T. Eiter, N. Leone and D. Sacca. On the partial semantics for disjunctive deductive databases. Annals of Math. and AI., 19(1-2): 59-96, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....stable models are expressed using unfounded sets. Another common semantics for disjunctive logic programs is the three valued stable semantics introduced by [Prz91] With three valued stable models, it is possible for some propositions to remain unknown, i.e. they are neither true nor false. In [ELS97] a characterization of these three valued stable models is given in terms of unfounded sets, which are different from the unfounded sets in [LRS97] Also the well founded semantics for normal logic programs has been extended to disjunctive logic programs, albeit in different ways: BLM89] uses a ....

....single rule a b and consider I = fa; bg. Then M : fa; bg but M fl P fa; bg. 4 Unfounded Sets vs. Forcing The intuition of forcing negative literals strongly resembles the intuition underlying socalled unfounded sets as defined in [GRS88] for disjunctive free logic programs and in [LRS97, ELS97] for disjunctive logic programs. In this section we will investigate and formalize this connection. We will use a slightly more general definition than the one defined in [LRS97] Definition 7 Let P be a disjunctive logic program and let I be an interpretation for P . A set X BP is called an ....

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Thomas Eiter, Nicola Leone, and Domenico Sacca. On the Partial Semantics for Disjunctive Deductive Databases. Annals of Mathematics and Atificial Intelligence, 19(1--2):59--96, 1997.

....all the important properties that have been proven for D WFS. We prove that WFDS is equivalent to D WFS . We also provide a bottom up evaluation procedure for WFDS (and D WFS ) Second, we define a new notion of unfounded sets which is a generalization of the unfounded sets defined in [7, 5]. Based on this new notion of unfounded sets, we define a well founded semantics U WFS for disjunctive programs. We show that U WFS is equivalent to WFDS (and thus D WFS ) Moreover, in [14] we have developed a top down procedure D SLS Resolution which is sound and complete with respect to our ....

....model [12] is given in term of unfounded sets and it has been proved that the notion of unfounded sets constitutes a powerful and intuitive tool for defining semantics for logic programs. This notion has also been generalized to characterizing stable semantics for disjunctive logic programs in [7, 5]. However, the two kinds of unfounded sets defined in [7, 5] can not be used to define an intended well founded semantics for disjunctive programs. Example 5. 3 a b c not a; not b 3 This example is due to Jurgen Dix (personal communication) Intuitively, not c should be derived from the ....

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T. Eiter, N. Leone and D. Sacca. On the partial semantics for disjunctive deductive databases. Annals of Math. and AI., 19(1-2): 59-96, 1997.

....To deal with negation, Przymusinski uses a generalised (3 valued) version of the Gelfond Lifschitz reduction (described below) It is therefore sensitive to the syntactic shape of program formulas. A second variant of partial stability is that of P stable model, due to Eiter, Leone and Sacc a [8]. It also uses 3 valued interpretations or models, but the semantics is described using a notion of unfounded set. This in turn also appeals to the syntax or program formulas, in particular to the fact that formulas can be split into two distinct parts: a head and a body . P stable and 3 valued ....

....or models, but the semantics is described using a notion of unfounded set. This in turn also appeals to the syntax or program formulas, in particular to the fact that formulas can be split into two distinct parts: a head and a body . P stable and 3 valued stable models are shown in [8] to be equivalent. Neither of these variants describe (partial) stable models as minimal models in any previously studied nonclassical logic. A third approach to partial stability was taken by the present author in [26] There, so called back and forth models are defined as particular kinds of ....

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Eiter, T, Leone, N, & Sacc`a, D, On the Partial Semantics for Disjunctive Deductive Databases, Ann Math & Artificial Intelligence 19 (1997), 59-96.

....of Pi, or in some suitable, universal language) In this case Gamma(I ) represents the set of false atoms. 4 Disjunctive Logic Programs There is no general agreement on how to extend WFS or stationary semantics to disjunctive programs; different proposals can be found e.g. in [27] 28] 4] [6, 7]. The back and forth semantics turns out to be equivalent to the partial stable (or P stable) semantics recently extended to disjunctive programs by Eiter, Leone and Sacc a [6, 7] this is in turn equivalent to Przymusinski s [27] 3 valued stable semantics. The P stable semantics is defined in ....

.... to extend WFS or stationary semantics to disjunctive programs; different proposals can be found e.g. in [27] 28] 4] 6, 7] The back and forth semantics turns out to be equivalent to the partial stable (or P stable) semantics recently extended to disjunctive programs by Eiter, Leone and Sacc a [6, 7]; this is in turn equivalent to Przymusinski s [27] 3 valued stable semantics. The P stable semantics is defined in terms of what are called unfounded sets. The authors use a slightly different notion of model or interpretation. For them an interpretation M = M [ M Gamma is a consistent ....

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Eiter, T, Leone, N, & Sacc`a, D, On the Partial Semantics for Disjunctive Deductive Databases, Ann Math & Artificial Intelligence 19 (1997), 59-96.

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T. Eiter, N. Leone, and D. Sacca. On the Partial Semantics for Disjunctive Deductive Databases. Annals of Mathematics and Arti cial Intelligence, 17(1/2): 59-96, 1997.

.... 32, 55, 70, 77, 6] One of the attractions of disjunctive logic programming (DLP) is its capability of allowing the natural modeling of incomplete knowledge [7, 73] Much research has been spent on the semantics of disjunctive logic programs, and several alternative semantics have been proposed [10, 47, 55, 76, 85, 88, 86, 92, 93] (see [2, 24, 73, 77, 78] for comprehensive surveys) The most widely accepted semantics is the answer sets semantics proposed by Gelfond and Lifschitz [55] as an extension of the stable model semantics of normal logic programs [54] According to this semantics, a disjunctive logic program may ....

T. Eiter, N. Leone, and D. Sacca. On the Partial Semantics for Disjunctive Deductive Databases. Annals of Mathematics and Artificial Intelligence, 19(1--2):59--96, April 1997.

....it does not assign a model to each program. In particular, meaningful programs may have no total stable model. To overcome this drawback, a number of partial model semantics have been recently proposed, which relax the notion of total stable model and assign a meaning to a wider class of programs [5,23,44,49,48,58,59]. In a sense, these partial models approximate total stable models. The first relaxation of total stable was the notion of partial stable model (also 1 An abstract of this paper has been presented at the Workshop on Logic in Databases (LID 96) San Miniato, Italy, July 1996. 2 Partially ....

....only when necessary (i.e. a good semantics should tend to minimize the set of undefined atoms) The attempt to minimize undefinedness in partial models led to three main notions of partial models: maximal stable, regular, and least undefined stable models. The maximal stable (M stable) models [23,50,47,48] are those partial stable models which are maximal under set inclusion (where a partial model is represented by the set of ground literals true in the model) On disjunction free programs, M stable models coincide with the preferred extensions of [20] the regular models of [58] the maximal ....

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T. Eiter, N. Leone, and D. Sacc`a. On the Partial Semantics for Disjunctive Deductive Databases. Annals of Mathematics and Artificial Intelligence, special issue on advances in logic-based database languages, 1997.

.... of disjunction in the rules heads because it makes disjunctive logic programming inherently nonmonotonic, i.e. new information can invalidate previous conclusions) Much research has been done on the semantics of disjunctive logic programs, and several alternative semantics have been proposed [10, 21, 30, 44, 52, 50, 51, 56, 58] (see [1, 15, 37] for comprehensive surveys) One widely accepted semantics is the extension to the disjunctive case of the stable model semantics of Gelfond and Lifschitz [31] According to this semantics [30, 50] a disjunctive logic program may have several alternative models (but possibly ....

....weakly stratified, and modularly stratified normal logic programs. 34 7 Related Work The notion of unfounded sets presented in this paper generalizes from normal to disjunctive programs the corresponding notion defined by Van Gelder, Ross and Schlipf in [64] as proven in Proposition 3. 3) In [21], to characterize the 3 valued stable models of Przymusinski [50] in terms of unfounded sets, Eiter et al. provide a definition of unfounded sets for disjunctive logic programs. In that definition, Condition 3 of Definition 3.1 is replaced by the weaker requirement H(r) 6 ( I [ X) because (H(r) ....

Eiter, T., Leone, N. and Sacc'a, D. (1997), On the Partial Semantics for Disjunctive Deductive Databases, Annals of Mathematics and Artificial Intelligence, J. C. Baltzer AG, Science Publishers, Forthcoming.

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T. Eiter, N. Leone and D. Sacca. On the partial semantics for disjunctive deductive databases. Annals of Math. and AI., 19(1-2): 59-96, 1997.

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T. Eiter, N. Leone and D. Sacca. On the partial semantics for disjunctive deductive databases. Annals of Math. and AI., 19(1-2): 59-96, 1997.

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T. Eiter, N. Leone, and D. Sacca. On the partial semantics for disjunctive deductive databases. AMAI 19(1-2): pp. 59-96, 1997.

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