M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A Model-Theoretic Reconstruction of the Operational Semantics of Logic Programs. Information and Computation, 103(1):86{ 113, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....we have that T =# ffiT . Also, this abstraction is complete, i.e. for any I 2 (Atom) #(T (I ) #(T (#(I ) viz. ffi #=# ffiT . Hence, by Proposition 4.3, this implies that for any P 2 Program, # ( P ] P ] # . This last observation has been firstly reported in [13]. It is worth noting that we have derived it by exploiting the techniques offered by abstract interpretation, which are intrinsically language independent. Herbrand s semantics is an abstraction of Clark s semantics through the following Galois insertion: Atom) b Deltac; bAtomc) ....

....ffid Deltae, i.e. the immediate consequence operator is the best correct approximation of the semantic operator of Clark s semantics. This abstraction is also complete, namely b DeltacffiT ffib Deltac. Again by Proposition 4. 3, we get that c, another observation already reported in [13]. Finally, composing the previous two abstractions, we get the abstraction between s semantics and Herbrand s semantics. This is defined in terms of the G.i. Atom) b Deltac; bAtomc) d Deltae) where, by a slight abuse of notation, we again denote by d Deltae the right adjoint to b Deltac ....

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M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi.A model theoretic reconstruction of the operational semantics of logic programs. Inf. & Comp., 103(1):86--113, 1993.

....minimal model. As argued in [7] the key issue consists in a suitable choice of the notion of model. In [4] we can find a reconstruction of the semantics of CLP, obtained by defining various model notions, each corresponding to a specific operationally observable property, as firstly defined in [3] for the pure logic programming case. In this paper, we extend some results related to the pure logic programming and presented in [8] dealing with an alternative way to characterize the operational behaviour of logic programs. The main idea is that we can consider a possibly infinite collection ....

....I iff [c2p( X ) I] ffl A clause H c2B 1 ; B n is true in I iff for each solution # of c, fB 1 #; B n #g [I] implies H# 2 [I] Thus, a model of a CLP program P is any interpretation in which all the clauses of P are true. We can observe that the mechanism introduced in [2, 3] to allow non ground atoms in the Herbrand base may be generalized in CLP, by allowing constrained atoms into the base. Each constrained atom c2p( X ) in fact, represents the set of instances p( X)#, where # is an solution of the constraint c. Thus, it implicitely represents a possibly ....

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M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A Model-Theoretic Reconstruction of the Operational Semantics of Logic Programs. Technical Report TR 32/89, Dipartimento di Informatica, Universit`a di Pisa, 1989. To appear in Information and Computation.

....and on a simple nondeterministic programming language which is a generalization of Dijkstra s language of guarded commands. Section 4 recalls some basic definitions and explains the notation used in the coming sections. Section 5 is a sketch of the S semantics. The S semantics is due to [8] and we use it as the semantics of a logic program. Section 6 handles the main results of partial deduction. As refinement is restricted to definite logic programs in this work, only the results concerning pure logic programs are presented. Section 7 discusses refinement of logic programs. Two ....

....p 5 : p q(a) q(b) P 5 [f pg has an SLD refutation but P 5 [ f pg does not. Obviously, P 5 [ f pg is not fq(b)g closed because the atom q(a) in P is not an instance of q(b) 6 Semantics This chapter is devoted to a description of the semantics of logic programs given in [8]. The S semantics is declarative. However, it corresponds exactly to the computed answer substitution semantics of a program. Convenient features of the S semantics, similar to properties of the standard Herbrand semantics, are the existence of a minimal model and a corresponding fix point ....

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M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A model-theoretic reconstruction of the operational semantics of logic programs. Technical Report TR-32/89, Dipartimento di Informatica, Universit`a di Pisa, 1989.

....tools [57, 21] Logic programming, however, has developed within a different semantic tradition than that of functional or imperative programming. The divide has narrowed in the last ten years, with the development of new denotational, operational, and abstract interpretations for logic programs [11, 39, 40, 14, 31, 38]. There has been a growing interest in a categorical formulation of these ideas, essentially for the same reasons they proved of interest in other programming paradigms. Categorical approaches to logic programming features appeared in the mid 1980 s in Rydeheard and Burstali s treatment of ....

M. Martelli M. Falaschi, G. Levi and C. Palamidessi. A model-theoretic reconstruction of the operational semantics of logic programs. Information and Computation, 102(1):86-113, 1993.

....in general, are applied to real programs, Prolog s choices wrt (ND1) and (ND2) become relevant for preserving the observables one is interested in. Useful observables usually represent the results of computation, which for Prolog programs can be characterized by the Computed Answer Substitutions [FLMP93] and the Finite Failure Set (when negation is used) But since Prolog replaces (ND2) by backtracking, also termination properties are essential, as they guarantee the effective reachability of solutions. In this paper we intend to give an overview of some of the transformation systems which have ....

M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A ModelTheoretic Reconstruction of the Operational Semantics of Logic Programs. Information and Computation, 102(1):86--113, 1993. 22

....model, and for others not. Secondly, in general it matches the procedural interpretation of logic programs only for ground queries. So the procedural behaviour of the program cannot be completely retrieved from this model. The least term model of Clark [6] or C semantics of Falaschi et al. [8]) is another natural candidate for the declarative semantics, and in fact it has been successfuly used in the probably most elegant and compact proof of the strong completeness of the SLD resolution due to Stark [12] However, it shares with the least Herbrand model the same deficiencies. The ....

....yields different computed answer substitutions w.r.t. to each program. 2 So in general, the M semantics is not a function of the operational behaviour of a program. 2. 2 The Least Term Model, or C semantics This semantics was introduced by Clark [6] and more extensively studied in Falaschi et al. [8]. It associates with each program its least term model. Identifying each term model with the set of atoms true in it, we can equivalently define this semantics as C(P ) fA 2 B j P j= Ag: As we shall see in Section 4, when the signature contains infinitely many constants, this semantics is ....

[Article contains additional citation context not shown here]

M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A Model-Theoretic Reconstruction of the Operational Semantics of Logic Programs. Information and Computation, 102(1):86-- 113, 1993.

No context found.

M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A Model-Theoretic Reconstruction of the Operational Semantics of Logic Programs. Information and Computation, 103(1):86--113, 1993.

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M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A model-theoretic reconstruction of the operational semantics of logic programs. Information and Computation, 1991. To appear. Also available as technical report TR 32/89 at the Department of Computer Science, Pisa.

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M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A model-theoretic reconstruction of the operational semantics of logic programs. Information and Computation, 103(1):86--113, 1993.

.... i.e. the usual encoding of conditions by means of the predefined function if [11] 3 The semantic framework In order to formulate a semantics for functional logic programs modeling computed answers, the usual Herbrand base has to be extended to the set of all (possibly) non ground equations [27,28]. V denotes the V Herbrand universe which allows variables in its elements, and is defined as #(# V ) # = where is the equivalence relation induced by the preorder of relative generality between terms. For the sake of simplicity, the elements of V (equivalence classes) have the ....

M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A Model-Theoretic Reconstruction of the Operational Semantics of Logic Programs. Information and Computation, 103(1):86--113, 1993.

....the equations have the form s t when we consider needed narrowing ( needed) 2. 1 Denotation of a Functional Logic Program In order to formulate a semantics modeling computed answers, the usual Herbrand base has to be extended to the set of all (possibly) non ground equations modulo variance [16, 17]. H V denotes the V Herbrand universe which allows variables in its elements, and is de ned as ( V ) where = is the equivalence relation induced by preorder of relative generality between terms. For the sake of simplicity, the elements of H V have the same representation as ....

M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A Model-Theoretic Reconstruction of the Operational Semantics of Logic Programs. Information and Computation, 103(1):86-113, 1993.

.... i.e. the usual encoding of conditions by means of the predefined function if [lO] 3 The semantic framework In order to formulate a semantics for functional logic programs modeling computed answers, the usual Herbrand base has to be extended to the set of all (possibly) non ground equations [26,27]. 7 y denotes the V Herbrand universe which allows variables in its elements, and is defined as ( U V) where is the equivalence relation induced by the preorder of relative generality between terms. For the sake of simplicity, the elements of 7 y (equivalence classes) have the same ....

M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A Model-Theoretic Reconstruction of the Operational Semantics of Logic Programs. Information and Computation, 103(1):86-113, 1993.

....leftmost outermost narrowing derivations also holds. 3 Denotation of a Functional Logic Program In order to formulate a semantics for functional logic programs modeling computed answers, the usual Herbrand base has to be extended to the set of all (possibly) non ground equations modulo variance [18, 19]. H V denotes the V Herbrand universe which allows variables in its elements, and is de ned as ( V ) For the sake of simplicity, the elements of H V have the same representation as the elements of ( V ) and are also called terms. B V denotes the V Herbrand base, namely, the set of ....

M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A Model-Theoretic Reconstruction of the Operational Semantics of Logic Programs. Information and Computation, 103(1):86-113, 1993.

....occurrence of the right hand side of the head of a rule in R by the corresponding left hand side. In order to formulate a semantics for functional logic programs modeling computed answers, the usual Herbrand base has to be extended to the set of all (possibly) non ground equations modulo variance [23, 24]. H V denotes the V Herbrand universe which allows variables in its 6 elements, and is de ned as ( V ) For the sake of simplicity, the elements of H V have the same representation as the elements of ( V ) and are also called terms. B V denotes the V Herbrand base, namely, the set ....

M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A Model-Theoretic Reconstruction of the Operational Semantics of Logic Programs. Information and Computation, 103(1):86-113, 1993.

....of the right hand side of the head of a rule in R by the corresponding left hand side. 6 In order to formulate a semantics for functional logic programs modeling computed answers, the usual Herbrand base has to be extended to the set of all (possibly) non ground equations modulo variance [22, 23]. H V denotes the V Herbrand universe which allows variables in its elements, and is defined as ( Sigma [ V ) For the sake of simplicity, the elements of H V have the same representation as the elements of ( Sigma [ V ) and are also called terms. B V denotes the V Herbrand base, namely, the ....

M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A Model-Theoretic Reconstruction of the Operational Semantics of Logic Programs. Information and Computation, 103(1):86--113, 1993.

....in this paper can also be a source of further investigations concerning the analysis of programs and the development of new observable semantics. In particular, the semantics could be extended in order to cope with observables like the non ground success set and computed answer substitutions [FLMP93] of LO programs. To this aim, we plan to formulate the constraintbased semantics presented here using a more traditional approach based on substitutions and most general uni ers. While the constraint based formulation was particularly suitable to study the connection with TPNs, a formulation ....

M. Falaschi and G. Levi and M. Martelli and C. Palamidessi. A ModelTheoretic Reconstruction of the Operational Semantics of Logic Programs. Information and Computation, 102(1):86-113, 1993.

....in P and has no refutation in Q. Because of the equality between the success set and the least Herbrand model this means that A 2 M(P ) n M(Q) Contradiction. As for the second equivalence, first observe that by using the definitions it is easy to show that 17 M(P ) Ground(A(P ) see also [18]) This proves the implication A(P ) A(Q) M(P ) M(Q) For the other implication, by the strong soundness and completeness theorem in [10] A(P ) fA j A 7 P 2g. Assume now that M(P ) M(Q) and there exists an atom A such that A has a refutation with empty computed answers in P and ....

M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A Model-Theoretic Reconstruction of the Operational Semantics of Logic Programs. Information and Computation, 102(1):86-- 113, 1993.

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M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A Model-Theoretic Reconstruction of the Operational Semantics of Logic Programs. Information and Computation, 103(1):86{ 113, 1993.

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M. Falaschi, G. Levi, M. Martelli, C. Palamidessi, "A model-theoretic reconstruction of the operational semantics of logic programs", Information and Computation, 103, pp.86-113, 1993.

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M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A Model-Theoretic Reconstruction of the Operational Semantics of Logic Programs. Information and Computation, 102(1):86--113, 1993.

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M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A model-theoretic reconstruction of the operational semantics of logic programs. Theoretical Computer Science, 103(1):86--113, 1993.

No context found.

M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A Model-Theoretic Reconstruction of the Operational Semantics of Logic Programs. Technical Report TR 32/89, Dipartimento di Informatica, Universit`a di Pisa, 1989. To appear in Information and Computation.

No context found.

M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A Model-Theoretic Reconstruction of the Operational Semantics of Logic Programs. Information and Computation, 103(1):86-113, 1993.

No context found.

M. Falaschi, G. Levi, M. Martelli, and C. Palamidessi. A Model-Theoretic Reconstruction of the Operational Semantics of Logic Programs. Information and Computation, 103(1):86-113, 1993.

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Falaschi, M., Levi, G., Martelli, M. and Palamidessi, C. (1993). A Model-Theoretic Reconstruction of the Operational Semantics of Logic Programs. Information and Computation, 102 (1).

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