Drabent, W., What is Failure? An Approach to Constructive Negation, Acta Informatica, 32:1, pp.27-59, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....completeness one need a resolution system which never flounders, which can process negative subgoals making substitutions, and when it stops, always returns an answer. Many such resolution systems have been considered, see for instance [Chan88, Chan89] Przymusi nski89] Plaza90, Plaza92f] and [Drabent95] which consider various forms of constructive negation. For an overview of other directions see [AB94] In this paper we cannot argue whether these systems satisfy the lifting property ( but for the researchers working on these systems it should be straightforward to produce appropriate ....

What is Failure? An Approach to Constructive Negation, Acta Informatica, to appear.

....leaves 2 f l . These leaves respectively represent successful, failed, temporarily) undefined, and floundering derivations (see Definition 9 3. 5) In this paper, we shall not discuss floundering Gamma a situation where a non ground negative literal is selected by a computation rule R (see [5, 10, 14, 19] for discussion on such topic) Therefore, in the sequel we assume that no SLT trees contain flounder leaves. The construction of SLT trees can be viewed as that of SLDNF trees [8, 15] enhanced with the following loop handling mechanisms: 1) Loops are detected using ancestor lists of subgoals. ....

W. Drabent, What is failure? An approach to constructive negation, Acta Informatica 32(1):27-59 (1995).

....(model based) meaning of programs. On the other hand, the works of Kunen, Fages and, Lucio, Orejas and Pino [5, 11] provide fixpoint operators to compute its logical consequences (i.e. the set of correct answers) Finally, constructive negation, as introduced by Chan [1] Stuckey [14] and Drabent [3], is accepted as a complete and sound mechanisms to describe the operational semantics of the whole class of normal programs. However, from an implementation viewpoint, the proposed operational semantics for constructive negation (see [3, 5, 14] for a representative group of them) are difficult to ....

....as introduced by Chan [1] Stuckey [14] and Drabent [3] is accepted as a complete and sound mechanisms to describe the operational semantics of the whole class of normal programs. However, from an implementation viewpoint, the proposed operational semantics for constructive negation (see [3, 5, 14] for a representative group of them) are difficult to implement in a practical way. In general, the core of the difficulties for developing practical implementations are the need of (complex) subsidiary computations each time a negative goal is selected during the computation and or the need of ....

[Article contains additional citation context not shown here]

W. Drabent. What is a failure? An approach to constructive negation. Acta Inform'atica, 32:27--59, 1995.

....(model based) meaning of programs. On the other hand, the works of Kunen, Fages and, Lucio, Orejas and Pino [5, 11] provide fixpoint operators to compute its logical consequences (i.e. the set of correct answers) Finally, constructive negation, as introduced by Chan [1] Stuckey [14] and Drabent [3], is accepted as a complete and sound mechanisms to describe the operational semantics of the whole class of normal programs. However, from an implementation viewpoint, the proposed operational semantics for constructive negation (see [3, 5, 14] for a representative group of them) are difficult to ....

....as introduced by Chan [1] Stuckey [14] and Drabent [3] is accepted as a complete and sound mechanisms to describe the operational semantics of the whole class of normal programs. However, from an implementation viewpoint, the proposed operational semantics for constructive negation (see [3, 5, 14] for a representative group of them) are difficult to implement in a practical way. In general, the core of the difficulties for developing practical implementations are the need of (complex) subsidiary computations each time a negative goal is selected during the computation and or the need of ....

[Article contains additional citation context not shown here]

W. Drabent. What is a failure? An approach to constructive negation. Acta Inform'atica, 32:27--59, 1995.

....with del C an abducible predicate. Abducing the atom del C corresponds to deleting C. By adding arguments to del C, it is possible to delete instances of this program clauses. Recently, 54] proposes an interesting form of abductive resolution. It is an abductive extension of the SLDFA resolution [19], a generic form of resolution which provides a framework for constructive negation. In principle, the abductive extension of SLDFAresolution of [54] provides a generic framework for abductive procedures which solve the floundering abduction and negation problem. However, the problems to implement ....

W. Drabent. What is failure? an approach to constructive negation. Technical Report LITH-IDA-R-91-23, Linkoping University, 1993.

....of the underlying constraint structure. We prove that the admissible closure condition is also necessary to guarantee the existence of an e ective implementation of Constructive Negation. Keywords: Constraint Logic Programming, Constructive Negation. 1 Introduction Constructive Negation (CN) [3, 2, 6, 8, 15] is a technique for handling negation in (Constraint) Logic Programming. The technique relies on the explicit construction of answers to a goal which may possibly involve negation. This is commonly achieved by explicitly computing the negation of the solutions to the corresponding positive goal. ....

....to be ground, and answers are not limited to true false. The term Constructive Negation was rst introduced in [3] as a technique for extending the NAF rule in the context of Logic Programming. The semantic properties of CN in logic programming have been studied by various authors (e.g. [6, 13]) CN has been extended to the more general context of Constraint Logic Programming (CLP) by Stuckey [15] who gave the rst completeness result for this method. In [8] Fages introduced a pruning technique to implement Constructive Negation in CLP and Concurrent Constraint languages. In [15] ....

W. Drabent. What is Failure? An Approach to Constructive Negation. Acta Informatica, 32(1):27-29, 1995.

....is allowed in goals. Although normal logic programming is an old topic, from a semantical point of view, it has remained active for a long time. For instance, until few years ago, a (sound and complete) operational semantics for the whole class of normal programs had not been defined (see [11, 37]) Moreover, just last year, a model theoretic semantics for normal programs which is monotone with respect to program inclusion has been defined (see [26] Regarding modularity, one of the approaches for providing logic programming with this kind of feature, is to extend Horn logic programming ....

....program and goal, respectively. Then (a) The computation of G w.r.t P does not flounder. b) Each computer answer of G w.r. t P is a ground substitution for var(G) 12 The problem of floundering was overcome by proposing an extension of negation by finite failure called constructive negation [11]. Later, we refer to that kind of resolution. The Completion of Programs Given a normal program P , P SLDNF :A but P 8 2 :A because the Herbrand base of P containing all the ground atoms is always a model of P 8 . Thus, soundness and completeness results cannot be obtained for SLDNF ....

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W. Drabent. What is a failure? An approach to constructive negation. Acta Inform'atica, 32:27--59, 1995.

....is the detection of the cases where the universal quantification does not work in order to avoid the overhead of the for all predicate when it cannot find a solution. Of course, we will need to use full constructive negation, hard to implement and, probably, not very efficient. The work of [10] could help on this task. In any case, it will be the last resource to be used and will ensure the completeness of the method. ....

W. Drabent. What is a failure? An approach to constructive negation. Acta Informatica., 33:27--59, 1995.

....oe ; c denote the constraints with only positive part oe; Proof. Idea) The proof proceeds by using the T Pi operator, combining the completeness of lazy narrowing and the completeness proof of [27] 5 Related work The work uses some of the techniques developed for constructive negation [4, 5, 27, 7]. However, they are adapted to a more general framework. The reader can find a discussion about the differences in [24] In [4, 5] an implementation technique based on coroutining is proposed: every negated predicate is annotated with some delay clauses to suspend the execution until the variables ....

W. Drabent. What is Failure? An Approach to Constructive Negation. Acta Informatica 32, 27-59, Springer Verlag, 1995.

....which the corresponding positive literal is evaluated. In [5, 29, 32] a negative literal is solved using Clark s completed definitions at run time, possibly with partial evaluation. Quantified complex formulas have to be transformed into a disjunctive normal form and be dealt with explicitly. In [11, 12, 17], substitutions called fail answers are generated for variables in a negative literal A based upon a frontier of the positive literal A. This is a powerful technique since A does not have to be completely evaluated before an answer for A is derived. Since a subgoal can have many different ....

....the choice of frontiers. In [2, 4, 10, 15, 21] constraint answers of a negative literal are derived by taking the negation of the disjunction of all the answers of its positive counterpart. In terms of the semantics, most of the previous work on constructive negation, with notable exceptions of [10, 11, 21], uses Clark s completion as the corresponding declarative semantics. It is known, however, that Clark s completion has various drawbacks [24] The well founded semantics [30] has been accepted as a more natural and robust semantics for logic programs. Przymusinski first studied constructive ....

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W. Drabent. What is failure? an approach to constructive negation. Acta Informatica, 32(1):27--59, 1995.

....program, the problem also occurs in extended logic programs that are not general logic programs. This problem can be solved by using a form of constructive negation, instead of SLDNF resolution. For instance, W. Drabent presented SLDFA resolution, which uses a form of constructive negation, in [Dra92] and proved that this proof procedure is sound and complete with respect to three valued completion semantics. So, we can use the program transformation together with SLDFA resolution as a sound and complete proof procedure for extended logic programs. 7. Conclusion In this paper we presented a ....

Wlodzimierz Drabent. What is failure? an approach to constructive negation. Updated version of a Technical Report LITH-IDA-R-91-23 at Linkoping University, 1992.

....trees de ned by the top down rewriting relation are exactly the trees of the bottom up semantics. For lack of space we cannot give more details, moreover a precise comparison of this top down semantics (automatically) synthesized from the xpoint semantics, and the known ones of for instance [20] [7] or [8] is not easy to establish, and should serve further investigation. 7 Conclusion and Perspectives We have shown that the hierarchy of semantics for de nite logic programs de ned in [12] can be generalized to normal CLP programs. Note that this result, when restricted to de nite CLP ....

W. Drabent, \What is failure? An approach to constructive negation", Acta Informatica, 32:1, pp.27-59, 1995.

....unit must be shown to be compositional with respect to the kind of module operations considered, but the non monotonic nature of negation in Logic Programming does not seem to fit too well with compositionality. In particular, for different reasons, none of the various operational semantics [7,11,26], neither the different model theoretic approaches (see e.g. 2] nor the completion semantics [6,17] seem to be adequate to be the basis for defining a compositional semantics for normal logic program units. To our knowledge, only [8, 14, 19] provide some compositional semantic constructs for ....

....[3] This kind of restriction is not needed in our work. We have not directly related our approach with other kinds of semantics, although the relation established with completion implies, by transitivity, that our semantics can be considered equivalent to constructive negation approaches as [7,26]. Actually, the relation to [7] is quite more direct, in the sense that the construction of our least models is closely related to ranked resolution as defined there. There is also a certain relation between the construction of our least models and Fitting s fixpoint semantics [9] or rather with ....

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W. Drabent, What is failure? An approach to constructive negation, Acta Informatica, 32, 1995, pp. 27-59.

....modular unit must be shown to be compositional with respect to the kind of module operations considered, but the non monotonic nature of negation in Logic Programming does not seem to t too well with compositionality. In particular, for di erent reasons, none of the various operational semantics [13, 11, 32], neither the di erent modeltheoretic approaches (see e.g. 3] nor the completion semantics [12, 25] seems to be adequate to be the basis for de ning a compositional semantics for normal logic program units. To our knowledge, only [17, 19, 27, 35, 9] provide some compositional semantic ....

....the given semantics is too concrete to be of any use. We have not directly related our approach with other kinds of semantics, although the relation established with completion implies, by transitivity, that our semantics can be considered equivalent to constructive negation approaches as [13, 32]. Actually, the relation to [13] is quite more direct, in the sense that the construction of our least model is closely related to ranked resolution as de ned there. There is also a certain relation between the construction of our least model and Fitting s x point semantics [20] or rather with ....

[Article contains additional citation context not shown here]

Drabent, W., What is failure? An approach to constructive negation, Acta Inform atica 32:27-59 (1995).

....completeness one need a resolution system which never flounders, which can process negative subgoals making substitutions, and when it stops, always returns an answer. Many such resolution systems have been considered, see for instance [Chan88, Chan89] Przymusi nski89] Plaza90, Plaza92f] and [Drabent95] which consider various forms of constructive negation. For an overview of other directions see [AB94] In this paper we cannot argue whether these systems satisfy the lifting property ( but for the researchers working on these systems it should be straightforward to produce appropriate ....

What is Failure? An Approach to Constructive Negation, Acta Informatica, to appear.

....unit must be shown to be compositional with respect to the kind of module operations considered, but the non monotonic nature of negation in Logic Programming does not seem to fit too well with compositionality. In particular, for different reasons, none of the various operational semantics [14, 12, 37], neither the different model theoretic approaches (see e.g. 3] nor the completion semantics Address correspondence to Fernando Orejas, UPC Department LSI, Campus Nord, C Jordi Girona Salgado, 1 3, 08034 Barcelona, SPAIN. Tel: 34 3 4017018, Fax: 34 3 4017014, e mail: orejas lsi.upc.es ....

....the given semantics is too abstract to be of any use. We have not directly related our approach with other kinds of semantics, although the relation established with completion implies, by transitivity, that our semantics can be considered equivalent to constructive negation approaches as [14, 37]. Actually, the relation to [14] is quite more direct, in the sense that the construction of our least model is closely related to ranked resolution as defined there. There is also a certain relation between the construction of our least model and Fitting s fix point semantics [21] or rather with ....

[Article contains additional citation context not shown here]

Drabent, W., What is failure? An approach to constructive negation, Acta Inform'atica 32:27-59 (1995).

....used as a test and never computes answers. The problem of handling non ground literals was tackled by various extensions of Negation As Failure, called constructive negation. Examples are intensional negation [3, 4] Chan s constructive negation [7, 8] fail substitutions [20] and fail answers [11, 10]. The idea of intensional negation, originally sketched in [25] and then formalized for positive logic programs in [3, 4] is the following. Given a normal program P , we derive a new program P 0 , which contains clauses which allow us to compute the answers to negative queries. Example 1. Let ....

....management of disjunctions, which are handled by using essentially the SLD Gammatree structure of positive Horn clauses. The resulting theory allows us to identify commonalities and differences between the various constructive negation techniques. It is worth noting that there exists one example [11, 10] of constructive negation technique, which is not based on the program completion and is not therefore easily comparable to our technique. The second contribution of the paper is related to the formal semantics. None of the existing semantics for constructive negation correctly models answer ....

W. Drabent. What is Failure? An Approach to Constructive Negation. Acta Informatica, 1993. To appear.

....as its answers [14] Since answers to negative goals can t in general be represented by a finite number of substitutions, Ma luszy nski and Naslund s approach sometimes needs to return an infinite number of fail substitutions. Drabent defines SLDFA resolution over the Herbrand universe [8]. Chan s first method works only when the negated sub goal has a finite number of answers. SLDFA overcomes this by constructing answers for the negative goal from a finite number of answers to the negated sub goal. Fage proposes a simple concurrent pruning mechanism over standard SLD derivation ....

....rule for each of these three kinds of property. The simplification procedure in [4] consists of rewrite rules for these kinds of property plus some miscellaneous rewrite rules such as : x y) x y) provided x and y range over the domain of numbers. Unlike other constructive negation methods [3, 8, 9, 14, 16], the method in [4] does not necessarily rely on SLD resolution to obtain a frontier of the negated sub goal, and can be used both as a constructive rule and as a simplification rule. Though the method was proposed for arithmetic constraints, the basic principles behind the method carries over to ....

W. Drabent. What is failure? An approach to constructive negation. Acta Informatica, 32:27--59, 1995.

....a test and never computes answers. The problem of handling non ground literals was tackled by various extensions of Negation As Failure, called constructive negation. Examples are intensional negation [3, 4] Chan s constructive negation [6, 7] the fail substitutions [23] and the fail answers [10, 9] techniques. The idea of intensional negation, originally formalized for positive logic programs [3, 4] is the following. Given a normal program P , we derive a new program P 0 , which contains clauses which allow us to compute the answers to negative queries. Example 1.2 Let P be the program ....

....management of disjunctions, which are handled by using essentially the SLD Gammatree structure of positive Horn clauses. The resulting theory allows us to identify commonalities and differences between the various constructive negation techniques. It is worth noting that there exists one example [10, 9] of constructive negation technique, which is not based on the program completion and is not therefore easily comparable to our technique. Another problem is related to the formal semantics. In fact the existing semantics do not correctly model answer constraints and are therefore useless for ....

W. Drabent. What is Failure? An Approach to Constructive Negation. Acta Informatica, 1993. To appear.

....) modulo a certain syntactic transformation) St a96] and (3) soundness of SLDNF resolution w.r.t. 3 valued completion semantics [Doe94] 2 The Theorem 4.4 is valid for any operational semantics, which is sound w.r.t. 3 valued completion semantics. This includes constructive negation (cf. Dra95] and the references therein) and extensions of SLDNF resolution allowing selecting non ground negative literals under certain conditions [Llo87,St a96] 4.2 Completeness of normal programs To discuss completeness we need to refer to the notion of SLDNF tree. We will follow the de nition of Apt ....

W. Drabent. What is failure? An approach to constructive negation. Acta Informatica, 32(1):27-59, 1995.

....normal programs we assume SLDNFresolution, as de ned by Apt and Doets [AD94] We recall this de nition in the section on completeness. Our results on correctness are valid for any operational semantics, which is sound w.r.t. 3 valued completion semantics. This includes constructive negation (cf. Dra95] and the references therein) and extensions of SLDNF resolutions allowing selecting non ground negative literals under certain conditions [Llo87, St a96] De nition 4.2 Let L be a rst order language. Let Q be a formula or a set of formulae (e.g. a query or a program) of L. Let us extend L by ....

W. Drabent. What is failure? An approach to constructive negation. Acta Informatica, 32(1):27-59, 1995.

....The next section contains the outline of the paper. Section 3 presents the concepts necessary for our work. Among others we need a constraint representation of resolution where instead of applying mgu s the corresponding equations are added to the goals. That section also presents SLDFA resolution [Dra95] which is a generalization of SLDNF resolution for constructive negation. A completeness result for SLDFA resolution [Dra95] is a starting point for our work. The next two sections introduce SLDNF1 resolution and discuss floundering. SLDNF1 resolution can be seen as an alternative definition of ....

....need a constraint representation of resolution where instead of applying mgu s the corresponding equations are added to the goals. That section also presents SLDFA resolution [Dra95] which is a generalization of SLDNF resolution for constructive negation. A completeness result for SLDFA resolution [Dra95] is a starting point for our work. The next two sections introduce SLDNF1 resolution and discuss floundering. SLDNF1 resolution can be seen as an alternative definition of SLDNF resolution. We introduce it in order to be able to deal with fairness. Section 6 presents our completeness results for ....

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W. Drabent. What is failure? An approach to constructive negation. Acta Informatica, 32(1):27--59, February 1995.

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Drabent, W., What is Failure? An Approach to Constructive Negation, Acta Informatica, 32:1, pp.27-59, 1995.

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) Drabent, W. What is Failure? An Approach to Constructive Negation. Acta Informatica, 32(1):27-29, 1995.

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Drabent, W., What is failure? An approach to constructive negation, Acta Informatica 32:27-59 (1995).

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