A. V. Gelder, K. A. Ross, and J. S. Schlipf. The well-founded semantics for general logic programs. Journal of the ACM, 38(3):620--650, 1991.  Home/Search   Document Details and Download   Summary   ACM   TOC   Related Articles   Check

....of all base predicates and corresponds to the notion of a database state that is changed by transactions. For Datalog (with negation) there are several di erent semantics such as strati ed semantics [3, 29] in ationary semantics [8] stable model semantics [12] and well founded semantics [11]. To be general enough, we don t restrict ourselves to any particular semantics for our intensional databases. Instead, we introduce the following notion. Definition 23 Let P = IDB;TDB) be a well de ned program and EDB an extensional database. Then M(EDB; IDB) denotes the intended semantics of ....

A. V. Gelder, K. A. Ross, and J. S. Schlipf. The Well-Founded Semantics for General Logic Programs. Journal of ACM, 38(3):620-650, 1991.

....applied to standard query languages. Relational calculus can express non eventually computable queries, but a positive fragment can be defined that only expresses eventually computable queries. The Datalog : languages yield some surprises: the standard semantics, stratified and well founded [51], are ill suited for expressing eventually computable queries, whereas the inflationary semantics [8, 69] turns out to be naturally suited to express such queries, and thus has an advantage over the first two semantics [10] 3.2 Query Languages The query languages proposed in the context of the ....

A. V. Gelder, K. Ross, and J. Schlipf. The well-founded semantics for general logic programs. J. ACM, 38:620--650, 1991.

....report, read, Sam) for each working day of 1997 and 1998 (from R 1 ) and we cannot derive any authorization from R 2 . If we evaluate first R 2 , we derive (technical staff, 9 Due to the properties of the resulting program, in this case stable models are identical to wellfounded models [Gelder et al. 1991]. An Access Control Model Supporting Periodicity Constraints and Temporal Reasoning Delta 19 report, write, Sam) for each working day of 1997 and 1998, and we cannot derive any authorization from R 1 . From the point of view of the semantics, the property of always having a unique set of ....

....becomes only dependent on the number of authorizations and rules in TAB. However, we prefer to adopt a less restrictive approach, refusing the insertion of a derivation rule only if its insertion into the existing TAB leads to a corresponding logic program that is neither locally stratified [Gelder et al. 1991], nor equivalent to a locally stratified one, and, hence, with a non clear choice for the rules evaluation order. We accept the insertion of all other rules, even those identified above, which could cause the generation of a high number of levels. We believe that real world specifications will ....

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Gelder, A. V., Ross, K., and Schlipf, J. S. 1991. The well-founded semantics for general logic programs. Journal of the ACM 38, 3 (July), 620--650.

....expressive by using negated literals in the rule bodies. For our purposes, there are two relevant extensions of pure Datalog by negation: Datalog with stratified negation [Apt et al. 1988] where negation does not interact with recursion, and the more expressive Datalog with well founded negation [Gelder et al. 1991]. The advantages of the Datalog query languages are: ffl Datalog is a purely declarative query language with a clear and simple semantics; it facilitates modular specifications, where intermediate properties can be expressed by separate groups of rules and reused. ffl Datalog has polynomial data ....

....query ( Pi : W ) For example, the single rule query ( Pi; W ) Wx (8z:Exz)Mz is rewritten by the query ( Pi : W ) which contains the two rules Wx :W : x and W : x Exz; Mz. For recursive Pi however, Pi : will in general not be stratified. The well founded semantics [Gelder et al. 1991] though assigns the correct meaning to the query: Theorem 18 The rewriting operation Pi 7 Pi : is a conservative embedding of Datalog LITE into well founded Datalog. Thus, up to trivial rewriting operations, Datalog LITE is a fragment of well founded Datalog; by the following result, we ....

Gelder, A. V., Ross, K. A., and Schlipf, J. S. (1991). The well-founded semantics for general logic programs. J. ACM, 38(3):620--650.

....which are briefly defined and explained. Most of the semantics are accompanied with their multi valued model theory, giving them a new perspective. The survey also presents new results regarding the embedding of part of these semantics into normal logic programs under WellFounded Semantics [20], Partial Stable Model Semantics (or stationary semantics) 48] and Stable Model Semantics [21] Furthermore, a concise recapitulation of other related paraconsistent formalisms is made. The reader is assumed to have a good knowledge of the semantics of normal logic programs. We believe a ....

A. V. Gelder, K. A. Ross, and J. S. Schlipf. The well-founded semantics for general logic programs. Journal of the ACM, 38(3):620--650, 1991.

....with an overview of the properties of some wellknown semantics (see also [BD95b] for interesting characterizations of STABLE) Theorem20 [BD95c] Properties of Logic Programming Semantics Semantics Domain El. Taut. GPPE P. N. Red. Nonmin. Clark s comp [Cla78] Nondis. ffl ffl ffl WFS [vGRS91] Nondis. ffl ffl ffl ffl GCWA [Min82] Pos. ffl ffl (trivial) ffl WGCWA [RLM89] 5 Pos. ffl (trivial) Positivism [BH86] Dis. ffl ffl ffl STABLE [GL91, Prz91a] Dis. ffl ffl ffl ffl Strong WFS [Ros89] Dis. ffl STATIONARY [Prz91b] Dis. ffl ffl ffl ffl STATIC [Prz95] ....

Allen van Gelder, Kenneth A. Ross, and John S. Schlipf. The well-founded semantics for general logic programs. Journal of the ACM, 38:620--650, 1991.

....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 negation under the perfect model semantics and developed SLSC resolution for constructive negation of stratified programs [21] In [11] Drabent described SLSFA resolution for ....

....of a rule that is undefined in I. I is a three valued stable model of P if I is the least three valued model LPM ( P I ) The set of all three valued stable models of P is denoted by ST 3(P ) The notion of three valued stable models is a generalization of both the well founded partial model [30] and the (two valued) stable models [13] Theorem 2.2 ( 23] Let P be a program, and WF(P ) be the well founded partial model of P . Then WF(P ) is the smallest three valued stable model of P . Stable models as defined by Gelfond and Lifschitz coincide with two valued stable models. 3. ....

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A. Van Gelder, K.A. Ross, and J.S. Schlipf. The well-founded semantics for general logic programs. Journal of ACM, 38(3):620--650, July 1991.

....between those semantics. Introduction In general, approaches to semantics follow two major intuitions: scepticism and credulity [30] In logic programming, the credulous approach includes such semantics as stable semantics [7] and preferred extensions [3] while well founded semantics [31] is the sole representative of scepticism [3] Recently, several authors have stressed and shown the importance of including a second kind of negation in logic programs, for use in deductive databases, knowledge representation, and non monotonic reasoning [8, 9, 10, 11, 13, 21, 22, 23, 24, 32] ....

.... 13, 21, 22, 23, 24, 32] Different semantics for logic programs extended with an explicit negation (extended logic programs) have appeared [6, 8, 11, 15, 17, 19, 26, 27, 28, 32] Many of these semantics are either a generalization of stable models semantics [7] or of well founded semantics (WFS) [31] (cf. 1] for a comparison) Others are based on constructive logic [12, 13, 14] While generalizations of stable models semantics are clearly credulous in their approach, no semantics whatsoever has attempted to seriously explore the sceptical approach. A closer look at the works generalizing ....

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A. Van Gelder, K. A. Ross, and J. S. Schlipf. The well-founded semantics for general logic programs. Journal of ACM, 1990.

....predicates and corresponds to the notion of a database state that is changed by transactions. Static Semantics For Datalog (with negation) there are several di erent semantics such as strati ed semantics [3, 26] in ational semantics [8] stable model semantics [12] and well founded semantics [11]. To be general enough, we don t restrict ourselves to any particular semantics. Instead, we introduce the following notion. Let P = IDB;TB) be a program and EDB a database. Then M(EDB; IDB) denotes the intended semantics of EDB and IDB. Let L be a ground literal. We use M(EDB; IDB) j= L and ....

A. V. Gelder, K. A. Ross, and J. S. Schlipf. The Well-Founded Semantics for General Logic Programs. Journal of ACM, 38(3):620-650, 1991.

....Programming. SLG is a generalization of SLD resolution with tabling. A form of SLD with tabling has been shown in [13] to be asymptotically equivalent to a variant of magic templates [11] Among properties relevant to deductive databases, SLG evaluates programs according to the well founded model [16], terminates for programs with bounded term size, and has polynomial data complexity for Datalog programs with negation. SLG is amenable to efficient implementation, as shown by the performance of the XSB system [12] In particular, the XSB system has been shown to compute in memory deductive ....

A. van Gelder, K. A. Ross, and J. S. Schlipf. The well-founded semantics for general logic programs. Journal of the ACM, 38(3), 1991.

....by ROSS TOPOR in [38] confluence.tex; 13 03 1997; 15:54; no v. p.19 20 Stefan Brass and Jurgen Dix Table I. An Overview of Semantics and Their Properties. Properties of Logic Programming Semantics Semantics Domain Taut. GPPE Contra Non Min. Clark s comp [16] Norm. no ffl no ffl WFS [41] Norm. ffl ffl no ffl WFS [17] 7 Norm. ffl no no ffl GCWA [27] Pos. ffl ffl triv. ffl WGCWA [36] 8 Pos. no ffl triv. no Positivism [6] Dis. no ffl no ffl STABLE [25, 33] Dis. ffl ffl ffl ffl Strong WFS [37] Dis. no no no no STATIONARY [34] Dis. ffl ffl no ffl STATIC [35] Dis. ffl ....

Allen van Gelder, Kenneth A. Ross, and John S. Schlipf. The well-founded semantics for general logic programs. Journal of the ACM, 38:620--650, 1991.

....in the past two decades. A whole spectrum of semantic theories for logic programs have been proposed, ranging from those that infer very little information from a logic program ( skeptical ) to those that infer a great deal ( credulous ) The most skeptical semantics is the well founded semantics [4] while the most credulous is the the stable model semantics [6] and its different but equivalent three valued versions, including 3 stable models [8] partial stable models [9] and preferred extensions [2] The chief drawback of the stable semantics is that a two valued stable model is not ....

....revising mechanism as we do in [10] does enable us to assign the proper meaning to the program P 1 . In the quasi stable semantics, P 1 has fpg or equivalently fp; not qg as its unique quasi stable model. Example 3. 2 Consider the program P 2 with the following four rules, which is borrowed from [4]: a : Gamma not b: b : Gamma not a: p : Gamma not p: p : Gamma not b: It is easy to see that the program P 1 2 with only the first two rules has two stable models: fa; not bg and fnot a; bg. But when the third rule is added to P 1 2 , the resulting program P 2 2 has no stable models ....

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A. van Gelder, K. A. Ross, and Schlipf J. S. The well-founded semantics for general logic programs. Journal of the Association for Computing Machinery, 38(3):620--650, 1991.

....this section we present the above mentioned parametrizeable schema. First we begin by defining two generic semantics for normal logic programs extended with an extra kind of negation: one extending the stationary semantics [18, 19] for normal programs (itself equivalent to well founded semantics [23]) another extending the stable model semantics [5] We dub these semantics generic because they assume little about the extra kind of negation introduced. The meaning of the negation by default is however completely determined in each of the two semantics (both stationary and stable models) that ....

A. Van Gelder, K. A. Ross, and J. S. Schlipf. The well-founded semantics for general logic programs. Journal of ACM, pages 221--230, 1990.

....( Cha88] further extended by Przymusinski in [Prz89] In the latter category, a canonical model is taken as the meaning of a program. This approach was initiated by the idea of stratification (see [Min88] and extended in a number of ways such as stable models ( GL88] well founded models ([vGRS91]) well founded by case models ( Sch90] and valid semantics ( BRSS92] These models do not necessarily coincide always. Approaches through other systems of logic such as linear logic or modal logic have also been considered. A survey of most of these semantics in the context of negation as ....

Van Gelder, A., Ross, K., and Schlipf, J. S.: The Well-Founded Semantics for General Logic Programs, Jnl. of ACM, Vol. 38, No. 3, Jul 1991, pp. 620--650.

....for the corresponding first order theory, the completed database. Historically, this was the first declarative semantics for programs with negation as failure. Supported sets were defined in [ Apt et al. 1988 ] Well founded and unfounded literals were introduced (for normal programs) in [ Van Gelder et al. 1990 ] and [ Przymusinski, 1991 ] This concept is often used as a semantical foundation for logic programming. According to the well founded semantics, only well founded literals are counted as consequences of the program. This approach and its extensions are applied to knowledge representation in ....

Allen Van Gelder, Kenneth Ross, and John Schlipf. The wellfounded semantics for general logic programs. Journal of ACM, pages 620--650, 1990.

....been followed be Schaerf in [Sch93, Sch95] and by Bonatti in an even more general context ( Bon93] Thus our idea is that some theories carry in their syntactic form one or more computational procedures that can be associated with that theory. In this we are taking a position similar to that of [ABW88, Prz88, vGRS91]. While Schaerf considered Weak STABLE and WeakSupported, we investigate in this paper the two semantics ffl Weak M supp P , and ffl Weak WFS. Results about properties of Weak M supp P have been already given in [DGM94] These results are now extended to Weak WFS and more properties of ....

A. van Gelder, K. A. Ross, and J. S. Schlipf. The well-founded semantics for general logic programs. Journal of the ACM, 38:620--650, 1991. 17

....for disjunctive information in the assumption set or program. The ability to express and process indefinite information and case constructions occur in real life and mechanisms to handle such specifications are important. Attention has focused on the semantics of disjunctive logic programming [Pry90, GRS91, LMR89], proof procedures [Lov87, RLS91] and applications to disjunctive databases [Min82, RT88, YH85] One point of view of each of these topics appears in the book [LMR92] The basic requirement of disjunctive logic programming, that disjunctive information be representable in the assumption set, ....

A. Van Gelder, K.A. Ross, and J.S. Schlipf. The well-founded semantics for general logic programs. J. ACM, 38(3):620--650, 1991.

....literals fL; Lg in Lang, we implicitly assume the constraint L; L. The set of all objective literals of a program P is called its extended Herbrand base and is represented as H E (P ) We consider the Extended Well Founded Semantics (WFSX ) that extends the well founded semantics (WFS ) [20] for normal logic programs to programs extended with explicit negation, besides the implicit or default negation of normal programs. WFSX is obtained from WFS by adding the coherence principle (CP) relating the two forms of negation: if L is an objective literal and :L belongs to the model of a ....

Van Gelder, A., K. A. Ross, and J. S. Schlipf: 1991, `The Well-founded Semantics for General Logic Programs'. Journal of the ACM 38(3), 620--650.

....logic. Because of the negation as failure rule, logic programming is also a system of nonmonotonic reasoning. The first semantics for logic programs with negation as failure was given by Clark [1978] Many other semantics followed, the most influential being the well founded semantics [ Van Gelder et al. 1990 ] and the stable model semantics [ Gelfond and Lifschitz, 1988 ] The connection between logic programming and nonmonotonic reasoning was clarified by translations from logic programming into the general nonmonotonic formalisms. Gelfond [1987] for example, showed how to translate logic programs ....

Allen Van Gelder, Kenneth Ross, and John Schlipf. The well-founded semantics for general logic programs. Journal of ACM, pages 221-- 230, 1990.

....model of P . Then WF (P ) is the smallest three valued stable model of P . In [50] Przymuzinski points out that the stable models as defined by Gelfond and Lifschitz [31] coincide with two valued stable models under the definitions provided here. Furthermore, the well founded partial model [80] for a program P coincides with the smallest partial model for P . 2.2 SLG Resolution In order to compute three valued models of non stratified programs, SLG delays evaluation of those literals whose truth value may be undefined. Delayed literals are represented explicitly in X clauses. ....

....That is, no answers are produced at all for p, for q, or for r. When the three subgoals are completely evaluated, they can be completed, and the truth of s derived. As an aside, we point out that the second cycle, consisting of the subgoals fp; q; rg fulfills the definition of an unfounded set ([80]) in the interpretation where fp; q; rg are neither true nor false, while the first cycle of subgoals fp; q; rg does not. Accordingly, the second cycle can be judged false under the definition of the well founded semantics, while the first cannot be. p q r s Figure 6: CDG for ....

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A. van Gelder, K.A. Ross, and J.S. Schlipf. The well-founded semantics for general logic programs. JACM, 38(3), 1991. BIBLIOGRAPHY 168

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A. V. Gelder, K. A. Ross, and J. S. Schlipf. The well-founded semantics for general logic programs. Journal of the ACM, 38(3):620--650, 1991.

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A. V. Gelder, K. A. Ross, and J. S. Schlipf. The well-founded semantics for general logic programs. J. ACM, 38(3):619--649, 1991.

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Gelder, A.V., Ross, K.A., Schlipf, J.S.: The well-founded semantics for general logic programs. J. ACM 38 (1991) 620--650

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A. V. Gelder, K. A. Ross, and J. S. Schlipf. The well-founded semantics for general logic programs. Journal of the ACM, 38(3):620--650, 1991.

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A. V. Gelder, K. A. Ross, and J. S. Schlipf. The well-founded semantics for general logic programs. Journal of the ACM, 38(3):620--650, 1991.

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