Abiteboul, Vianu 1991 Serge Abiteboul and Victor Vianu, "Nondeterminism in logic-based languages", Annals of Math and AI, no. 3, 151--186, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....cannot be expressed in relational algebra. This has led to the definition of queries expressible in FO plus a fixpoint operator (fixpoint queries) Datalog with inflationary negation, and related concept that will be discussed later in this paper. More recently the work of Abiteboul and Vianu [2, 3, 4, 5] has brought into focus the the need for having non deterministic operators in such languages in addition to recursion and fixpoint. Therefore, they proposed the a non deterministic construct called the witness [2, 3, 4, 5] for the fixpoint extensions of FO. They also proposed non deterministic ....

....later in this paper. More recently the work of Abiteboul and Vianu [2, 3, 4, 5] has brought into focus the the need for having non deterministic operators in such languages in addition to recursion and fixpoint. Therefore, they proposed the a non deterministic construct called the witness [2, 3, 4, 5] for the fixpoint extensions of FO. They also proposed non deterministic operational semantics for Datalog (a la production systems) giving rise to the class of N Datalog languages. The referenced work also characterized the expressive power of languages with these constructs for both ....

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S. Abiteboul, V. Vianu. Non-Determinism in Logic Based Languages. Annals of Mathematics and Artificial Intelligence 3 (1991). pp. 151-186.

....Datalog with strati ed negation. However, non deterministic constructs provide a very e ective vehicle for achieving #####; this observation led to the parallel but independent introduction of a witness operator for ## languages and a choice operator for Datalog. The work of Abiteboul and Vianu [1, 2, 3, 4] brought into focus the need for having nondeterministic operators in such languages in addition to recursion or xpoint. Therefore, they proposed the non deterministic construct called the witness [2, 3, 4] for the xpoint extensions of ##. They also proposed a non deterministic procedural ....

....for ## languages and a choice operator for Datalog. The work of Abiteboul and Vianu [1, 2, 3, 4] brought into focus the need for having nondeterministic operators in such languages in addition to recursion or xpoint. Therefore, they proposed the non deterministic construct called the witness [2, 3, 4] for the xpoint extensions of ##. They also proposed a non deterministic procedural semantics for Datalog# ( a la production systems) giving rise to the class of N Datalog languages. The referenced work also characterized the expressive power of languages with these constructs for both ....

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S. Abiteboul, V. Vianu. Non-Determinism in Logic Based Languages. Annals of Mathematics and Articial Intelligence, 3 (1991). pp. 151-186.

.... to fully support updatable views in object oriented database systems, i.e. derived information that is to be explicitly added in the database [AB91, HS91a] as well as database restructuring [AK89, GPVG90] The natural links between object creating and non deterministic database transformations [AV91b] were recently explored by the authors [VdBVG92] for the special case of queries and views (modeled as type increasing transformations. In the present paper, we widen our scope to arbitrary updates, present some new results and indicate some new open problems. Research Assistant of the ....

....context of object oriented database systems. 3 Semi determinism IQL is a determinate, hence nearly deterministic language. In order to express arbitrarily non deterministic transformations one can add the witness operation to the language. See [Abi88] for motivations for non determinism, and [AV91b] for a survey. Witness is a non deterministic choice operation. Let r be a relation, and let X be a subset of its attributes. Then WX (r) evaluates to a sub instance of r, obtained by choosing exactly one representative from each class of X equivalent tuples of r. Here, two tuples are ....

S. Abiteboul and V. Vianu. Non-determinism in logic-based languages. Annals of Mathematics and Artificial Intelligence, 3:151--186, 1991.

....semi deterministic approach rather than the constructive. To evaluate the semi deterministic approach we need to consider languages in which semi deterministics queries can be expressed. The most obvious way to obtain such a language is augmenting IQL with a choice operation. Abiteboul and Vianu [3] considered a choice operation, called witness, in the context of general non deterministic queries. In [17] it was shown, however, that (i) it is undecidable to check at compile time whether a program in IQL witness expresses a semi deterministic query, and (ii) runtime checking for ....

S. Abiteboul and V. Vianu. Non-determinism in logic-based languages. Ann. Math. Artif. Intell., 3:151--186, 1991.

....it from the shop or borrowing it from the neighbor. Clearly the corresponding computations of the production system are both plausible and there is no intuitive reason to prefer one to the other. The need for nondeterministic rule based languages has been pointed out by many authors (see, e.g. [1]) Indeed, nondeterministic rule based languages have been mainly studied with respect to their expressive power and computational complexity as opposed to purely deterministic languages. In this paper, we argue that nondeterminism is needed to naturally represent real life problems. Some work in ....

S. Abiteboul and V. Vianu. Non-determinism in logic-based languages. Annals of Mathematics and Articial Intelligence, 3:151-186, 1991.

....may depend on the particular order accessed; now if the order is not visible the queries can become non deterministic because different outcomes depending of the order used will be possible. Two main non deterministic constructions have been proposed in query languages: the witness operator of [1] which, applied on a relation R, allows to choose non deterministically a tuple of R and the choice construct of [11,13,14] in Datalog programs which allows to introduce particular goals (the so called choice goals) in the premises of the rules. Such choice goals are of the form Choice( X) Y) ....

....particular goals (the so called choice goals) in the premises of the rules. Such choice goals are of the form Choice( X) Y) where X and Y are lists of variables and their function is to enforce the functional dependency X Y to the intensional predicate occurring in the head of the rule. In [1] it has been proved that adding the witness operator to the Fixpoint Queries allows to capture the class NDB Ptime of the non deterministic queries which are computable in polynomial time by a non deterministic Tring machine. In the same spirit a particular semantics of the choice construct, the ....

Abiteboul S. , Vianu V., Non-Determinism in Logic Based Languages. Annals of Mathematics and Artificial Intelligence 3 (1991) p. 151-186.

....by stable models, and in [49] that DATALOG 6= augmented with dynamic choice expresses exactly the non deterministic queries computable in polynomial time. The deterministic fragment of this language (DET DATALOG 6= choice) expresses precisely all queries computable in polynomial time (cf.[50]) however, it can not be recognized. Notice that it is conjectured that no query language for precisely the polynomial time queries exists (see [29] We conclude by outlining possible issues for future work on DQL. In the de nition of query Section IV A open defaults are quanti er and ....

S. Abiteboul and V. Vianu, \Non-Determinism in Logic-Based Languages", Annals of Mathematics and Articial Intelligence, vol. 3, pp. 151-186, 1991.

....for the witness choices. ii) a priori even two consecutive witness applications to the same need not return the same predicates. The second, and somewhat disturbing feature of plain FO[witness] is remedied in a variant FO[witness] This is the variant of [1] denoted FO W in [2, 3], and also the variant to be considered here. For FO[witness] FO itself is regarded as a query language that assigns relational values to new predicates. Correspondingly, the witness operation can be used in assignments of the form R : witness y (x; y) which effectively serve to freeze ....

....corollary to the proof of Theorem 4 to be given below. Theorem 5 Deterministic FO[witness] is strictly more expressive than FO over finite relational structures (databases) Theorem 5 explicitly answers a question or actually refutes one part of a conjecture of Abiteboul and Vianu [3], and Abiteboul, Simon, and Vianu [2] The other part of their conjecture, concerning the weaker variant FO[witness] without the freezing option, remains open. It is clear that deterministic FO[witness] is contained in FO[ffl] inv , since the witness operation can be simulated in FO[ffl] ....

S. Abiteboul and V. Vianu, Non-determinism in logic-based languages, Annals of Mathematics and Artificial Intelligence, 3, 1991, pp. 151--186.

....whereby the complexity of a query is de ned as the complexity of establishing if a given tuple belongs to the result relation, for a given input database. On the other hand, non deterministic queries have not been the subject of a systematic study, except for some interesting, recent exceptions [3, 2, 9], mainly for two reasons. The rst reason is that the classical QOT works ne for deterministic queries, since the entire answer query answer can be constructed tuple after tuple, but fails for non deterministic ones to measure the complexity of nding all the tuples of an answer as two tuples ....

....be executed in polynomial time using a re ning single valued function, we introduce the class NQPF having this simple characterization: both the QOR and the QOS for the queries in the class are in P. We stress that another polynomial time computable query class is already known in the literature [3]: NQPTIME, that is, the class of all queries computed by polynomial time transducers such that for each input, each branch of the transducer s computation halts into an accepting state. But this class su ers from a severe drawback: the QOR is not in P unless P=NP. Therefore, while nding a result ....

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S. Abiteboul and V. Vianu. Non-determinism in logic-based languages, Annals on Mathematics and AI, Vol. 3, No. II-IV, 1991.

....for the witness choices. ii) a priori even two consecutive witness applications to the same need not return the same predicates. The second, and somewhat disturbing feature of plain FO[witness] is remedied in a variant FO[witness] This is the variant of [1] denoted FO W in [2, 3], and also the variant to be considered here. For FO[witness] FO itself is regarded as a query language that assigns relational values to new predicates. Correspondingly, the witness operation can be used in assignments of the form R : witness y (x; y) which effectively serve to freeze ....

....corollary to the proof of Theorem 4 to be given below. Theorem 5 Deterministic FO[witness] is strictly more expressive than FO over finite relational structures (databases) Theorem 5 explicitly answers a question or actually refutes one part of a conjecture of Abiteboul and Vianu [3], and Abiteboul, Simon, and Vianu [2] The other part of their conjecture, concerning the weaker variant FO[witness] without the freezing option, remains open. It is clear that deterministic FO[witness] is contained in FO[ffl] inv , since the witness operation can be simulated in FO[ffl] ....

S. Abiteboul and V. Vianu, Non-determinism in logic-based languages, Annals of Mathematics and Artificial Intelligence, 3, 1991, pp. 151--186.

....deterministic queries from non deterministic ones. First the well known semantics, Possible and Certain, taking respectively the union and the intersection of the possible outcomes of a query. These techniques were introduced in the context of query languages in [ASV90] and further investigated in [AV91b]. We then introduce the semantics Possible is Certain, which is shown to characterize the functional fragment of non deterministic languages. Finally, we define three other semantics, Disjoint, Co Disjoint, and Unique, which reflect various techniques to control the non determinism. S. Grumbach ....

....The approach followed here emphasizes a specific viewpoint, namely the use of non determinism in logical formalisms. Results in the same spirit concerning the classes NP, co NP, and DP have been obtained in the context of logic programming with rule languages with the inflationary semantics [AV91b], and with the stratified and the wellfounded semantics [SZ90, GPSZ91, GSZ95] We devote a particular attention to the class NQNP T of total non deterministic queries computable in NP, which is closed under complement. We prove that the functional fragment (subset of deterministic queries) of ....

S. Abiteboul and V. Vianu. Non-determinism in logic-based languages. Annals of Math. and AI, 3:151--186, 1991.

....semi deterministic approach rather than the constructive. To evaluate the semi deterministic approach we need to consider languages in which semi deterministics queries can be expressed. The most obvious way to obtain such a language is augmenting IQL with a choice operation. Abiteboul and Vianu [5] considered a choice operation, called witness, in the context of general non deterministic queries. In [22] it was shown, however, that (i) it is undecidable to check at compile time whether a program in IQL witness expresses a semi deterministic query, and (ii) run time checking for ....

S. Abiteboul and V. Vianu. Non-determinism in logic-based languages. Ann. Math. Artif. Intell., 3:151--186, 1991.

....OE. The results of the paper do not depend upon this choice, and we will consider (OE ) a short notation for ( OE (3OE ) Nondeterminism Nondeterminism is not only useful in modeling choices in pragmatic situations, but also important to the expressive power of database languages [2]. Example 2.4 Nondeterminism is naturally supported using multiple rules. Consider the graph orientation update from [2] Let edge be a binary relation containing edges in a graph. For every pair of edges (X; Y ) and (Y; X) one of the edges is removed and the other is preserved. orientation ....

....(3OE ) Nondeterminism Nondeterminism is not only useful in modeling choices in pragmatic situations, but also important to the expressive power of database languages [2] Example 2.4 Nondeterminism is naturally supported using multiple rules. Consider the graph orientation update from [2]. Let edge be a binary relation containing edges in a graph. For every pair of edges (X; Y ) and (Y; X) one of the edges is removed and the other is preserved. orientation : 8 X.8 Y. pair(X,Y) choose(X,Y) pair(X,Y) edge(X,Y) edge(Y,X) choose(X,Y) edge(X,Y) Gammaedge(Y,X) ....

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Abiteboul, S. and Vianu, V. Non-determinism in logic-based languages. Annals of Mathematics and Artificial Intelligence, 3:151--186, 1991.

....if this property is checkable, it will be a promising approach to the problem of finding efficient languages, that are more powerful than known deterministic database languages, such as Fixpoint or Fixpoint Counting. Unfortunately, it was shown that in general functionality is undecidable [AV1]. In this paper, we investigate an alternative approach to this problem, using restricted non determinism. In [AV1] a choice operator W, called Witness, is introduced in the context of general non determinism. We consider here choice operators which are sound, that is they produce always ....

....that are more powerful than known deterministic database languages, such as Fixpoint or Fixpoint Counting. Unfortunately, it was shown that in general functionality is undecidable [AV1] In this paper, we investigate an alternative approach to this problem, using restricted non determinism. In [AV1] a choice operator W, called Witness, is introduced in the context of general non determinism. We consider here choice operators which are sound, that is they produce always isomorphic results at any application. Requiring soundness is a reasonable way to use non determinism. Actually one can ....

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S.Abiteboul and V.Vianu. Non-determinism in logic-based languages. Annals of Math. and Artif. Int., 3 :151-186, 1991.

.... but it can be exploited to express non determinism in a purely declarative framework for instance, as shown in [15, 34] stable models provide a formal declarative semantics to non deterministic pruning constructs of deductive databases, such as the choice construct of [20] As discussed in [2, 3], in addition to enable a simpler and more natural writing of programs, non determinism provides a higher expressive power for instance, it has been shown that multiple stable models can be used to express NP hard problems [32, 33, 36] Observe that a non deterministic model based semantics does ....

S. Abiteboul and V. Vianu. Non-determinism in logic-based languages. Annals of Mathematics and Artificial Intelligence 3, 1991, pp. 151-186.

....was defined in [3] Definition 2.3 Query Q is called determinate if whenever Q(I; J 1 ) and Q(I; J 2 ) then J 1 and J 2 must be I isomorphic, i.e. there must be an permutation f of U, that is the identity on adom(I) such that f(J 1 ) J 2 . We now define an operation, W (Witness, [7]) which allows for arbitrary non determinism. Let S be a scheme, I 2 inst(S) and R 2 S with X f1; a(R)g. A relation r of arity a(R) is a possible result of WX (R) applied to I if r is a subset of I(R) obtained by choosing for each class of X equivalent tuples of I(R) exactly one ....

S. Abiteboul and V. Vianu. Non-determinism in logic-based languages. Annals of Mathematics and Artificial Intelligence, 3:151--186, 1991.

....many sorted structures where every sort comes with its own default element. We devote two sections to the operator. The main part of the paper is devoted to the investigation of FO ffi. Finally, we consider briefly an alternative independent choice logic and the witness operator studied in [Abiteboul Vianu 1991]. 1.1 The Operator The operator was introduced in [Hilbert and Bernays 1939] for proof theoretic purposes and played an important role in proof theory [Leisenring 1969] Here we are interested in model theory. The extension FO of first order logic with the operator is the object of ....

....On the other hand, there might be a better element b that belongs to the set Z in every evaluation. Shouldn t we choose b instead of a In Section 8, we present another semantics for ffi that reflects this idea. We discuss also the relative advantages of the two semantics of ffi. In [Abiteboul and Vianu 1991], a nondeterministic witness choosing operator was introduced in the context of relational algebra. The semantics is described informally there. We suggest a formalization and make a couple of observations in Section 9. 2 Predicate and Functional First Order Logics We discuss two versions of ....

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Abiteboul, Vianu 1991 Serge Abiteboul and Victor Vianu, "Nondeterminism in logicbased languages", Annals of Math and AI, no. 3, 151--186, 1991.

....The characterization of the PTIME queries over dense inputs deserves some discussion. No language expressing precisely the PTIME queries is known. Previous characterizations of the PTIME queries over flat relations involve trade offs such as access to an order [Imm86, Var82] or non determinism [AV90, ASV90] In a dense, non flat database, the order assumption is no longer necessary, because the inputs are large enough to allow the efficient construction of the necessary orderings of the domains of types, induced by orderings of the atomic constants. In this respect, the result can be viewed ....

S. Abiteboul and V. Vianu. Non-determinism in logic-based languages. In To appear in Annals of Math. and AI, 1990.

....Nondeterministic languages are discussed in Section 6, and a value inventing language is presented in Section 7. Lastly, some conclusions are presented, including a discussion of procedural vs. declarative semantics for rule based languages. This survey is inspired by the presentations in [Bid91a, AV91c, AHV95] Many proofs can be found in [AHV95] and, of course, in the original papers, to which pointers are provided. 2 Background In this section we review some terminology relating to relational databases. In particular, we recall some of the traditional query languages, including iterative ....

....As discussed, it is conjectured that there is no deterministic language expressing exactly the queries computable in polynomial time. On the other hand, there are nondeterministic languages expressing exactly the (deterministic and nondeterministic) queries computable in polynomial time. See [AV91c] for a survey on nondeterminism in logic based languages, which inspired this presentation. 6.1 Nondeterministic Datalog : We next consider nondeterministic versions of the Datalog : languages. Recall that the procedural, deterministic semantics for these languages was the result of ....

S. Abiteboul and V. Vianu. Non-determinism in logic-based languages. Annals of Math. and Artif. Int., 3:151--186, 1991.

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Abiteboul, Vianu 1991 Serge Abiteboul and Victor Vianu, "Nondeterminism in logic-based languages", Annals of Math and AI, no. 3, 151--186, 1991.

No context found.

S. Abiteboul and V. Vianu, Non-determinism in logic-based languages, Annals of Mathematics and Artificial Intelligence, 3, 1991, pp. 151--186.

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S. Abiteboul and V. Vianu. Non-determinism in logicbased languages, Annals on Mathematics and AI, Vol. 3, No. II-IV, 1991.

No context found.

S. Abiteboul and V. Vianu. Non-determinism in logic-based languages, Annals on Mathematics and AI, Vol. 3, No. II-IV, 1991.

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