Verbaeten, S., Denecker, M., and Schreye, D. D. 2000. Compositionality of normal open logic programs. Journal of Logic Programming 41, 151-183.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....or, similarly, that open programs should not include any clause de ning an open predicate. This restriction makes impossible the incremental de nition of a predicate, for instance through some form of inheritance [2] On the other hand, none of these approaches provide full abstraction results. In [21] a slightly more general framework is considered. In particular they study open programs where the open predicates can be axiomatized by arbitrary rst order axioms. However, compositionality is proved under certain sucient conditions that are quite close to the restrictions imposed in [7] In ....

Verbaeten, S., Denecker, M., De Schreye, D., Compositionality of normal open logic programs, to appear in: Proc. of ILPS'97, 1997.

....reasons, none of the various operational semantics [13, 11, 32] neither the di erent modeltheoretic approaches (see e.g. 3] nor the completion semantics [12, 25] seems to be adequate to be the basis for de ning a compositional semantics for normal logic program units. To our knowledge, only [17, 19, 27, 35, 9] provide some compositional semantic constructs for normal logic programs. In section 6 we compare the results presented in this paper and these approaches. It must be noted that compositionality is a very important property for de ning the semantics of a modular unit. In particular, if the ....

....program fragments which is compositional and fully abstract with respect to standard program union. Actually, other kind of units and composition operations can be seen just as a special case. The kind of compositionality results obtained are quite more powerful than the results presented in [17, 19, 27, 35, 9]. In [17, 19, 27] di erent semantic de nitions are provided for certain kinds of modular units which are shown to be compositional. However, they all impose (at least) the restriction (not needed in our work) that, for putting together (through the corresponding composition operation) two units, ....

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Verbaeten, S., Denecker, M., De Schreye, D., Compositionality of normal open logic programs, to appear in: Proc. of ILPS'97, 1997.

....UPC Department LSI, Campus Nord, C Jordi Girona Salgado, 1 3, 08034 Barcelona, SPAIN. Tel: 34 3 4017018, Fax: 34 3 4017014, e mail: orejas lsi.upc.es [13, 27] seems to be adequate to be the basis for defining a compositional semantics for normal logic programs units. To our knowledge, only [18, 20, 29, 40, 9] provide some compositional semantic constructs for normal logic programs. In section 6 we compare the results presented in this paper and these approaches. It must be noted that compositionality is a very important property for defining the semantics of a modular unit. In particular, if the ....

....program fragments which is compositional and fully abstract with respect to standard program union. Actually, other kind of units and composition operations can be seen just as a special case. The kind of compositionality results obtained are quite more powerful than the results presented in [18, 20, 29, 40, 9]. In [18, 20, 29] different semantic definitions are provided for certain kinds of modular units which are shown to be compositional. However, they all impose (at least) the restriction (not needed in our work) that, for putting together (through the corresponding composition operation) two units, ....

[Article contains additional citation context not shown here]

Verbaeten, S., Denecker, M., De Schreye, D., Compositionality of normal open logic programs, to appear in: Proc. of ILPS'97, 1997.

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Verbaeten, S., Denecker, M., and Schreye, D. D. 2000. Compositionality of normal open logic programs. Journal of Logic Programming 41, 151-183.

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S. Verbaeten, M. Denecker, and D. De Scheye. Compositionality of normal open logic programs. journal of Logic Programming, 1(3):151-183, 2000.

....Each one of the techniques mentioned above has its own limitations and or drawbacks. For instance, in order to properly translate the underlying data to a speci c form, formalisms that are based on rewriting techniques must assume This property is sometimes called compositionality ; see, e.g. [30]. that the underlying data (or some part of it, such as the set of integrity constraints) has a speci c syntactical structure. Other formalisms (e.g. that of [20] are based on propositional languages, and so in both cases the expressiveness is limited. In some of the non classical formalisms ....

S.Verbaeten, M.Denecker, D.De Schreye. Compositionality of normal open logic programs. Journal of Logic Programming 41(3), 151-183, 2000.

....if 8x:F [x] G[x] is a tautology in 3 valued logic 5 . De ne the composition of two de nitions P red 1 : C 1 and P red 2 : C 2 as the de nition P red 1 [P red 2 : C 1 [ C 2 . In general, substituting a pair of de nitions by their composition is not equivalence preserving. [32] presents an extensive study of when merging de nitions is equivalence preserving in the context of open logic programming, a sub formalism of the logic de ned here. One important example is that a de nition hierarchy (De nition 3) is equivalent with its composition. Note that the composition of a ....

S. Verbaeten, M. Denecker, and D. De Schreye. Compositionality of normal open logic programs. Journal of Logic Programming, 41(3):151-183, March 2000.

....(incomplete) expert knowledge. A theory with several models, expresses the fact that the expert who wrote the theory, has no complete knowledge about the problem area. A theory in which all the predicates are de ned can at most have one model (namely the well founded model [14] In previous work [18] (an extended version of [17] the composition of two OLP FOL theories T 1 and T 2 , was investigated. It was argued that the composition of two such theories should contain exactly the sum of the knowledge of the components. By continuing our intuitive interpretation, this means that we have two ....

....we want to represent the situation in which these two experts put together their knowledge. Formally, this means that the set of models of the composition T of the theories T 1 and T 2 , is exactly equal to the intersection of the sets of models of T 1 and T 2 : Mod(T ) Mod(T 1 ) Mod(T 2 ) In [18], two theories, with non intersecting sets of de ned predicate symbols, are considered and several conditions on T 1 and T 2 are given, such that their composition is simply the union, that is, such that Mod(T 1 ) Mod(T 2 ) Mod(T 1 [ T 2 ) Note that in [18] the composition of T 1 and T 2 is ....

[Article contains additional citation context not shown here]

S. Verbaeten, M. Denecker, and D. De Schreye. Compositionality of normal open logic programs. Accepted for publication in the Journal of Logic Programming. 25

....A theory with several models, expresses the fact that the expert who wrote the theory, has no complete knowledge about the problem area. A theory in which all the predicates are de ned can at most have one model (namely the well founded model [14] In previous work [18] an extended version of [17]) the composition of two OLP FOL theories T 1 and T 2 , was investigated. It was argued that the composition of two such theories should contain exactly the sum of the knowledge of the components. By continuing our intuitive interpretation, this means that we have two experts whose knowledge is ....

.... a situation is considered where two (or more) experts have more or less disjunct subdomains of expertise and represent their knowledges independently in two theories, T 1 and T 2 , with non intersecting sets of de ned predicate symbols, i.e. Def (T 1 ) Def (T 2 ) The problem considered in [17], is how to combine these two theories in one united theory T . They argue that the composition T of two theories T 1 and T 2 should contain exactly the sum of the knowledges of the separate theories. Because OLP FOL has a possible state semantics, the compositionality criterion has the following ....

[Article contains additional citation context not shown here]

S. Verbaeten, M. Denecker, and D. De Schreye. Compositionality of normal open logic programs. In J. Maluszynski, editor, Proc. of ILPS, pages 371-386. The MIT Press, 1997.

....8x:F [x] G[x] is a tautology in 3 valued logic 6 . ffl Define the composition of two definitions P red 1 : f C 1 g and P red 2 : f C 2 g as the definition P red 1 [ P red 2 : f C 1 [ C 2 g. In general, substituting a pair of definitions by their composition is not equivalence preserving. (Verbaeten, Denecker, De Schreye 2000) presents an extensive study of when merging definitions is equivalence preserving in the context of open logic programming, a sub formalism of the logic defined here. One important example is that a definition hierarchy (Definition 3) is equivalent with its composition. Note that the composition ....

Verbaeten, S.; Denecker, M.; and De Schreye, D. 2000. Compositionality of normal open logic programs. Journal of Logic Programming 41(3):151--183.

....well founded semantics [16] An OLP FOL theory T = T d ; T c ) divides the set of predicate symbols in two disjoint subsets: the defined predicates, which occur in the head of a clause of T d , and the open predicates, which occur at the most in the body of the clauses of T d . In previous work [19], the composition of two OLP FOL theories, with non intersecting sets of defined predicate symbols, was studied. It was argued that their composition is given by the set of common models. Here, we investigate the possibility of composing two OLP FOL theories, which define the same predicate. ....

....(incomplete) expert knowledge. A theory with several models, expresses the fact that the expert who wrote the theory, has no complete knowledge about the problem area. A theory in which all the predicates are defined can at most have one model (namely the well founded model [16] In previous work [19], the composition of two OLP FOL theories T 1 and T 2 , with non intersecting sets of defined predicate symbols, was investigated. It was argued that the composition of these two theories should contain exactly the sum of the knowledges of the theories. Formally, this means that the set of models ....

[Article contains additional citation context not shown here]

S. Verbaeten, M. Denecker, and D. De Schreye. Compositionality of normal open logic programs. In J. Maluszynski, editor, Proc. of the International Logic Programming Symposium, pages 371--386. The MIT Press, 1997. 16

....[x] G[x] is a tautology in 3 valued logic 8 . De ne the composition of two de nitions P red 1 : n C 1 o and P red 2 : n C 2 o as the de nition P red 1 [P red 2 : n C 1 [ C 2 o . In general, substituting a pair of de nitions by their composition is not equivalence preserving. [36] presents an extensive study of when merging de nitions is equivalence preserving in the context of a sub formalism of the logic de ned here. One important example is that a de nition hierarchy (De nition 3.3) is equivalent with its composition. Note that the composition of a de nition hierarchy ....

S. Verbaeten, M. Denecker, and D. De Schreye. Compositionality of normal open logic programs. Journal of Logic Programming appear, 41(3):151-183, March 2000. 22

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S. Verbaeten, M. Denecker, and D. De Schreye. Compositionality of normal open logic programs. Journal of Logic Programming, 41(3):151--183, 2000.

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