A. Brogi, P. Mancarella, D. Pedreschi, and F. Turini. Composition Operators for Logic Theories. In J.W. Lloyd, editor, Computational Logic, Symposium Proceedings, pages 117--134. Springer-Verlag, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....general notion of refinement (Section 2) would be difficult to satisfy. Another problem is that the Herbrand semantics is not compositional. Given two programs, the least Herbrand model of the union of the programs cannot be expressed in terms of the least Herbrand model of the individual programs [3]. In [5] an operational point of view is taken to express statements about the correctness of a program. Partial) correctness is defined with respect to preconditions and postconditions which are assertions for the possible form of the arguments of a predicate. The preconditions impose ....

A. Brogi, P. Mancarella, D. Pedreschi, and F. Turini. Composition operators for logic theories. In J. W. Lloyd, editor, Computational Logic. Springer Verlag, 1990.

.... results could often only be obtained at the cost of using not fully automatic and or ad hoc techniques [16] In a recent paper [5] Brogi and Contiero address specialisation of a non ground vanilla like meta interpreter [31, 13, 32, 24] extended in order to deal with program compositions [6, 7, 3, 5]. Again, the interpretion overhead is removed by an ad hoc specialiser, specifically constructed to handle the extended interpreter. Supported by a specialisation grant of the Flemish Institute for the Promotion of Scientific Technological Research in Industry (IWT) Belgium. Postdoctoral ....

....operations needed for program composition: union, intersection and encapsulation. Single object programs are represented by statement(P; H;B) facts, where P is the program name, H the clause head and B the clause body. An elaborated discussion of these composition operators can be found in [6, 7, 3, 5]. In the following, D will denote the extended vanilla interpreter above. The combination of D and a fully instantiated composition of object programs e will be denoted by D e . In [5] a specific program specialisation technique is developed in order to deal with these program compositions. A ....

A. Brogi, P. Mancarella, D. Pedreschi, and F. Turini. Composition operators for logic theories. In J. W. Lloyd, editor, Proceedings of the Esprit Symposium on Computational Logic, pages 117--134. Springer-Verlag, November 1990.

.... the class of extended metainterpreters studied by [22] It includes many useful meta interpreters, such as a proof trees constructing meta interpreter [28] that can be used as a basis for explanation facilities in expert system, meta interpreters allowing reasoning about theories and provability [8, 21] or reasoning with uncertainty [28] Moreover, this class also describes a depth tracking tracer for Prolog, a reasoner with threshold cutoff [28] and a pure four port box execution model tracer [7] Note, that despite the similarity with Example 6, Example 6 is not a double extended ....

A. Brogi, P. Mancarella, D. Pedreschi, and F. Turini. Composition operators for logic theories. In J. W. Lloyd, editor, Proc. Esprit Symp. on Comp. Logic, pages 117--134. Springer Verlag, 1990.

....mechanisms have been introduced, usually considering algebras of logic programs and defining operators such as union, intersection, encapsulation, overriding union etc. to perform program composition. This approach, first introduced in [O K85] have been followed by various researchers [Bro93, BMPT90, MP88]. In the second approach, the language of Horn clauses has been extended to allow implication goals in the bodies. The pioneer work is presented in [Mil86] and the work in [MP89] is an eminent one. In [Bug92] an attempt was made to combine the two approaches, proposing SelfLog, a framework where ....

....It simply stands for the set theoretic union of their clauses. For example, if P = fq p; zg and Q = fq t; kg then P [ Q = fq p; z; q t; kg. The denotation of the union P [ Q of two programs P and Q can be 2 expressed by the following equation [BLM94] T P[Q (I) T P (I) TQ (I) In [BMPT90] the model theoretic semantics of the union of two logic programs is given by the minimal model of the resulting program which is: M P[Q = fM jM j= P M j= Qg = minfM jM j= P M j= Qg The union operator is monotonic. On the other hand, given two logic programs P and Q, their overriding union, ....

A. Brogi, P. Mancarella, D. Pedreschi, and F. Turini. Composition operators for logic theories. In J. W. Lloyd, editor, Proceedings of the Computational Logic Symposium, pages 117--134, November 1990.

....and intersection, that allow to combine programs together to get new ones. A third operator, closure [Bro92] joins with the previous ones to build up a set of basic operators that can be used in many fields: hierarchical and hypothetical reasoning, knowledge assimilation, modularity [Bro92, BMPT90, BMPT90a, BMPT92]. Union yields a combined program where the original ones cooperate each other during deduction, in the sense that partial conclusions of either program may possibly serve as premises for the other program; intersection yields a combined program where both the original programs are forced to agree ....

....reasoning, to modularity in logic programming, to knowledge assimilation, etc. In particular, they are a set of base operators for definition of higher level operators. Showing the fields of application of the meta operators is beyond the scope of this paper; meaningful examples are considered in [Bro92, BMPT90, BMPT90a]. 5 2.2 A meta interpretive view Intuitively, the operators introduced by definition 2.1 suggest particular interactions between the original programs during the refutation of a goal. That is, the union of two programs makes the original programs to cooperate each other during the ....

A.Brogi, P.Mancarella, D.Pedreschi, F.Turini. Composition Operators for Logic Theories. In J.W.Lloyd, editor, Computational Logic, Symposium Proceedings, pages 117-134. Springer-Verlag, Brussels,1990

.... results could often only be obtained at the cost of using not fully automatic and or ad hoc techniques [20] In a recent paper [7] Brogi and Contiero address specialisation of a non ground vanilla like meta interpreter [35, 19, 36, 29] extended in order to deal with program compositions [8, 9, 5, 7]. Again, the interpretion overhead is removed by an ad hoc specialiser, specifically constructed to handle the extended interpreter. On the other hand, research on partial deduction of logic programs meanwhile resulted in fully automatic and completely general specialisation techniques, not ....

....H; B) These clause predicates implement the classic notion of operations needed for program composition: union, intersection and encapsulation. Single object programs, then, are represented by statement(P; H; B) facts, where P is the program name, H the clause head and B the clause body. See [8, 9, 5, 7] for an elaborated discussion of these composition operators. In the following, D will denote the extended vanilla interpreter. The combination of D and a fully instantiated composition of object programs e will be denoted by D e . In [7] a specific program specialisation technique is developed ....

A. Brogi, P. Mancarella, D. Pedreschi, and F. Turini. Composition operators for logic theories. In J. W. Lloyd, editor, Proceedings of the Esprit Symposium on Computational Logic, pages 117--134. Springer-Verlag, November 1990.

....a modular approach to programming. These include the re use of existing software, the development of programs incrementally, non monotonic reasoning, and object orientation with inheritance. A number of operators that may be used to construct a complete program from a set of modules are defined in (Brogi, Mancarella, Pedreschi Turini 1990). These form a sort of command shell for building new programs out of existing ones. In (Brogi, Mancarella, Pedreschi Turini 1992) it is shown how meta programming techniques using the non ground representation, can be used to define and implement these operators. We discuss here the use of ....

....above clauses representing the Chase program, the goals OSolve(P [ Q; Chase(x; y) OSolve(P1 Q1; Chase(x; y) would both succeed with computed answer x = Tom; y = Jerry. Composing programs with operators allows for programs to be only partly specified. The following result was proved in (Brogi et al. 1990). OSolve(p; True) OSolve(p; b And c) OSolve(p; b) OSolve(p; c) OSolve(p; a) OClause(p; a; b) OSolve(p; b) OClause(p [ q; a; b) OClause(p; a; b) OClause(p [ q; a; b) OClause(q; a; b) OClause(p q; a; b And c) OClause(p; a; b) OClause(q; a; c) Fig. 11. The ....

Brogi, A., Mancarella, P., Pedreschi, D. & Turini, F. (1990), Composition operators for logic theories, in J. W. Lloyd, ed., `Computational Logic', Springer-Verlag, pp. 117--134.

....query evaluation phase the proper set of answer tuples is computed in a set at a time fashion. Our query evaluation scheme thus generalizes the evaluation scheme of most deductive database systems (see e.g. 6] Context extension and the composition of logic theories have also been studied in [2] and [3] In [22] an elaborated ML style module system for Prolog is presented. As opposed to our language, in [22] the configuration of modules is strictly separated from the logic language itself. Another approach uses higher order features to incorporate modules into a logic language ( 4] ....

Brogi A., Mancarella P., Pedreschi D., Turini F.: Composition Operators for Logic Theories. in J.W.Lloyd (Ed.), Computational Logic, Symp. Proc., Brussels, 1990, p. 117-134

....the modular construction of programs. Bugliesi, Lamma, and Mello [2] classify these proposals into two kinds: those that retain Horn clauses as the logical core but endow the framework with metalinguistic mechanisms for composing separately constructed program fragments, an approach exemplified by [1, 7, 14, 15], and those that extract composition and scoping mechanisms from an enrichment of the underlying logic, an approach exemplified by [3, 8, 10] We consider in this paper the implementation of a modularity notion in the language #Prolog [13] that arises from following the latter approach (see [9] ....

....of this clause contains a universal goal whose body is itself an implication goal. Notice that universal quantification over a program clause that is usually left implicit must be made explicit when the clause appears in the antecedent of an implication goal. Suppose now that the goal reverse ([1, 2], L) is invoked relative to the given procedure definition. This would lead to an attempt to solve the goal #rev aux ( rev aux ( L) # (#X #L1#L3 (rev aux ( X L1] L3) rev aux (L1, X L3] # rev aux ( 1, 2] The semantics of the universal quantifier dictates treating rev ....

[Article contains additional citation context not shown here]

A. Brogi, P. Mancarella, D. Pedreschi, and F. Turini. Composition operators for logic theories. In J. W. Lloyd, editor,<F4.777e+05> Computational Logic, Symposium<F5.267e+05> Proceedings, pages 117--134. Springer-Verlag, 1990.

....(1988) move from an object level to a function level and interpret a logic program as its immediate consequence operator, modeling a single deduction step. They define an algebra over operators, suitable for defining a union composition operator over sub programs. These results are extended in Brogi et al. 1990), where an additional operator, intersection, is added to the union operator. The composition operators are characterized both model theoretically and using meta interpreter techniques; both approaches are shown to be equivalent to each other and to the original algebraic characterization. A ....

Brogi, Antonio, Paolo Mancarella, Dino Pedreschi, and Franco Turini. 1990. Composition operators for logic theories. In J. W. Lloyd, editor, Computational Logic -- Symposium Proceedings, pages 117--134.

....as(Gold ; p) Honest(p) 17) as a theorem of O 2 . Resolving clauses 17 and 13 finally yields the theorem As good as(Gold ; Mary) in O 2 . This expressivity is similar to that obtained by Brogi, Mancarella, Pedreschi and Turini [9] when applying their work on composition operators for theories [8] to modules. In their work, a module can be constructed extensionally or intensionally, corresponding to the subgoals pO 1 x( a; b)q and pO 1 x( a; b) zq of clauses 2 and 10, respectively, that inspect either the extension or the intension of the theory O 1 . In other aspects ....

....transferred. There are also other formalisms where a comparison should be useful: ffl Our language is also related to languages proposed by Kowalski [22, 23] in the use of multiple theories. Our language is indeed an attempt to concretize these ideas. ffl Brogi, Mancarella, Pedreschi Turini [8, 9, 10] have investigated a collection of operators for composing theories. The meta interpretive definitions of the operators can be expressed directly in Alloy. Although theories in Alloy are not to be thought of as data structures, the language allows theories to be denoted by arbitrary ground ....

Brogi, A., Mancarella, P., Pedreschi, D. and Turini, F., Composition Operators for Logic Theories, in: J. W. Lloyd (ed.), Computational Logic, Springer-Verlag, Berlin, 1990.

....the notions of context switching and the composition operations of union, and overriding union. By composing database modules, we effectively combine the databases in those modules. Other ways of composing logic programs have been considered in the literature, such as intersection [4] retraction [5], and various forms of inheritance [6, 19] Utilising a larger repertoire of operators allows more kinds of compositions to be expressed in queries, but increases complexity. 3.1 Virtual Relations and Joins The LogicWeb goal, Module# Goal, causes the evaluation of the logic programming Goal in ....

A. Brogi, P. Mancarella, D. Pedreschi, and F. Turini. Composition Operators for Logic Theories. In J.W. Lloyd, editor, Computational Logic, symposium Proceedings, pages 117 -- 134. Springer-Verlag, 1990.

....general notion of refinement (Section 2) would be difficult to satisfy. Another problem is that the Herbrand semantics is not compositional. Given two programs, the least Herbrand model of the union of the programs cannot be expressed in terms of the least Herbrand model of the individual programs [3]. In [5] an operational point of view is taken to express statements about the correctness of a program. Partial) correctness is defined with respect to preconditions and postconditions which are assertions for the possible form of the arguments of a predicate. The preconditions impose ....

A. Brogi, P. Mancarella, D. Pedreschi, and F. Turini. Composition operators for logic theories. In J. W. Lloyd, editor, Computational Logic. Springer Verlag, 1990.

....that the language and inference rules of a collection of theories is fixed, we may characterize each theory by its set of nonlogical axioms. Brogi, Mancarella, Pedreschi Turini have studied operations on theories and propose an algebra on theories with operations such as union and difference [10]. This work is representative of a common approach (employed, e.g. in LOG [16] to represent a theory by some data structure (e.g. a list) which contains as parts a representation of every nonlogical axiom of the theory. Kowalski has proposed a quite different approach [55] where each ....

Brogi, A., Mancarella, P., Pedreschi, D. and Turini, F., Composition Operators for Logic Theories, in: J. W. Lloyd (ed.), Computational Logic, SpringerVerlag, Berlin, 1990.

....of Horn clauses and their algebraic composition is modeled in terms of various operations on the component clauses: union, deletion, closure and combination of the above. The compositional frameworks of Mancarella and Pedreschi [61] Gaifman and Shapiro [39] Bossi et al. 8] and of Brogi et al. [15, 12] can in fact be seen as different formulations of this idea. Information hiding and encapsulation can also be accounted for in this framework quite elegantly. Algebraic program composition can be made more selective so as to distinguish, within a module, predicates to be imported from other ....

....to model a rich set of mechanisms for program composition. We will then discuss the notions of program equivalence that arise for the different operators and finally describe the extension of this framework with import export facilities. Other operators, such as intersection [61] and deletion [15], which have been considered in the literature will not be taken into account in this survey since less relevant to the study of modular programming. 2.1. The Algebra of Programs and its Operators The Algebra. The language L for the programs of the algebra is defined by fixing ahead a signature ....

[Article contains additional citation context not shown here]

A. Brogi, P. Mancarella, D. Pedreschi, and F. Turini. Composition Operators for Logic Theories. In J.W. Lloyd, editor, Computational Logic, Symposium Proceedings, pages 117--134. Springer-Verlag, 1990. 60

....(5) If Alloy were to be extended with negation, then negative introspection is also easy: A p B not pB pq q not pB qq p Names q 6. 3 Program Composition Operators Brogi, Mancarella, Pedreschi and Turini have proposed an algebra of operators for composing logic programs [9]. The operators are P [Q, P Q, P and P Q, for union, intersection, encapsulation and import of programs, respectively. Their meta interpretive definition can be coded elegantly in Alloy, provided that we choose one unary and three binary function symbols for constructing theory terms that ....

Brogi, A., Mancarella, P., Pedreschi, D. and Turini, F., Composition Operators for Logic Theories, in: J. W. Lloyd (ed.), Computational Logic, Springer-Verlag, Berlin, 1990.

....mechanisms, an approach which originated with the work of Miller [Mil86, Mil89] Moreover, meta linguistic operations are quite powerful. For instance, the compositional systems of Mancarella and Pedreschi [MP88] Gaifman and Shapiro [GS89] Bossi et al. BBG 93] and Brogi et al. BLM92, BMPT90] can be seen as different instances of this idea. Furthermore, the typical mechanisms of the objectoriented paradigm, such as encapsulation and information hiding, as well as more complex form of composition mechanisms in which we may distinguish between imported, exported, and local (hidden) ....

A. Brogi, P. Mancarella, D. Pedreschi, and F. Turini. Composition Operators for Logic Theories. In J. W. Lloyd, editor, Proc. Symposium on Computational Logic, pages 117--134. Springer-Verlag, Basic Research Series, 1990.

....extend programs by linguistic mechanisms, an approach which originated with the work of Miller [23, 24] Moreover, meta linguistic operations are quite powerful. For instance, the compositional systems of Mancarella and Pedreschi [22] Gaifman and Shapiro [12] Bossi et al. 2] and Brogi et al. [4, 5] can be seen as different instances of this idea. Furthermore, the typical mechanisms of the object oriented paradigm, such as encapsulation and information hiding, as well as more complex form of composition mechanisms in which we may distinguish between imported, exported, and local (hidden) ....

A. Brogi, P. Mancarella, D. Pedreschi, and F. Turini. Composition Operators for Logic Theories. In J. W. Lloyd, editor, Proc. Symposium on Computational Logic, pages 117--134. Springer-Verlag, Basic Research Series, 1990.

....require is a semantics that essentially resembles context switching from one rule set to another and that can deal with higher order terms in a Hilog like fashion [10] There has been a considerable amount of well documented work on the definition of a semantics for contextual goals. Among others, [7, 8, 9, 22] study a compositional semantics of logic programs with static scoping. 13, 16, 18, 24] base the semantics of modules with static scoping on the semantics of embedded implications [23] We would like to emphasize that we are not going to present a full blown objectoriented deductive database ....

A. Brogi, P. Mancarella, D. Pedreschi, and F. Turini. Composition operators for logic theories. In J. Lloyd, editor, Computational Logic, Symp. Proceedings, pages 117--134, Brussels, 1990.

No context found.

A. Brogi, P. Mancarella, D. Pedreschi, and F. Turini. Composition Operators for Logic Theories. In J.W. Lloyd, editor, Computational Logic, Symposium Proceedings, pages 117--134. Springer-Verlag, 1990.

....to plain programs. Let M = P Q be a module, where P and Q are the following plain programs: P Q p(x) q(x) q(a) Recall from Section 2.3 that the implementations of P and Q are the pairs (P; 0) and (Q; 0) respectively. As usual, we want to define the pair (M V ; MH ) in terms 26 Delta A. Brogi, P.Mancarella, D.Pedreschi and F.Turini of (P; 0) and (Q; 0) Clearly the program MH implementing the hidden part of M should make the extension of Q visible to M V and not visible to the external world. This can be simply achieved by replacing all the predicates in Q with fresh system predicates. In our example this would yield the following ....

Brogi, A., Mancarella, P., Pedreschi, D., and Turini, F. 1990a. Composition Operators for Logic Theories. In J. Lloyd (Ed.), Computational Logic, Symposium Proceedings, pp. 117--134. Springer-Verlag.

....programs. The well founded meaning of the amalgamated language is provided by the equivalence of the two semantics. The proposal of this paper builds upon a long stream of research on the use of algebras of logic programs as a means for implementing common sense reasoning and program structuring [3, 7, 8, 9]. The novelty here is amalgamation: For the first time we are able to allow program expressions within clause bodies (and not only in top level goals) and to handle the formal semantics of the resulting amalgamated language. A second contribution of the paper is to show that the proposed ....

A. Brogi, P. Mancarella, D. Pedreschi, and F. Turini. Composition Operators for Logic Theories. In J.W. Lloyd, editor, Computational Logic, Symposium Proceedings, pages 117--134. Springer-Verlag, 1990.

....Actually, these operations enjoy a number of interesting algebraic properties [3] which allow us to identify an algebra of program expressions. We have shown elsewhere the power of the approach by extending logic programming with features for knowledge representation and program structuring. In [4] reasoning with defaults and exceptions is considered. In [3, 5, 8] the use of the operations for structuring knowledge in a hierarchical fashion and for exploiting the hierarchies for deduction is presented. In [3, 7] it is shown how the operations can be used to add to logic programming a notion ....

....the metainterpreter written in Prolog, the compilation into Prolog and the extended WAM, trade completeness for efficiency, as it is always the case when moving from pure Horn Clause Logic to Prolog like operational semantics. The lack of completeness weakens also some of the algebraic laws [4], which are valid in theory for the operators. As it is usual, laws and properties break down when the application of the operators create loops in which the depth first left to right evaluation rule of Prolog get trapped. It is worth discussing briefly a useful extension of the proposed ....

A. Brogi, P. Mancarella, D. Pedreschi, and F. Turini. Composition Operators for Logic Theories. In J.W. Lloyd, editor, Computational Logic, Symposium Proceedings, pages 117--134. Springer-Verlag, 1990.

No context found.

A. Brogi, P. Mancarella, D. Pedreschi, and F. Turini. Composition operators for logic theories. In J. W. Lloyd, editor, Proc. Esprit Symp. on Comp. Logic, pages 117--134. Springer Verlag, 1990.

No context found.

Brogi, A., Mancarella, P., Pedreschi, D., Turini, F.: Composition operators for logic theories. In Lloyd, J.W., ed.: Computational Logic. Springer-Verlag, Berlin (1990) 117--134

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