLLAPSE(list object) list object : Returns a list by concatenating all the lists within the input list in the same order. LIST APPLY(list object ....

....not a commutative operation. Example 4. 2: Suppose we have two lists L 1 and L 2 with values 4 2 5 and 7 9 6 , then LIST PRODUCT(L 1 ; L 2 ) has value o 1 ; o 2 ; o 9 where o i for i = 1; 2; 9 are the oids of tuples with values [4 7] 4 9] 4 6] 2 7] 2 9] 2 6] 5 7] [5 9], and [5 6] respectively. LIST DE(list object , eq op) list object : Eliminates duplicates from lists. The first object is retained. LIST COLLAPSE(list object) list object : Returns a list by concatenating all the lists within the input list in the same order. LIST APPLY(list object , ....

[Article contains additional citation context not shown here]

C. Beeri, S. Naqvi, R. Ramakrishnan, O. Shmueli, and S. Tsur. Sets and negation in a logic database language (LDL1). Proc. of ACM PODS Symposium, 1987.

....analysis of that basic case. Problems implied by the 2 Preliminary versions of these ideas also appeared in [11] and [5] introduction of intensional sets, such as fx 2 S : g, were already addressed in [7] but no precise solution has emerged there. It is also the central problem discussed in [3]. It is well accepted that this problem is strongly connected with that of introducing negation in Horn clause logic. A proposal for embedding intensional sets in the CLP based language of this paper augmented with intensional negation is under development at present [5] By allowing membership to ....

C. Beeri, S. Naqvi, O. Shmuelli, and S. Tsur. Sets and Negation in a Logic Database Language. Proc. 6th ACM SIGMOD Symp., 1987.

....languages there has also been some work in the direction of extending rule based languages (DATALOG) to deal with complex structures. In [3] a rule language has been presented and compared with the algebra and the safe calculus. LDL has also been extended to deal with set valued attributes ([17], see also the chapter of this volume) Another calculus for complex objects has been presented in [10] Recent research dealing with set values in logic based languages, such as [6, 2, 7, 25, 54, 62, 64, 71, 21] was carried out in the framework of object oriented models, but the impacts of ....

C. Beeri, S. Naqvi, R. Ramakrishnan, O. Shmueli, and S. Tsur. Sets and negation in a logic database language (LDL1). In Proc. ACM SIGACT/SIGMOD Symp. on Principles of Database Systems, pages 21--37, San Diego, March 1987. ACM, New York.

.... construct in the definition of a predicate, for instance: minimum p (X) minimum(Set;N) minimum(fy : p(y)g; X) N 2 Set; 8Z 2 Set) lessorequal(N; Z) In order to compute minimum p we should be able to collect the set of computed answers of another predicate (set grouping facility [1]) Let us try to define such a facility using the language defined so far: subsetof p (X) 8Y 2 X) p(Y ) such a predicate however does not compute fy : p(y)g but all its subsets. Actually, we need a negative information, in order to be able to say: there does not exist any element Z not ....

C. Beeri, S. Naqvi et al. Set and Negation in a Logic Database Language. In Proceedings 6 th ACM SIGMOD Symposium, 1987.

....devoted to embedding sets into logic programming languages. Indeed such languages seem to be good candidates for hosting set data abstractions, thanks to their highly declarative nature. Attention to incorporating sets into logic based languages has come first from the field of deductive databases [1, 6, 7, 33, 42]. Recently, however, a number of papers have addressed the problem also in a wider setting. General purpose set constructs and basic operations on sets have been added to general logic based frameworks: pure logic programming languages [16, 17] equational logic languages [28, 29] and Constraint ....

....30 A. DOVIER et al. is first translated to the equivalent goal : Gamma setof p(S1) setof q(S2) S1 = S2 where setof q provide the required set collection facility and S1 and S2 will be instantiated to set terms. The set collection mechanism could be a built in feature of the language as in [6, 42]. The programmer could then write clauses (called grouping clauses) of the form s(hXi; Y 1 ; Yn ) Gamma p(X; Y 1 ; Yn ) The informal interpretation of such a clause is that, for a given instantiation of Y 1 ; Yn , all the values of X for which p(X; Y 1 ; Yn ) ....

[Article contains additional citation context not shown here]

Beeri, C., Naqvi, S., Ramakrishnan, R., Shmueli, O., and Tsur, S., Sets and Negation in a Logic Database Language (LDL1), in: Proceedings of the 6th ACM SIGMOD Symposium, 1987.

....problem with bottom up computation is that it does not naturally make use of ground terms in a literal in the same goal driven way that a top down computation does. A direct consequence is that many irrelevant facts may be generated during a bottom up computation. The magic set approach [3, 6, 15, 5, 1] to deductive databases performs a compile time transformation of the database, based on the query, into an equivalent form that enables a bottom up computation to focus on the relevant tuples. The magic set solution is well suited to exploiting ground information in computing relevant facts. A ....

C. Beeri, S. Naqvi, R. Ramakrishnan, O. Shmueli, and S. Tsur. Sets and negation in a logic database language (ldl1). In Proceedings of the 6th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pages 21--37, San Diego, California, 1987.

....On the other hand, deductive databases rely on a flat data model and do not support data abstraction. It therefore can be expected that combining the two paradigms will pay off in a big way. A great number of attempts to combine the two approaches has been reported in the literature (e.g. [1, 2, 3, 14, 17, 18, 35, 58, 60, 68, 66, 73, 93, 11]) but, in our opinion, none was entirely successful. These approaches would either seriously restrict object structure and queries; or they would sacrifice declarativity by adding extra logical features; or they would omit important aspects of object oriented systems, such as typing and ....

....involves the use of negation as failure, too. Therefore, comparing sets in F logic and LDL has the same complexity. 12 DATA MODELING IN F LOGIC 47 Data restructuring. The next example is an adaptation from [3] The issue here is the representation of data functions of COL [2] and grouping of LDL [17]. Consider a relation, graph(X; Y ) whose tuples represent edges of a graph. The task is to re structure this graph by representing it as a set of nodes, such that each node points to a set of its descendants. The corresponding F program is very simple: rebuiltGraph [nodes Node ....

C. Beeri, S. Naqvi, O. Shmueli, and S. Tsur. Sets and negation in a logic database language (LDL). Technical report, MCC, 1987.

....data from one world or the other, etc. can be specified using a single declarative set of rules. It should be noted that the language we use to define correspondence rules is very limited. Similar correspondences could be easily derived using more powerful languages previously proposed (e.g. LDL [5] or IQL [4] However, it would be much more difficult in these languages to derive translation rules from given correspondence rules. As will be seen, correspondence rules have a very simple and intuitive graphical representation. Indeed, the present work is intended to serve as the basis for a ....

....The correspondence predicates may have arbitrary arity, and also, because of data duplication, some n m correspondences may be introduced. 4 The Core Language In this section, we develop the core language. This is in the style of rule based languages for objects, e.g. IQL [4] LDL [5], F logic [15] and more precisely, of MedMaker [19] Observe however that the language we present in this section is tailored to correspondence derivation, and thus in some sense more limited. However, we will consider in a next section a powerful new feature. We assume the existence of two ....

C. Beeri, S. Naqvi, R. Ramakrishnan, O. Shmueli, and S. Tsur. Sets and negation in a logic database language (LDL1). In Proc. ACM SIGMOD/SIGACT Conf. on Princ. of Database Syst. (PODS), pages 21--37, 1987.

....If there are no inconsistencies, the result is meaningful, i.e. has a unique minimal model semantics. 3.6 Comparison to other approaches In this section, we will summarize some of the main differences of existing rule based languages for complex objects or object oriented data models. ffl LDL [11], COL [3] and HILOG [12] are complex object languages including set constructors, set valued functions or nested relations. The underlying model of these languages does not include the concepts of object identity, classes and inheritance. The handling of sets is different to our approach. The ....

....partial order (see Definition 14) This is in the spirit of [8] and we achieve the desired monotonicity property. Hence, using the classification of Kifer [25] the semantics presented here is first order, i.e. no meta concept like stratification is needed as, for instance, in COL [3] or in LDL [11]. On the other hand, the expressiveness of the language is slightly restricted with respect to the manipulation of sets. For both kinds of attributes set valued or function valued 4 OBJECT RULES AND THEIR SEMANTICS 41 different operations and selection conditions are expressible. Hence, ....

C. Beeri, S. Naqvi, R. Ramakrishnan, O. Shmueli, and S. Tsur. Sets and negation in a logic database language (LDL1). In Proc. ACM SIGACT/SIGMOD Symp. on Principles of Database Systems, volume 6, pages 21--37. ACM New York, 1987.

....On the other hand, deductive databases normally use flat data model and do not support object identity and data abstraction. It therefore can be expected that combining the two paradigms will yield significant benefits. A number of attempts to combine the two approaches [AB88, AG87, BK89, BNST87, BNT88, CW89] KW89, Kup87, KV84, Mai86, RKS85] have been reported in the literature, but, in our opinion, none of them succeeds in meeting all of the above goals. These approaches either do not support object identity, or restrict the kinds of complex objects and queries one can use, or do not ....

....has to offer. Unfortunately, in order to be able to group elements into sets under Egli Milner s ordering, we would have to change F logic syntax by introducing variables over sets. Particularly, instead of being first order, as in O logic [KW89] set grouping will become second order, as in LDL [BNST87] which makes handling of sets an expensive proposition. 2.4 Databases and Queries A database is a set of formulae. We distinguish between the extensional part of a database (the set of F terms) and its intensional part (the set of formulae more complex than F terms) If S is a set of ....

C. Beeri, S. Naqvi, O. Shmueli, and S. Tsur. Sets and negation in a logic database language (LDL). Technical report, MCC, 1987.

....algebra operations. The language in which we express the syntax and semantics of the built in predicates for extended relational algebra operations is LDL=NR, a logic database language for nested relations. LDL=NR replaces predicate symbols and function symbols, as used in logic database languages [2] [9] 15] by tuple terms and set terms, respectively as used in [4] 5] so that LDL=NR can uniformly handle nested relations at arbitrary levels of nesting in a hierarchical structure and has full expressive power for manipulating mutually nested tuples and sets. LDL=NR, as defined, is a ....

C. Beeri, S. Naqvi, R. Ramakirishnan, O. Shmueli, and S. Tsur. Sets and Negation in a Logic Database Language (LDL1). In Proceedings of the Sixth ACM SIGACTSIGMOD Symposium on Principles on Database Systems, New York, 1987. ACM.

.... DeltaD. If a new clause includes equalities, it can be used for back demodulation, i.e. rewriting applied to clauses from D. This loop is used in most implementations of binary resolution and hyperresolution [Rob65, Rob65a] the inverse method [Mas67, Vor92] implementations based on magic sets [BMSU86, BNRST87], tabled computations of logic programs [TS86, War92, SR93] various deductive databases procedures, for example query answering and integrity checking [LT85, LST86, Dec86, Das92] bottom up static analysis of logic programs [CD93] constraint logic programming, parsing [TR94] production ....

C. Beeri, Sh. Naqvi, R. Ramakrishnan, O. Shmueli, and Sh. Tsur. Sets and negation in a logic database language (LDL1). In Proc. 6th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pages 21--36. ACM Press, 1987.

....and semantic models, languages that allow one to access such structures are important and worthy of study. We consider a calculus based language (similar to the one proposed by Jacobs [37] and those in [34, 41] an algebra, and a logic programming language (similar to those presented in [15, 3, 16, 44, 42]) 1 In the original report [2] we used the term complex object instead of complex value. Since then, this term has been more and more associated to the object oriented paradigm and we decided not to use it. Note that in particular, our complex values have no identity. 2 Our main results ....

....to our strict safety, are exhibited in [30] We study also here a rule based language. In the rule based paradigm, nesting can be expressed in many ways. Indeed, a main difference between various proposals of logic programming with a set construct is in their approach to nesting: grouping in LDL [15], data functions in COL [3] and a form of universal quantification in [42] In [43] equivalence of various rule based languages is proved. In [31] it is shown that various programming primitives are interchangeable: powerset, fixpoint, various iterators. As already mentioned, the current paper ....

[Article contains additional citation context not shown here]

Beeri, C.,S. Naqvi, R. Ramakrishnan, O. Shmueli, and S.Tsur, Sets and Negation in a Logic Database Language. Proc. 6th PODS (March 1987).

No context found.

Catriel Beeri, Shamim Naqvi, Raghu Ramakrishnan, Oded Shmueli, and Shalom Tsur. Sets and negation in a logic database language. In Proceedings of the ACM Symposium on Principles of Database Systems, pages 21--37, San Diego, California, March 1987.

....work [11, 13] they can be used for sophisticated text searching (where the events are the various characters in the text) and they can also be used to examine histories in the context of historical databases. Event expressions can also be incorporated into query languages such as SQL [4] or LDL [1] by using a relation to record the event and the event order [7] APPENDIX 1. OCCURRENCE TUPLES If v is an event occurrence in a history, h, then succ(v) denotes the event occurrence immediately following v in h (i.e. succ(v) is the event occurrence w whose event identifier is larger than ....

C. Beeri, S. Naqvi, R. Ramakrishnan, O. Shmueli and S. Tsur, "Sets and Negation in a Logic Database Language", Proc. 6th Symp. Principles of Database Systems, San Diego, Calif., March 1987, 21-37.

....and semantic models, languages that allow one to access such structures are important and worthy of study. We consider a calculus based language (similar to the one proposed by Jacobs [31] and those in [28, 35] an algebra, and a logic programming language (similar to those presented in [13, 14, 37, 36, 4]) 1 Note that the word object as used in complex object , and in this paper, does not refer to the notion of object as known in object oriented database models. In particular, our objects have no identity that is distinct from their values. They are essentially composite values. Our main ....

....that this would result in no gain of expressivity, i.e. complex value fixpoint is no more expressive than (complex value) calculus. In the same spirit of introducing recursion, we now present a simple language based on recursive rules. We handle negation using the concept of layers as in [9, 4, 13, 40, 49] and others. Given a database scheme, the relation names in it, b R 1 ; b R n , are called base relations. The language will use names of additional relations, called derived relations. The language is based on the calculus. Thus, we define atomic formulas as before, except that ....

Beeri, C., S. Naqvi, R. Ramakrishnan, O. Shmueli, and S.Tsur, Sets and Negation in a Logic Database Language. Proc. 6th PODS (March 1987).

....many possible variations of the rewrite strategy, and it is important to understand how to choose between them. This is an important problem that needs to be addressed. An important issue is the generalization of these algorithms for dealing with negation in rule bodies, and we address this in [Beeri et al. 87] The problem is also studied in [Balbin et al. 87] 12. Acknowledgements We wish to thank Francois Bancilhon for stimulating our interest in this work, and Oded Shmueli, Jeffrey Ullman and Carlo Zaniolo for many useful discussions. 13. ....

"Sets and Negation in a Logic Database Language (LDL1)," C. Beeri, S. Naqvi, R. Ramakrishnan, O. Shmueli and S. Tsur, Proc. 6th ACM SIGMOD-SIGACT Symposium on Principles of Database Systems, 1987.

No context found.

C. Beeri, S. Naqvi, R. Ramakrishnan, O. Shmueli, and S. Tsur. Sets and negation in a logic database language. In Proceedings of the Sixth ACM Symposium on Principles of Database Systems, pages 21--37. ACM Press, 1987.

No context found.

C. Beeri, S. Naqvi, R. Ramakrishnan, O. Schmueli, and S. Tsur. Sets and Negation in a Logic Database Language (LDL1). In Proc. 6th ACM Symp. on Principles of Database Systems, pages 21--37, 1987.

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