Serge Abiteboul and Richard Hull. Data functions, datalog and negation. In Proceedings of ACM SIGMOD 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of OO databases are proposed. Bancilhon [8] and Atkinson et al. in the ObjectOriented Database System Manifesto [6] list a number of features which they argue are essential for OO database systems. Parallel to this, a number of formalizations of OO models have been proposed, such as COL [1, 2, 3], F logic [33] HILOG [13] ILOG [29] IQL [4, 5] formalizations of 02 [36, 35] OBJ and related languages [20, 21, 22, 23, 25, 38] OBLOG [15, 19, 17, 43] and CMSL [50, 46] Beeri [9] gives a survey of some issues. Even though these papers are top down, there is not yet any root concept from ....

S. Abiteboul and R. Hull. Data functions, Datalog and negation. In ACM-SIGMOD International Conference on Management of Data, pages 143 153, Chicago, June 1-3 1988. ACM. Sigmod Record, Vol. 17.

....every input instance possibly allowing for nonfunctionality (resp. non finiteness) Unfortunately,itturns out[12]thatthe problems of decidingwhether a given program is finiteorfunctional is in general unsolvable. In particural, functionalityisundecidable even for programs without oid invention [2]. 19 6 Instances as Herbrandinterpretations In this section webrieflyexplain howanIsaLog instance can be represented bymeans of a set of facts, a preliminary tool for thedescription of other semantics for IsaLog programs. Givenascheme S = C#R#F#typ# isa) the Herbrand universe U S for S is ....

S. Abiteboul and R. Hull. Datafunctions, Datalog andnegation. In ACM SIGMOD InternationalConf. on Management of Data, pages 143--153, 1988.

....when restricted to Datalog programs, are trivially decidable since the relevant relations are finite. When we wish to determine FDs using only the IDB and FDs on the EDB these problems are undecidable, even in the case of Datalog programs. This follows from a result due to Abiteboul and Hull [1]. Faced with uncomputability, we suggest the following methodology for establishing FDs: To establish an FD d over the t relation R corresponding to a rule r, find a set T of FDs over relations of GC such that: ffl T b d and for each FD fpg I J in T ffl Let f be a fact in F i (GC) and g ....

S. Abiteboul and R. Hull, Data functions, datalog and negation. In Proceedings of the ACM SIGMOD International Conference on Management of Data, 143--153, Chicago, IL, June 1988.

....supplies(s 1 ; p 1 ) can be treated as an object representing supplies and participates in other relationships and also as a relationship between s 1 and p 1 . Note that although the function symbols in functor objects are uninterpreted, interpreted functions such as those used in COL [2] and [4] are also supported in ROL by means of attribute labels. Definition 7 Let O 1 ; On be terms. Then hO 1 ; On i is a partial set term. If O 1 ; On are ground, then hO 1 ; On i is a partial set. A partial set itself is not an object in ROL. It is used to denote part of a set. ....

S. Abiteboul and R. Hull. Data functions, datalog and negation. In Proc. ACM SIGMOD Intl. Conf. on Management of Data, pp. 143--153, Chicago, Illinois (1988).

....called Fun that is based on calculus. Although this is a functional programming language rather than a logic programming language, this work does provide insight into strongly typed object oriented languages. Single valued data functions have also been included in logic programming languages [5]. Allowing single valued data functions provides a way to state functional dependencies explicitly. For example, it provides a way of showing that a person has only one age. Thus more information can be expressed in the program, which in turn can be used in query optimization. Abiteboul and Hull ....

....Allowing single valued data functions provides a way to state functional dependencies explicitly. For example, it provides a way of showing that a person has only one age. Thus more information can be expressed in the program, which in turn can be used in query optimization. Abiteboul and Hull [5] extend Datalog to incorporate single valued data functions. These data functions can be facts or derived using clauses. Obviously, a program may not be consistent because a derived function may evaluate to something that is not single valued. The authors show that detecting consistency is ....

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S. Abiteboul and R. Hull. Data-functions, datalog and negation. In Proc. of the ACM SIGMOD International Conference on the Management of Data, pages 143--153, 1988.

....instance possibly allowing for nonfunctionality (resp. non finiteness) Unfortunately, it turns out [12] that the problems of deciding whether a given program is finite or functional is in general unsolvable. In particural, functionality is undecidable even for programs without oid invention [2]. 19 6 Instances as Herbrand interpretations In this section we briefly explain how an IsaLog instance can be represented by means of a set of facts, a preliminary tool for the description of other semantics for IsaLog programs. Given a scheme S = C; R;F;typ; isa) the Herbrand universe U S ....

S. Abiteboul and R. Hull. Data functions, Datalog and negation. In ACM SIGMOD International Conf. on Management of Data, pages 143--153, 1988.

....defined as a method on all objects, what obviously the programmer did not have in mind. A correct definition could look like the following rule: X[apply (F) Y] X[F Y] 4. The results of computed methods have to be unique. For general F logic programs the uniqueness of methods is not decidable [2], but once a model is computed it can be checked for inconsistencies. However, since computed methods are not materialized we need sufficient syntactical restrictions to ensure their uniqueness. For example the following definition is ambigous: M[selfRef O] O[M O] The method selfRef yields ....

S. Abiteboul and R. Hull. Data functions, datalog and negation. In H. Boral and P.-A. Larson, editors, Proc. ACM SIGMOD Intl. Conference on Management of Data, pages 143--153, 1988.

....bolts north 40 20 south 10 This language is an extension of our previous works [2,5,7] It has a modeltheoretic semantics and an equivalent fixpoint semantics. Its semantics has been set up by combining techniques stemming from Hilog [3] F logic [8] and Datalog with single valued data functions [1]. Examples including summary and grouping specification illustrating its applicability for complex OLAP manipulations, as well as formal developments, can be found in the full paper [6] ....

S. Abiteboul and R. Hull. Data functions, datalog and negation. In Proc. ACM SIGMOD, pages 143--153, Chicago, IL, Jun. 1988.

.... by combining techniques stemming from previous works done in the area of databases and logic programming: Intregation of constraint solving and logic as in CLP [9] and as in Datalog with constraints [10,12] Semantics of monovaluation as in Datalog with single valued data functions [2]. Higher order syntax as in Hilog [5] allowing schema browsing as in F logic [11] The main contribution of this paper is twofold. Firstly, we define a modeltheoretic declarative semantics, that allows a high level specification of tabular data manipulations. Secondly, we give a formal ....

....A set I of ground atoms is consistent if 8A 1 ; A 2 2 I; ref(A 1 ) ref(A 2 ) A 1 = A 2 , where = is the syntactical equality. An interpretation is a consistent set of ground atoms. This consistency criterion is drawn from the semantics of Datalog with singlevalued data functions [2]. Valuation. A valuation is a function = an [ cv , where an is a total function from V an into D an , and cv is a total function from V cv into D cv . is extended to be the identity on D an and D cv , and it is extended in a straightforward manner to map atoms to ground atoms. We also ....

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S. Abiteboul and R. Hull. Data functions, datalog and negation. In Proceedings of the ACM SIGMOD International Conference on Management of Data, pages 143--153, Chicago, Illinois, USA, June 1988. ACM press.

....properties for IsaLog programs have been studied, namely, functionality and model finiteness. The corresponding problems of deciding functionality and finiteness of a given IsaLog program are shown to be unsolvable in the general case. The problem of functionality has been previously studied in [1] for Datalog programs, where is also shown to be undecidable, even in presence of functional dependencies. With respect to model finiteness, an interesting class of programs, the weakly recursive programs, has been introduced. These programs, which basically do not involve recursion through oid ....

S. Abiteboul and R. Hull. Data functions, Datalog and negation. In ACM SIGMOD International Conf. on Management of Data, pages 143--153, 1988.

....used as data) This difficulty is overcome by combining techniques stemming from previous works done in the area of databases and logic programming: ffl the use of a totally ordered domain (e.g. 3, chap. 17] ffl the semantics of monovaluation as in Datalog with single valued data functions [2], and ffl a higher order syntax as in Hilog [6] allowing schema browsing as in F logic [11] The main contributions of this paper are the following: first, we define a model theoretic declarative semantics, that allows a high level specification of multidimensional data manipulations. Next we ....

....atom A. A set I of ground atoms is consistent iff 8A 1 ; A 2 2 I ; ref(A 1 ) ref(A 2 ) A 1 = A 2 , where = is the syntactical equality. An interpretation is a consistent set of ground atoms. This consistency criterion is drawn from the semantics of Datalog with single valued data functions [2]. Remark A Standard stable model semantics and well founded semantics for normal programs can be generalized for languages with second order syntax and first order semantics like Hilog [14] and can also be used in our case. However, a restricted form of negation in the spirit of semipositive ....

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S. Abiteboul and R. Hull. Data functions, datalog and negation. In Proc. ACM SIGMOD, pages 143--153, Chicago, IL, Jun. 1988.

....(ii) that either are functional, or arrive in nodes with different labels. Unfortunately, given an arbitrary GOOD program, i.e. a sequence of GOOD operations, statically checking the consistency of an edge addition in the program is undecidable in general, as can be shown using results from [1, 22]. So in general, some limited run time checks have to be name Info String Classical Music Figure 14: Example of a node deletion. performed. In practice, one can always construct a program in such a way that the edge additions are guaranteed to succeed. 3.3 Node deletion In order to remove ....

S. Abiteboul and R. Hull. Data functions, datalog and negation. In H. Boral and P.A. Larson, editors, 1988 Proceedings SIGMOD International Conference on Management of Data, pages 143--153. ACM Press, 1988.

....of yet. It is also unknown whether superfiniteness is decidable for Extended Datalog with FD s. As mentioned earlier, this problem is undecidable for the regular finiteness. Furthermore, decidability of weak finiteness for Datalog with function symbols is also an open problem. Abiteboul and Hull [1] have shown that a related problem of whether a given FD holds in a relation computed by a Datalog IDB from an EDB that satisfies certain FD s is undecidable. The answer to a similar question for FC s is unknown. The latter problem for FC s is closely related to decidability of finiteness for ....

S. Abiteboul and R. Hull. Data functions, Datalog and negation. In ACM SIGMOD Conference on Management of Data, pages 143--154, New York, 1988. ACM.

....sum would be 3. The resulting sum operation would be nonmonotonic and nonstandard. If the cost argument functionally depends upon the other arguments then such difficulties do not arise. In general, determining whether a derived recursive predicate satisfies a functional dependency is undecidable [1]. Nevertheless, for small strongly connected components either ad hoc arguments or some sufficient conditions (such as those developed in Section 2.5) could be used to establish functional dependencies. Definition 2.4: Aggregate Subgoal) Consider a domain D and a range R. Let M(D) denote the ....

S. Abiteboul and R. Hull. Data functions, Datalog and negation. In Proceedings of the ACMSIGMOD International Conference on Management of Data, pages 143--153, 1988.

.... y = hx; Childi:last name; y = hx; Studenti:address Gamma z 2 hx; Childi:parents, y = z:address] Note that the problem of verifying the semantic constraint that an attribute is single valued when defined by a rule of head y = x:a is not investigated in this paper (regarding this question see [AH88] Another semantic constraint (inclusion dependency) satisfied by an attribute a of signature c fl(c 0 ) if for each object o in class c, ho; ci:a results in objects that are actually in the population of class c 0 is not considered in this work either. These classes of constraints will be ....

.... one may wish to verify that an attribute a of signature c fl(c 0 ) is single valued when defined by a rule of head y = x:a and, that for each object o in class c, ho; ci:a results in objects that are actually in the population of class c 0 (inclusion dependency constraints) In [AH88] it is shown that for relational algebra functional dependency single valuedness is undecidable, but syntactic conditions can be developed to ensure single valuedness. It is open for the views in RDM whether single valuedness is decidable. We can address the problem of querying the view. The ....

S. Abiteboul and R. Hull. Data Functions, Datalog and Negation. In Proc. ACM SIGMOD Symp. on the Management of Data, pages 143--153, 1988.

....it allows intuitive definitions of relationships between cells, and provides a declarative way to specify table querying and restructuring. Formal semantics for this language has been set up by combining techniques stemming from previous works done in the area of databases and logic programming [6, 1] and can be found in [9, 11] The specification of spreadsheets at a logical level has already been envisaged in [3, 4] but has not been published yet. The main contribution of this paper is to present a method for generating the physical level of a spreadsheet from its logical definitions. The ....

S. Abiteboul and R. Hull. Data functions, Datalog and negation. In Proc. ACM SIGMOD, pages 143--153, Chicago, IL, Jun. 1988.

....the syntax of datalog extends datalog with methods, classes and inheritance. We also set up the basis for the two semantics considered in the following two sections. At a fundamental level, datalog can be seen as a variant of extensions of datalog with data functions proposed in [AG88, AH88] 2.1 Inheritance and datalog We consider countably infinite pairwise disjoint sets of elements D, predicate names P and variables V. Predicates have a certain arity. A term is either an element or a variable. The atoms in datalog are expressions of the form p(t 1 ; t n ) where ....

....syntax to distinguish them from ordinary predicates (see example) Methods and objects are assigned to classes organized in a hierarchy using super clause. Note that we allow ordinary predicates in addition to methods. We could also have allowed functions in the style of the data functions of [AH88] To simplify the presentation, we do not. The semantics of datalog will be given by rewriting into datalog . The benefit of this approach is the ability to apply already existing evaluation techniques to datalog . In Figure 3, we give a rewriting of the datalog program of Figure 2 ....

S. Abiteboul and R. Hull. Data functions, datalog and negation. In Proc. SIGMOD, 1988.

.... : Given a Datalog query Gamma, a functional dependency (FD) R : 1 2 over some binary EDB predicate R of Gamma, and an FD S : 1 2 over some binary IDB predicate S of Gamma, is it true that for each instance I over the EDB predicates, I j= R : 1 2 implies Gamma 1 (I) j= S : 1 2 Fact [AH88]: The FD implication problem for Datalog is undecidable. Let Gamma 1 , R : 1 2, S : 1 2 be an instance of the FD implication problem for Datalog. Let f lip; f lop; continue be new unary predicates and b R a binary predicate. Consider the Datalog program Gamma; S defined by: ....

....R : 1 2, and J 6j= S : 1 2. Let S(a; b) S(a; b 0 ) be two facts in J with b 6= b 0 . Such facts exist since J 6j= S : 1 2. Let I 0 be an instance of S such that: 2 We restrict somewhat the problem by requiring that the predicates R and S are binary. The undecidability is shown in [AH88] for this restricted version of the problem. 11 ffl for each EDB predicate Q of Gamma 1 , I 0 [Q] I[Q] ffl I 0 (f lip) fbg; I 0 (f lop) fb 0 g, and continue is nonempty. We consider the computation of Gamma on input I 0 . By construction, I 0 j= R : 1 2, and Rule (1 b) ....

S. Abiteboul and R. Hull. Data functions, Datalog and Negation. In Proc. ACM SIGMOD Conference on Management of Data, pages 143--153, 1988.

....manner whereas others are in essence functional and are not naturally described in relational terms. Compare for instance the two queries: R(x,w) father(x,y) mother(y,z) boss(z,w) R(x,john) father(mother(boss(john) More motivations for having both methods and relations are given in [4]. Furthermore, as we shall see in Section 3.6, methods are also used to obtain an extensible language. The essential aspect in using methods is inheritance. Specialization and generalization lead to different ways of inheriting methods . For instance, if a method is defined on basepart, it is ....

....and complex object models (e.g. 1] Finally, some of these concepts will turn out to be essential to integrate new features in the following sections. Methods will be used to obtain extensibility and oid s are central for updates. 3 A RULE BASED LANGUAGE The language is built around the COL [2, 4] and IQL [5] languages. An implementation of COL is described in [9] In this section, we are concerned with a core language roughly that of [2] Fancier features are considered in the next sections. In particular, we assume here that methods are not overloaded (they are simply functions) and the ....

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S. Abiteboul and R. Hull. Data-functions, Datalog and Negation. In Proc. ACM SIGMOD, 143--153, 1988.

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Serge Abiteboul and Richard Hull. Data functions, datalog and negation. In Proceedings of ACM SIGMOD 1988.

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