P. Dung. A fixpoint approach to declarative semantics of logic programs. In Proc. North American Conf. on Logic Programming, pages 604--625, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....instances without using extra variables. Theorem 2. There exists a polynomial time reduction from a 2 literal program P to a set of clauses S, without using extra variables, such that M is a stable model of P iff M is a model of S. We prove this theorem using Dung s result on fixpoint completion [5], which is based on a mechanism of reducing a program to a quasi program. We sketch our proof below. A quasi program is a collection of quasi rules. A quasi rule is of the form a not c 1 ; not c n where n 0. Given program rules h a 1 ; a k ; not c 1 ; not c n a i not d i;1 ....

P. Dung. A fixpoint approach to declarative semantics of logic programs. In Proc. North American Conf. on Logic Programming, pages 604--625, 1989.

....can not only make our proofs simpler but also provides a canonical form for disjunctive programs with respect to various semantics, including our argumentation theoretic semantics and the disjunctive stable semantics. The program transformation Lf t is based on the idea of Dung and Kanchansut [13] and Bry [12] It is also independently defined by Brass and Dix [8, 10] To define Lf t for disjunctive programs, we first extend the notion of the Herbrand base B P to the generalized disjunctive base GDB P of a disjunctive logic program P . GDB P is defined as the set of all negative ....

Dung, P., Kanchansut K., A fixpoint approach to declarative semantics of logic programs, in: Lusk E. and Overbeek R. (eds.) Proceedings of North American Conference, MIT Press, 1989. 46

....of SQL, too, where user rules have to be stratified. Bottom up approaches to the computation of well founded models based on the alternating fixpoint operator introduced by Van Gelder [16] have been proposed in [10, 15] while in [5, 6] the computation is based on the residual program suggested by [7, 8]. Despite of the advantages of the residual program approach, its notion of conditional facts is hard to implement in a database context. We will therefore concentrate on the efficient implementation of the alternating fixpoint procedure and on its well known drawback of repeated computations. ....

Dung P. M., Kanchanasut K.: A Fixpoint Approach to Declarative Semantics of Logic Programs. NACLP 1989: 604-625.

....is su#cient to guarantee that the resulting transformation system preserves a variety of seman tics for normal logic programs, such as the well founded model, stable model, partial stable model, and stable theory semantics. Central to this proof is the result due to Dung and Kanchanasut [5] that preserving the semantic kernel of a program is su#cient to guarantee the preservation of the di#erent semantics for negation listed above. The notion of semantic kernel is a powerful one, since it captures the commonality of various semantics of normal logic programs. An equivalent notion, ....

....semantics of normal logic programs. This proof proceeds in three steps. First, we show that positive ground derivations (introduced in Definition 2) are preserved by the transformations. Secondly, we show that preserving positive ground derivations is equivalent to preserving semantic kernel [5]. Finally, following [1] preserving semantic kernel implies that the transformation system is correct with respect to various semantics for normal logic programs including well founded model [7] and stable model semantics [8] We begin with a review of semantic kernels. 3.1. Semantic Kernel of ....

[Article contains additional citation context not shown here]

P.M. Dung and K. Kanchanasut. A fixpoint approach to declarative semantics of logic programs. In North American Conference on Logic Programming, pages 604--625, 1989.

....can be accomplished by a suitable generalization of Clark s completion but it only works for a restricted class of knowledge bases, namely those whose clauses do not have any objective premises. Such residual databases were previously introduced and investigated in the class of logic programs [Bry89, Bry90, DK89a, DK89b, BD97c, BD95]. Here we give a slightly more general definition. 10 Definition 3.1 (Residual Knowledge Bases [BD95] By a residual knowledge base we mean an arbitrary non monotonic knowledge base whose clauses do not contain any objective (positive) premises, i.e. a (possibly infinite) set of arbitrary ....

P. M. Dung and K. Kanchansut. A fixpoint approach to declarative semantics of logic programs. In E.L. Lusk and R.A. Overbeek, editors, Proceedings of North American Conference Cleveland,Ohio, USA. MIT Press, October 1989.

....of T Phi as usual: We start with Gamma 0 : and then iterate Gamma i : T Phi ( Gamma i Gamma1 ) until nothing changes. This must happen because our program is finite and propositional. The operator T Phi and the idea of using conditional facts already appeared in work of Dung Kanchansut ([DK89]) and Bry ( Bry89, Bry90] for nondisjunctive programs. Theorem 12 in [BD95a] formally shows that our operator realizes exactly the GPPE and the Elimination of Tautologies. It remains to perform the reductions. Again, we define an operator operating on sets of conditional facts: Definition10 ....

P. M. Dung and K. Kanchansut. A fixpoint approach to declarative semantics of logic programs. In E.L. Lusk and R.A. Overbeek, editors, Proceedings of North American Conference Cleveland,Ohio, USA. MIT Press, October 1989.

....can be accomplished by a suitable generalization of Clark s completion but it only works for a restricted class of knowledge bases, namely those whose clauses do not have any objective premises. Such residual databases were previously introduced and investigated in the class of logic programs [16, 17, 26, 27, 10, 7]. Here we give a slightly more general definition. 14 Definition 3.1 (Residual Knowledge Bases [7] By a residual knowledge base we mean an arbitrary non monotonic knowledge base whose clauses do not contain any objective (positive) premises, i.e. a (possibly infinite) set of arbitrary clauses ....

P. M. Dung and K. Kanchansut. A fixpoint approach to declarative semantics of logic programs. In E.L. Lusk and R.A. Overbeek, editors, Proceedings of North American Conference Cleveland,Ohio, USA. MIT Press, October 1989.

....extension is sufficient to guarantee that the resulting transformation system preserves a variety of semantics for normal logic programs, such as the well founded model, stable model, partial stable model, and stable theory semantics. Central to this proof is the result due to Dung and Kanchanasut [6] that preserving the semantic kernel of a program is sufficient to guarantee the preservation of the different semantics for negation listed above. However, in contrast to [1] where this idea was used to prove the correctness of Tamaki Sato style transformations, we present a two step proof which ....

....semantics of normal logic programs. This proof proceeds in three steps. First, we introduce the notion of positive ground derivations and show that it is preserved by the transformations. Secondly, we show that preserving positive ground derivations is equivalent to preserving semantic kernel [6]. Finally, following [1] preserving semantic kernel implies that the transformation system is correct with respect to various semantics for normal logic programs including well founded model, stable model, partial stable model, and stable theory semantics. We begin with a review of semantic ....

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P.M. Dung and K. Kanchanasut. A fixpoint approach to declarative semantics of logic programs. Proceedings of North American Conference on Logic Programming, 1:604--625, 1989.

....extension is sufficient to guarantee that the resulting transformation system preserves a variety of semantics for normal logic programs, such as the well founded model, stable model, partial stable model, and stable theory semantics. Central to this proof is the result due to Dung and Kanchanasut [5] that preserving the semantic kernel of a program is sufficient to guarantee the preservation of the different semantics for negation listed above. However, in contrast to [1] where this idea was used to prove the correctness of Tamaki Sato style transformations, we present a two step proof which ....

....semantics of normal logic programs. This proof proceeds in three steps. First, we introduce the notion of positive ground derivations and show that it is preserved by the transformations. Secondly, we show that preserving positive ground derivations is equivalent to preserving semantic kernel [5]. Finally, following [1] preserving semantic kernel implies that the transformation system is correct with respect to various semantics for normal logic programs including well founded model, stable model, partial stable model, and stable theory semantics. We begin with a review of semantic ....

[Article contains additional citation context not shown here]

P.M. Dung and K. Kanchanasut. A fixpoint approach to declarative semantics of logic programs. Proceeding of North American Conference on Logic Programming, 1:604--625, 1989.

....obtained the proof of the Theorem 3.1 is largely similar to the proof in [14] of the following result: Theorem 3.2 [14] If P is order consistent then T P has at least a fixpoint In fact, the proof of the Theorem 3.1 can be deduced from the Theorem 3. 2 and from the correspondance etablished in [5] between the stable models of a program P and the fixpoints of the operator T SK(P) associated to the semantic kernel SK(P) of the program P: the semantic kernel of a logic program P is defined as the fixpoint of a continuous operator Q P on quasi interpretations [5] where a quasi interpretation ....

.... correspondance etablished in [5] between the stable models of a program P and the fixpoints of the operator T SK(P) associated to the semantic kernel SK(P) of the program P: the semantic kernel of a logic program P is defined as the fixpoint of a continuous operator Q P on quasi interpretations [5], where a quasi interpretation is a set of ground clauses whose premises are only negative literals and the operator Q P on quasi interpretations is defined as follows: 16 Q P (I) B 1 . B n Body 1 . Body m A there exist C Inst P and C i I, 1im s.t. C is of the form B 1 ....

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Dung P.M., Kanchana Kanchanasut, A fixpoint approach to declarative semantics of logic programs, in: Proc. North American Conf. on Logic Programming, Cleveland, Ohio (MIT Press, Cambridge,MA,1989) 601 - 625

....but that order consistency alone [17] 2] this condition generalizes call consistency [10] 18] it is independent of positive order consistency) is sufficient to ensure the existence of a stable model. The last result is based on a characterization of stable models due to [5] and on a generalization of the result of [17] on the consistency of Clark s completion to infinite logic programs. 2 Introduction and Notations A logic program Pi is a finite set of rules of the form L 1 ; L n A, where A is an atom, called the conclusion and denoted by concl(R) and the ....

....logic, hence it cannot be lifted to infinite logic programs. In fact there exist infinite negative cycle free programs, like f:P (s i (x) P (x) j i 0g; which have an inconsistent Clark s completion. 5 Existence of Stable Models, Part 2 This section makes use of the characterization due to [5] of the stable models of a logic program Pi by the Herbrand models of its fixpoint completion. We recall here the basic definitions with our notations. 9 A quasi interpretation Q is a possibly infinite set of ground rules without positive premise, i.e. of the form :A 1 ; A n A where ....

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P.M. Dung, K. Kanchanasut, A fixpoint approach to declarative semantics of logic programs, NACLP'89. MIT Press (1989). 12

.... that compute the well founded model of a normal program are: The alternating fixpoint approach, introduced by Van Gelder [23, 24] and further developed by Kemp, Stuckey and Srivastava [19] The residual program approach, suggested by Bry [8, 9] and independently by Dung Kanchanasut [15, 16], and extended by Brass and Dix [4, 5] The alternating fixpoint procedure is known to have efficiency problems, since in every iteration many facts have to be recomputed. The residual program approach avoids recomputations of this kind. But it is possible that the residual program can grow to ....

P. M. Dung and K. Kanchansut. A fixpoint approach to declarative semantics of logic programs. In Proc. North American Conference on Logic Programming (NACLP'89), pages 604--625, 1989.

....i.e. ground rules without positive body literals . Conditional facts result from delaying the negative body literals during a bottom up evaluation of an allowed logic program (the delayed literals are attached as conditions to the derived facts) Conditional facts have already been studied in [Bry89, Bry90, DK89b, DK89a, HY91] (for non disjunctive programs) We especially generalize the TP operator and the reductions introduced by Bry to the disjunctive case. However, our main result is the relation of this bottom up computation to our elementary program transformations. 2. A consequence of this is that the residual ....

....program. In contrast to the last section, we no longer work on instantiated programs. However, we use the allowedness condition to bind the variables and avoid floundering. Our approach is based on the notion of conditional facts , as developed by Bry in [Bry89, Bry90] and Dung Kanchansut in [DK89b, DK89a] (both for the non disjunctive case) The idea is to delay the evaluation of negative body literals, and to attach them as conditions to the derived (disjunctive) facts. Definition 3.1. Conditional Fact) A conditional fact is a rule without positive body literals, i.e. it is of the form A 1 ....

[Article contains additional citation context not shown here]

P. M. Dung and K. Kanchansut. A fixpoint approach to declarative semantics of logic programs. In E.L. Lusk and R.A. Overbeek, editors, Proceedings of North American Conference Cleveland,Ohio, USA. MIT Press, October 1989.

....program, but it does not satisfy the first rule in the original program. 4 Characterizations of the Semantics In this section we give characterizations of the semantics Weak SUPP, SUPP, GCWA, PERFECT and STABLE in terms of our abstract properties. We begin with a useful lemma (Dung Kanchansut in [DK89], Bry in [Bry90] and Hu Yuan in [HY91] also considered rules with only negative literals) Lemma 13 Normal Form. Let SEM be a semantics satisfying GPPE and Elimination of Tautologies. Then any program Phi is SEM equivalent to a program Phi 0 where all clauses have the form A :B Gamma ....

P. M. Dung and K. Kanchansut. A fixpoint approach to declarative semantics of logic programs. In E.L. Lusk and R.A. Overbeek, editors, Proceedings of North American Conference Cleveland,Ohio, USA. MIT, October 1989.

....semantical properties. Abstract semantical properties were already used for implementation purposes in [DM93] but here we show that our semantics can be implemented by only using these properties. Our method uses the notion of conditional facts developed by Bry ( Bry90] and Dung Kanchansut ([DK89]) which we generalize to the disjunctive case. The idea is to delay the evaluation of negative body literals during the fixpoint computation of derived facts, and then to perform some simple reductions. The result Phi is similar to the residual program of [CW93b] however, our (and Bry s) ....

....we define our bottom up evaluation procedure. In contrast to the last section we no longer work on instantiated programs. Of course we use the allowedness condition to bind the variables and avoid floundering. Our approach is based on the notion of conditional facts . This idea was introduced in [Bry89, DK89] but is now extended to the disjunctive case. The idea is to delay the evaluation of negative body literals. From winning(X) move(X; Y ) winning(Y ) and the fact move(a; b) we derive the fact winning(a) winning(b) Definition 3.1 (Conditional Fact) A conditional fact is a rule without ....

[Article contains additional citation context not shown here]

P. M. Dung and K. Kanchansut. A fixpoint approach to declarative semantics of logic programs. In E.L. Lusk and R.A. Overbeek, editors, Proceedings of North American Conference Cleveland,Ohio, USA. MIT, October 1989.

....can be accomplished by a suitable generalization of Clark s completion but it only works for a restricted class of knowledge bases, namely those whose clauses do not have any objective premises. Such residual databases were previously introduced and investigated in the class of logic programs [16, 17, 26, 27, 10, 7]. Here we give a slightly more general definition. Definition 3.1 (Residual Knowledge Bases [7] By a residual knowledge base we mean an arbitrary non monotonic knowledge base whose clauses do not contain any objective (positive) premises, i.e. a (possibly infinite) set of arbitrary clauses of ....

P. M. Dung and K. Kanchansut. A fixpoint approach to declarative semantics of logic programs. In E.L. Lusk and R.A. Overbeek, editors, Proceedings of North American Conference Cleveland,Ohio, USA. MIT Press, October 1989.

....can be accomplished by a suitable generalization of Clark s completion but it only works for a restricted class of knowledge bases, namely those whose clauses do not have any objective premises. Such residual databases were previously introduced and investigated in the class of logic programs [Bry89, Bry90, DK89a, DK89b, BD97c, BD95]. Here we give a slightly more general definition. Definition 3.1 (Residual Knowledge Bases [BD95] By a residual knowledge base we mean an arbitrary non monotonic knowledge base whose clauses do not contain any objective (positive) premises, i.e. a (possibly infinite) set of arbitrary clauses ....

P. M. Dung and K. Kanchansut. A fixpoint approach to declarative semantics of logic programs. In E.L. Lusk and R.A. Overbeek, editors, Proceedings of North American Conference Cleveland,Ohio, USA. MIT Press, October 1989.

.... and unfolding preserve the stable model, partial stable model, preferred extension, stationary expansion, complete scenaria, stable theory and well founded semantics, due to the fact that normal logic programs before and after the application of folding and unfolding have the same semantic kernel [6] and that normal logic programs and their semantic kernels have the same semantics ( for each of stable model, partial stable model, preferred extension, stationary expansion, complete scenaria, stable theory and well founded semantics) We will show that this technique, of proving the correctness ....

....We will see that their technique is equivalent to the method, used in section 4 (for unfolding) of proving that the attack relations before and after the transformation are identical. The method in [1] uses the notion of semantic kernel, given by the following definition which is adapted from [6]. Definition 11. Given a normal logic program Prog, let SProg be the operator on sets of variable free clauses of the form H Delta with Delta a (possibly empty) set of negative literals defined as follows: SProg (I) fH Delta 0 ; B 1 ; Bm j Delta 0 is possibly empty, m 0, ....

P.M. Dung, K. Kanchanasut, A fixpoint approach to declarative semantics of logic programs. NACLP`89 1:604--625

.... compute the well founded model of a normal program are: The alternating fixpoint approach, introduced by Van Gelder [27, 28] and further developed by Kemp, Stuckey and Srivastava [20] The computation of the residual program, suggested by Bry [9, 10] and independently by Dung Kanchanasut [16, 17], and extended by Brass and Dix [6, 7] The alternating fixpoint procedure is known to have efficiency problems, since in every iteration many facts have to be recomputed. The residual program approach avoids recomputations of this kind. But it is still possible that the residual program can grow ....

....and P 2 7 R P 3 . Thus, every program P has a unique normalform, which is called the residual program res(P ) of P . 2 Obviously, rules in the residual program cannot contain positive body literals, since then unfolding would be applicable. So the residual program is a set of conditional facts [9, 10, 16, 17]: Definition14 Conditional Fact. A conditional fact is a ground rule with only negative body literals, i.e. a rule of the form A notB 1 Delta Delta Delta notBn . 2 As shown in [6] the well founded semantics is the weakest semantics which allows the above transformations. We can directly ....

P. M. Dung and K. Kanchansut. A fixpoint approach to declarative semantics of logic programs. In Proc. North American Conference on Logic Programming (NACLP'89), pages 604--625, 1989.

....task can be accomplished by a suitable generalization of Clark s completion but it only works for a restricted class of belief theories, namely those whose clauses do not have any objective premises. Such residual theories were previously introduced and investigated in the class of logic programs [6, 7, 9, 10, 4, 1]. Here we give a slightly more general definition. Definition 3.1 (Residual Belief Theories [1] By a residual belief theory we mean an arbitrary belief theory whose clauses do not contain any objective (positive) premises, i.e. a (possibly infinite) set of arbitrary clauses BG 1 : BG k ....

P. M. Dung and K. Kanchansut. A fixpoint approach to declarative semantics of logic programs. In E.L. Lusk and R.A. Overbeek, editors, Proceedings of North American Conference Cleveland,Ohio, USA. MIT Press, October 1989.

....to provide proof for every semantics. Instead we wish to exploit the relationship among all these semantics. In this paper, we first observe that to show the correctness of unfold fold transformation system wrt various semantics of negation, it is enough if the correctness wrt the semantic kernel [16,17] of a normal program is shown. Later, we prove that the unfold fold framework preserves the semantic kernel of a normal program and obtain previous and new results of the field as corollaries of our main theorem. Apart from the correctness results for normal programs, we also show that it is easy ....

....other semantics of normal logic programs. To capture the intended meaning of a normal logic program in 2 [27] defines a computed answer substitution of a goal G wrt program P as a pair (G,q) s.t. there exists a proof tree of G wrt P with answer substitution q. Page: 5 19 a more natural way, in [16,17] Dung et al. defined the semantic kernel 3 of a normal program. The idea starts with the concept of a quasi interpretation, which is formally defined below. Definition 3.1 (Quasi interpretation) A quasi interpretation I is a set of ground program clauses of the form, A not B 1 , not B n ....

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Dung,P.M. and Kanchanasut,K., A fixpoint approach to declarative semantics of logic programs, in: E.L.Lusk and R.A.Overbeek (Eds.), Proc. of the North American Conference on Logic Programming, Vol.1, MIT Press, 1989, pp. 604-625.

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P. M. Dung and K. Kanchansut. A fixpoint approach to declarative semantics of logic programs. In E.L. Lusk and R.A. Overbeek, editors, Proceedings of North American Conference Cleveland,Ohio, USA. MIT Press, October 1989.

No context found.

P. M. Dung and K. Kanchansut. A fixpoint approach to declarative semantics of logic programs. In E.L. Lusk and R.A. Overbeek, editors, Proceedings of North American Conference Cleveland,Ohio, USA. MIT Press, October 1989.

No context found.

P. M. Dung and K. Kanchansut. A fixpoint approach to declarative semantics of logic programs. In E.L. Lusk and R.A. Overbeek, editors, Proceedings of North American Conference Cleveland,Ohio, USA. MIT Press, October 1989.

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