T. Przymusinski. A semantics for disjunctive logic programs. In Loveland, Lobo, and Rajasekar, editors, ILPS'91 Ws. in Disjunctive L.P., 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... 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] 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, ....

....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 well founded semantics [6, 15, 17, 19, 26, 27, 28] shows these generalizations to be rather technical in nature, where the different techniques introduced to characterize the well founded semantics of normal logic programs are slightly modified in some way to become applicable to the more general case. Our first contribution is the presentation ....

T. Przymusinski. A semantics for disjunctive logic programs. In Loveland, Lobo, and Rajasekar, editors, ILPS'91 Ws. in Disjunctive L.P., 1991.

.... showed the importance of having a second kind of negation in logic programs for use in deductive databases, knowledge representation, and nonmonotonic reasoning [6, 7, 8, 9, 13, 14, 15, 24] Different semantics for logic programs extended with : negation (extended logic programs) have appeared [1, 4, 6, 9, 11, 12, 17, 19, 24] but, contrary to what happens with semantics for normal logic programs, there is no general comparison among them, specially in what concerns the use and meaning of the newly introduced : negation. The goal of this paper is to contrast a variety of these semantics in what concerns their use and ....

....semantics for extended logic programs, where the parameters are two: one the axioms AX: defining : negation; another the minimality conditions not cond defining not negation. By adjusting these parameters in the schema we can then specify several semantics involving two kinds of negation [6, 11, 17, 19, 24]. Other semantics, dealing with contradiction removal [1, 4, 12, 22] are not addressed yet by the schema. The issue will be briefly touched upon in section 5, as well as that of incorporating disjunction. The structure of the paper is as follows: we begin with preliminary definitions; in section ....

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T. Przymusinski. A semantics for disjunctive logic programs. In Loveland, Lobo, and Rajasekar, editors, ILPS'91 Workshop in Disjunctive Logic Programs, 1991.

....KS90, PW90, PAA91b, PAA91d, PAA92b, PDA93b, PDA93c, PDA93a, PAA93, Wag91] BG93] makes an overview of the use of such programs in knowledge representation and NMR. Different semantics for extended logic programs with : negation (ELP) have appeared [DR91, GL90, KS90, PA92, PAA91a, PAA92a, Prz90, Prz91a, Sak92, Wag91] Each of these semantics is a generalization for ELP of either the stable models semantics (SM) GL88] or the well founded semantics (WFS) GRS91] of normal programs. In [Prz90, Dix91, Dix92] SM and WFS are contrasted, and it is argued that, by its structural properties, WFS is ....

T. Przymusinski. A semantics for disjunctive logic programs. In Loveland, Lobo, and Rajasekar, editors, ILPS'91 Ws. in Disjunctive Logic Programs, 1991.

....within CRSX 36 10 Related work 37 A CRSX Review 44 1. Introduction Recently, several authors have stressed and showed the importance of having an explicit second kind of negation within logic programs, for use in deductive databases, knowledge representation, and non monotonic reasoning [3, 6, 11, 18, 16, 32, 33, 34, 43, 39]. In non monotonic reasoning with logic programming there are two main ways of giving meaning to sets of rules when a given semantics is assigned to a program defined by the set of rules. We either accept as consequences the intersection of all models identified by some semantics, which is called ....

....a second kind of negation is suggested by Przymusinski in [38] Although the set of models identified by this extension enjoys the well founded property, it gives some less intuitive results [1] with respect to the coexistence of both forms of negation. Based on the XSM semantics Przymusinski [39] also introduces the Stationary semantics where the second form of negation is classical negation. Unfortunately, classical negation also implies that the logic programs under Stationary semantics no longer admit a procedural reading. Well Founded Semantics with Explicit Negation (WFSX) 26] is an ....

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T. C. Przymusinski. A semantics for disjunctive logic programs. In D. Loveland, J. Lobo, and A. Rajasekar, editors, ILPS Workshop on Disjunctive Logic Programs, 1991.

....the contradiction removal semantics coincides with WFSX. 1 Introduction Recently, several authors have stressed and showed the importance of having an explicit second kind of negation within logic programs, for use in deductive databases, knowledge representation, and nonmonotonic reasoning [2, 4, 5, 7, 6, 14, 15, 16, 23, 21]. Some proposals for extending logic programming semantics with a second kind of negation has been advanced. One such extension is the Answer Set semantics (AS) 4] which is shown to be an extension of Stable Model (SM) semantics [3] from the class of logic programs [8] to those with a second ....

....a second kind of negation is suggested by Przymusinski in [20] Although the set of models identified by this extension enjoys the well founded property, it gives some less intuitive results [1] with respect to the coexistence of both forms of negation. Based on the XSM semantics, Przymusinski [21] also introduces the Stationary semantics where the second form of negation is classical negation. But classical negation also entails that the logic programs under Stationary semantics no longer admit a procedural reading. On the other hand, WFSX 1 (Well Founded Semantics with eXplicit ....

[Article contains additional citation context not shown here]

T. C. Przymusinski. A semantics for disjunctive logic programs. In D. Loveland, J. Lobo, and A. Rajasekar, editors, ILPS Workshop on Disjunctive Logic Programs, 1991.

.... have underscored the advantages of extending logic programming with a second kind of negation : for use in deductive databases, knowledge representation, and nonmonotonic reasoning [GL90, KS90, PAA91, Wag91] Different semantics for extended logic programs with : negation (ELP) have appeared [DR91, GL90, KS90, PA92, Prz90, Prz91, Wag91]. AP92] contrasts some of these, where distinct meanings of : negation are identified: classical, strong and explicit. It is argued there that explicit negation is preferable. The well founded semantics with explicit negation (WFSX) PA92] incorporates this prefered : negation, and also ....

T. Przymusinski. A semantics for disjunctive logic programs. In Loveland, Lobo, and Rajasekar, editors, ILPS'91 Ws. in Disjunctive Logic Programs, 1991.

.... of extending logic programming with a second kind of negation : in addition to default negation, for use in deductive databases, knowledge representation, and nonmonotonic reasoning [GL90, KS90, PAA91b, Wag91] Different semantics for extended logic programs with : negation have appeared [DR91, GL90, KS90, PA92, Prz90, Prz91b, Wag91]. AP92] contrasts some of these, where distinct meanings of : negation are identified: classical, strong and explicit. It is also argued that explicit negation is preferable. Some work exists comparing extended logic programs semantics and nonmonotonic reasoning formalisms. In [GL90] the ....

....semantics of extended logic programs. The next theorem makes this statement precise for answer sets and WFSX semantics. It generalizes for almost every semantics of extended logic programs, the only exception being, to our knowledge, the stationary semantics with classical negation defined in [Prz91b], which is contrapositive. Theorem 1.1 Let P be an extended logic program, and T the theory obtained from P by means of translation (2) If T K EA E A, for no atom A; then: T K EA j P j= AS A j P j= WFSX A T K E A j P j= AS :A j P j= WFSX :A where S denotes, as usual, the consequence ....

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T. Przymusinski. A semantics for disjunctive logic programs. In Loveland, Lobo, and Rajasekar, editors, ILPS'91 Ws. in Disjunctive Logic Programs, 1991.

....representing non monotonic problems in logic programming. 1 Introduction Recently, several authors have stressed and showed the importance of introducing an explicit second kind of negation within logic programs, for use in deductive databases, knowledge representation, and nonmonotonic reasoning [2, 4, 6, 9, 8, 17, 18, 19, 25, 22]. It has been argued [18, 19, 17, 16] that semantics with the well founded property are adequate to capture nonmonotonic reasoning if we interpret the least model provided by the semantics (called the Well Founded Model of a program) as the skeptical view of the world, and the other models (called ....

....a second kind of negation is suggested by Przymusinski in [21] Although the set of models identified by this extension enjoys the well founded property, it gives some less intuitive results [1] with respect to the coexistence of both forms of negation. Based on the XSM semantics, Przymusinski [22] also introduces the Stationary semantics where the second form of negation is classical negation. But, classical negation entails that the logic programs under Stationary semantics no longer admit a procedural reading. On the other hand, Well Founded Semantics with Explicit Negation (WFSX ) 13] ....

T. C. Przymusinski. A semantics for disjunctive logic programs. In D. Loveland, J. Lobo, and A. Rajasekar, editors, ILPS Workshop on Disjunctive Logic Programs, 1991.

....step Phi P is not applicable then we end our iteration and say that P is contradictory. Otherwise we iterate until the least fixpoint of Phi P , which is the WFM of P . It is worth noting that this semantics is a generalization of the stationary semantics (or extended stable model semantics) [18, 19, 20], to programs with explicit negation. Theorem 3.6 For programs without explicit negation our semantics coincide with stationary semantics. 5 Top down procedures computing this semantics (for noncontradictory programs) can be easily obtained by adapting existing procedures for programs without ....

T. Przymusinski. A semantics for disjunctive logic programs. In ILPS'91 Workshop in Disjunctive Logic Programs, 1991.

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