Van Gelder, A. Negation as Failure Using Tight Derivations for General Logic Programs. In Proc. Third IEEE International Symposium on Logic Programming , (1986), 149--176.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....N4 : w N5 : p(X) Cp 2 Cp 1 Cp 2 N10 : r 2f Figure 1: The generalized SLT tree GT p(X) for (P 1 [ f p(X)g; SLT trees have some nice properties. Before proving those properties, we reproduce the definition of bounded term size programs. The following definition is adapted from [32]. Definition 3.4 A program has the bounded term size property if there is a function f(n) such that whenever a top goal G 0 has no argument whose term size exceeds n, then no subgoals and tabled answers in any generalized SLT tree GTG 0 have an argument whose term size exceeds f(n) The ....

A. Van Gelder, Negation as failure using tight derivations for general logic programs, Journal of Logic Programming 6(1&2):109-133 (1989).

....so that each negation refers to a set that has already been defined (the dependency graph must be acyclic) The database can then be interpreted as an iterated inductive definition (via some treatment of finite failure. Such databases are called stratified or free from recursive negation [44]. The main stream of (sound) research into negation [34] uses the mathematics of fixedpoints, ordinals, and inductive definitions, not that of classical first order logic. In di#erent situations, either view of logic programming inductive definitions or first order logic could be more ....

Van Gelder, A., Negation as failure using tight derivations for general logic programs, In Foundations of Deductive Databases and Logic Programming, J. Minker, Ed. Morgan Kaufmann, 1988, pp. 149--176

....the notion of de nite clause, we introduce a more general notion of a set of clauses de nite w.r.t. a set of relations. These relations are regarded as de ned by this set of clauses. 2. In logic programming, relations are often de ned in terms of other relations. The notion of strati cation [5, 1, 8] allows one to formalize the notion P is de ned in terms of Q . We use a similar idea of strati cation, but in our case strati cation must be related to a reduction ordering on literals. Consider another example. Example 2 The dicult problem is to nd automatically the right ordering that ....

A. Van Gelder. Negation as failure using tight derivations for general logic programs. In J. Minker, editor, Deductive Databases and Logic Programming, pages 149-177. Morgan Kaufmann, 1988.

....characterization of stable expansions in terms of their L free parts. Moore [99] and Halpern and Moses [42] observe that stable sets can be characterized using complete S5 structures. Gelfond [29] observes that the concept of stratification introduced in the context of 11 logic programs [13, 1, 147] can be carried over to autoepistemic logic as a condition guaranteeing a unique stable expansion. Marek and Truszczy nski [83, 87] extend Gelfond s notion of stratification. A more detailed comparison of the different approaches is presented in Chapter 3. ffl Tightly grounded autoepistemic ....

A. Van Gelder. Negation as failure using tight derivations for general logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 149--176. Morgan Kaufmann Publishers, Los Altos, 1988.

....was that of strati cation, with the underlying idea of restricting attention to certain kinds of programs in which recursion through negation is prevented. Apt, Blair, and Walker [ABW88] proposed a variant of resolution suitable for these programs, while Przymusinski [Prz88] and van Gelder [vG88] generalized the notion to local strati cation. Przymusinski [Prz88] developed the perfect model semantics for locally strati ed programs, and together with Przymusinska [PP90] generalized it later to a three valued setting as the weakly perfect model semantics. The semantics mentioned so far ....

Allen van Gelder. Negation as failure using tight derivations for general logic programs. In Jack Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 149-176. Morgan Kaufmann, Los Altos, CA, 1988.

.... negation is allowed in the bodies of the rules (we will write DATALOG TM to denote DATALG with negation) Of particular interest is stratified negation, which avoids the semantic and implementation problems connected with the unrestricted use of nonmonotonic constructs in recursire definitions [5,7, 38]. Simple, intuitive semantics leading to efficient implementation exists for stratified DATALOG; unfortunately, as shown in [20] this language has a reduced expressive power as it can only express a proper subset of fixpoint queries. The simplest step toward greater expressive power is to remove ....

Van Gelder, A.: Negation as failure using tight derivations for general logic programs. J Log Program 6(1), 109 133, 1989.

.... viewing the first rule containing the rain predicate as a short hand for the following rule: h path(Z, C) path(Z, Y, C) path(Z, CO,CX C) This has formal semantics, inasmuch as the negated conjunct in parenthesis can be defined by a new pred icate, yielding a stratified program [1,11]. However, a straightforward evaluation of such a stratified program would materialize the predicate path(Z,Y,C) and then choose the smallest cost tuple for every Z and . There are two problems with this approach: first, it is very inefficient, and second, the computation could be non ....

A. Van Gelder. Negation as failure using tight derivations for general logic programs. In I. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 149-176, Morgan-Kaufman, Los Altos, CA, 1988.

....lesser path(X, Y, C) a lesser path(X, Y, C) path(X, Y, C) path(X, Y, C # ) C # C. where a lesser path is a new predicate symbol not appearing elsewhere in the program. This has formal semantics because, by rewriting the min predicates by means of negation, we get a stratified program [3,36]. However, a straightforward evaluation of such a stratified program would materialize the predicate path and then choose the smallest cost tuple for every pair of nodes x and y. There are two problems with this approach: first, it is very ine#cient, and second, the computation could be ....

Van Gelder, A., Negation as failure using tight derivations for general logic programs. Foundations of Deductive Databases and Logic Programming (J. Minker ed.), 149--176 (1988).

....NLP v and all ground literals fi of P, it can be determined in time polynomial in jPj whether P j= s a fi and whether P j= s a fi. This is a significant positive result since stratified programs have proved to be sufficiently expressive for a wide variety of applications of logic programming [1, 21]. But contrast [8] 5 A Simple Fragment with Disjunction It is encouraging that there is any reasonably rich set of logic programs, namely the stratified logic programs, for which answering queries under the 2 The degree of the polynomial is at most 2v 2, given nice assumptions about the ....

A. Van Gelder. Negation as failure using tight derivations for general logic programs. In Proc. Third IEEE Symposium on Logic Programming, Salt Lake City, Utah, Springer-Verlag, New York, 1986.

....number. One important development in the direction of solving these problems was the identi cation of the Perfect Model Semantics. This semantics is based on the computation of an iterated least xed point of an operator over programs. Perfect Model Semantics is well de ned for strati ed programs [ABW88, Van88] (see also De nition 1.5) Intuitively, strati ed programs are those programs which can be decomposed into di erent layers, where predicates de ned in a given layer cannot depend negatively on predicates de ned in lower layers. The class of strati ed programs embodies a large group of programs, ....

Van Gelder, Allen. Negation as failure using tight derivation for general logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming. Morgan Kaufmann, Los Altos, CA, 1988. 20

....deciding PMS(P ) 6j= F is in NP, which implies membership of the problems in coNP. 5 Strati ed disjunctive programs The concept of strati cation, which had been discussed by Chandra and Harel [14] was introduced for logic programs independently by Apt, Blair, and Walker [2] and by van Gelder [64]; Przymusinski generalized it to DLPs (without integrity clauses) 48] A DLP P without integrity clauses is strati ed i it is possible to partition the atoms into strata hS 1 ; S r i, such that for every clause a 1 an b 1 ; b k ; not c 1 ; not c m in P there ....

A. van Gelder. Negation as Failure Using Tight Derivations for General Logic Programs. In Minker

.... have gained a lot of importance in connection with the search for nice declarative semantics for logic programs and the treatment of negative information in logic programming (e.g. Lloyd [10] Stratified programs were introduced into logic programming by Apt, Blair, and Walker [2] and van Gelder [17] not long ago. In mathematical logic, however, theories of this kind have been studied for more than 20 years under the general theme of iterated inductive definability. Indeed, stratified programs can be understood as systems for (finitely) iterated inductive definitions where the definition ....

Van Gelder, A., Negation as Failure Using Tight Derivation for General Logic Programs, in: J. Minker (ed.), Foundations of Deductive Databases and Logic Programming, pages 149--176, Morgan Kaufmann, Los Altos, 1987.

....allowed then # is an # goal for P . 3 # P is quasi definite if for every negative literal A in the body of a clause of P the atom A does not unify with the head of any clause in P . Now if P is quasi definite then P is an # program. 4 # The programs which are safe for negation of Van Gelder in [16] are # programs. Definition 18 A weak implication tree T for L with respect to P is defined like an implication tree for L (Definition 8) but clause (a ) is replaced by (a ) if A is a negative node of T then there exists a substitution # such that A# is finitely failed and A has no ....

A. Van Gelder. Negation as failure using tight derivations for general logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 149--176. Morgan Kaufmann, Los Altos, 1987. 25

....minimal model, Mod m (S) ffpgg, which is not stable, however. A sequent set, resp. logic program, without stable models will be called unstable. Example 9 S = fp oe q ) r; r ) pg is unstable. Observation 18 Stable reasoning is not cumulative. Proof: The following counterexample is due to [vG88]. Let S = f Gammar ) q ; Gammaq ) r ; Gammap ) p ; Gammar ) pg. Since Mod ms (S) ffp; qgg, and S j= ms p; q, but Mod ms (S [ fpg) ffp; qg; fp; rgg, and hence S [ fpg 6j= ms q. 2 5.3 Extended Logic Programs as Sequent Sets A sequent set S Seq 0 2 corresponds to an extended ....

A. van Gelder. Negation as failure using tight derivations for general logic programs. In Foundations of Deductive Databases and Logic Programming, pages 149--176. Morgan Kaufmann, San Mateo (CA), 1988.

....the semantic and implementation problems connected with the use of non monotonic The work of the rst two authors has been supported by the CNR project Sistemi Informatici e Calcolo Parallelo and by the MURST project Metodi Formali per Basi di Dati . constructs in recursive de nitions [4, 7, 29]. We will write DATALOG :s to denote DATALOG with strati ed negation. Simple, intuitive semantics, leading to ecient implementation exists for DATALOG :s . Unfortunately, DATALOG :s cannot express all polynomial time queries, and can only express a proper a proper subset of xpoint queries ....

A. Van Gelder. Negation as failure using tight derivations for general logic programs. Journal of Logic Programming, vol. 6, No. 1, pages 109-133, 1989.

....The three valued approach was introduced in Kunen [Kun89] The second one, in some cases considered for a limited class of general programs, involves restriction to a single (possibly three valued) Herbrand model. This approach was pursued in Fitting [Fit85] Apt et al. ABW88] van Gelder [vG88] van Gelder et al. vGRS88] and various other publications. The soundness and completeness results for SLDNF resolution and its modifications relate the procedural and declarative interpretation, usually for a selected class of general programs and queries. In contrast to the case of the ....

A. van Gelder. Negation as failure using tight derivations for general logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 149--176. Morgan Kaufmann, Los Altos, CA, 1988.

....parameters are insufficiently instantiated. For these predicates the computation may be delayed till the parameter instantiation is completed by other goals. Others try to detect a possible non termination at run time, and to avoid it by cutting off the corresponding branch of the computation tree [1, 2, 9, 13]. But this is not possible without changing the operational semantics of Prolog, therefore it is out of the scope of debugging. 3 3 A classification of non terminating computations The following classification arose from an examination of the behaviour of non terminating programs. It does not ....

A. Van Gelder. Negation as failure using tight derivations for general logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, chapter 3, pages 149--176. Morgan Kaufman, 1988.

....sequence of successive snapshots I s ; I s 1 ; I s w Gamma1 where w 2 N [ f1g is called a window of I Sigma . It is denoted I hs;wi , where s is the start and w the width of I hs;wi . 2 3 We may relax this restriction and admit programs with the bounded term size property [20]. Then for every query Q with maximal term size k, it is sufficient to consider derivations where the size of terms is bound by a function of k. Consequently, if we include Q in the program P , a finite subset of the Herbrand universe is sufficient to answer Q. Since it is in general undecidable ....

....by a function of k. Consequently, if we include Q in the program P , a finite subset of the Herbrand universe is sufficient to answer Q. Since it is in general undecidable whether a given program has the bounded term size property one has to define some decidable criterion which approximates it [20]. 7 Definition 4.7 (Models) Given a Sigma interpretation I Sigma , s 2 Sigma and R 2 B P we define I Sigma j= s] R iff R 2 Del(s) and I Sigma j= s] R iff R 2 True(s) For a Sigma ground rule r : 0 H 1 B 1 ; n B n we define I Sigma j= r iff I Sigma j= i B i ....

A. Van Gelder. Negation as failure using tight derivations for general logic programs. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 149--176. Morgan Kaufmann, 1988.

No context found.

Van Gelder, A. Negation as Failure Using Tight Derivations for General Logic Programs. In Proc. Third IEEE International Symposium on Logic Programming , (1986), 149--176.

No context found.

Van Gelder, A., Negation as failure using tight derivations for general logic programs. Journal of Logic Programming, Vol. 6, n. 1, pp. 109--133, 1989.

No context found.

Van Gelder, A., Negation as failure using tight derivations for general logic programs. Journal of Logic Programming, Vol. 6, n. 1, pp. 109--133, 1989.

No context found.

Van Gelder A., Negation as failure using tight derivations for general logic programs, In Minker J., editor, Foundations of Deductive Databases and Logic Programming, pages 149176, Morgan Kaufmann Publishers, Los Altos, CA, 1988.

No context found.

A. van Gelder. Negation as failure using tight derivations for general logic programs. In Foundations of Deductive Databases and Logic Programming, pages 149--176. Morgan Kaufmann, San Mateo (CA), 1988.

No context found.

A. van Gelder. Negation as failure using tight derivations for general logic programs. In J. Minker (ed.) Foundations of deductive databases and logic programming, pp. 149-- 176, Morgan Kaufmann Publishers Inc., 1988

No context found.

A. Van Gelder. Negation as Failure using tight derivations for general logic programs. In [Min88b], pp. 1149-176. 1988.

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