R. O'Keefe. Towards an algebra for constructing logic programs. In J. Cohen and J. Conery, editors, Proceedings of IEEE Symposium on Logic Programming, pages 152--160. IEEE Computer Society Press, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Note that LaTeX EMAX can be used either to specialize EMAX or as a futher specialization of RCS EMAX with the obvious consequences on the treatment of multiple revisions. 5 Related Work The work on modular extensions of logic programming was originally inspired by the proposal of R. O Keefe in [28]. His idea was to give a formal account of one of the fundamental principles of the software engineering view of programming: programs should be developed incrementally by defining several units together with their interfaces and then by composing those units. This led him to propose a modular ....

R. O'Keefe. Towards an algebra for constructing logic programs. In J. Cohen and J. Conery, editors, Proceedings of IEEE Symposium on Logic Programming, pages 152--160. IEEE Computer Society Press, 1985.

....paradigm are viewed as modules. An object is a module that encapsulates data. A method is a module that encapsulates behavior. The elements manipulated by the logic paradigm are also mapped to modules. Logic modules are defined as a set of Horn clauses following the definition of O Keefe [10]. In this way, two algebraic operators are applied for combining logic modules. These operators are named union and overriding union [3] Figure 1 shows a general scheme of the module composition, highlighting how an agent is built. Logic modules are presented as gray circles. Classes can define ....

R. O'Keefe. Towards an Algebra for Constructing Logic Programs. In J. Cohen and J. Conery (eds), Proceedings of IEEE Symposium on Logic Programming, IEEE Computer Society Press, New York, pages 152-160, 1985.

....achieved by two approaches. In the first, meta linguistic 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 ....

R. O'Keefe. Towards an algebra for constructing logic programs. In IEEE Symposium on Logic Programming, pages 152--160, 1985.

.... can be understood in logical terms since the set of all the (Herbrand) models is OR compositional [30] and correct wrt successful derivations) The only OR compositional semantics correct wrt computed answers are described in [24, 9, 8] while all the other OR compositional semantics [26, 33, 31, 30, 23] are only correct wrt successful derivations. Clearly, compositionality wrt program composition operators is a desirable property since it allows to define in a modular way and incrementally the semantics of structured programs. For example, a semantics compositional wrt a generalized composition ....

R. A. O'Keefe. Towards an Algebra for Constructing Logic Programs. In Proc. IEEE Symp. on Logic Programming, pages 152--160, 1985.

....model of a program cannot be determined by the least Herbrand models of its clauses. To tackle this problem, several compositional semantics for logic programs have been studied by using higher order semantics [Fitting 1987; Lassez and Maher 1984; Maher 1988; Mancarella and Pedreschi 1988; O Keefe 1985], Herbrand models [Brogi et al. 1992] and notions such as full abstraction [Gaifman and Shapiro 1989] A number of different approaches to modularizing logic programming have also been proposed. Some of them augment logic programming with constructs for declaring and using modules, much in the ....

....the clauses of a logic program into a collection of named programs. This first extension is however straightforward. It is little more than the usual practice of programming to partition a logic program into a set of files, and it has been already largely used by many authors (see, e.g. O Keefe 1985]) The ultimate contribution of this paper is the definition of a set of basic operations for composing logic programs. We follow a semantics driven approach in the design of these operations. The semantics of each operation is defined in terms of the standard semantics of logic programming, in ....

[Article contains additional citation context not shown here]

O'Keefe, R. 1985. Towards an algebra for constructing logic programs. In J. Cohen and J. Conery (Eds.), Proceedings of IEEE Symposium on Logic Modular Logic Programming \Delta 35 Programming, pp. 152--160. IEEE Computer Society Press.

....in the program. Although the absence of such facilities is not seriously felt in the development of small programs, structuring mechanisms become essential for programmingin the large. This fact has spurred investigations into mechanisms for constructing programs in a modular fashion (e.g. see [11, 14, 19, 20]) and has also resulted in structuring devices being This paper appears in the Proceedings of the Third International Workshop on Extensions of Logic Programming, Lecture Notes in Artificial Intelligence, Volume 660, pages 359 393, Springer Verlag, 1993. 1 included in some implementations of a ....

Richard O'Keefe. Towards an algebra for constructing logic programs. In 1985 Symposium on Logic Programming, pages 152--160, Boston, 1985.

....defined by nested implication with the semantics based on intuitionistic logic. In this module system, the modules are dynamic in the sense that they are created and deleted at run time. Thus a modification of SLDNFresolution is required for the procedural semantics. The module system given in [O Keefe, 1985] only deals with untyped programs where the predicates are considered to be local to the modules but the functions are assumed to be global. Thus abstract data types cannot be defined. A number of Prolog implementations supporting module systems similar to that described by O Keefe have been ....

R.A. O'Keefe. Towards an algebra for constructing logic programs. In Proceedings of the Symposium on Logic Programming, Boston, pages 152--160. IEEE, 1985.

....the mental state of the agent. A logic module records a sequence of clauses. The decision component of agents can combine these modules, manipulating thus rules to achieve the wanted behavior. Being logic modules are dened as a sequence of Horn clauses following the denition of O Keefe [O K85], two algebraic operators are applied for combining logic modules. These operators are named union and overriding union [BLM94] The Brainstorm approach also allows logic modules as part of methods for manipulating common dealing of mental attitudes of agents that belong to one agent class. In ....

R. O'Keefe. Towards an algebra for constructing logic programs. In J. Cohen and J. Conery, editors, Proceedings of IEEE Symposium on Logic Programming, pages 152160, New York, 1985. IEEE Computer Society Press.

....has been used and appreciated most widely. Overriding has been a difficult issue to address in logic, as it is related to negation, belief or theory revision, and non monotonic reasoning. Several approaches were appealing in modeling overriding in knowledge representation and in knowledge bases [9, 38, 11, 4, 26, 8, 35, 6, 22, 5, 31, 5, 2, 3, 29, 28, 39, 13, 14, 30, 19]. Most solutions were computationally expensive, or were heavily dependent on the user for capturing the intended semantics i.e, inheritance was almost hand coded into the program. In the latter case, logic did very little in capturing the spirit of overriding and thus, was error prone. ....

R. A. O'Keefe. Towards an algebra for constructing logic programs. In IEEE Symposium on Logic Programming, 1985.

....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] ....

Richard O'Keefe. Towards an algebra for constructing logic programs. In J. Cohen and J. Conery, editors,<F4.777e+05> 1985 Symposium on Logic Programming,<F5.267e+05> pages 152--160. IEEE Computer Society Press, 1985.

....: Qn ) The need for a modular extension for logic programming languages has always been agreed upon, as relations were viewed as providing too fine grained abstraction for the design of large programs. Two major tracks were taken: one, referred to as programming in the large and inspired by O keefe (1985), suggests a meta linguistic mechanism: modules are viewed as sets of Horn clauses and their composition is modeled in terms of operations on the components (such as union, deletion, closure etc. The other approach, known as programming in the small and originating with Miller (1986; 1989) ....

.... known as programming in the small and originating with Miller (1986; 1989) enhances logic programming with linguistic abstraction mechanisms that are richer than those offered by Horn clauses (see Bugliesi, Lamma, and Mello (1994) for a review of modularity in logic programming) Unlike O keefe (1985), who defines the denotation of a program to be the transformation operator obtained by applying deduction steps arbitrarily many times, Mancarella and Pedreschi (1988) move from an object level to a function level and interpret a logic program as its immediate consequence operator, modeling a ....

O'keefe, R. 1985. Towards an algebra for constructing logic programs. In J. Cohen and J Conery, editors, Proceedings of IEEE symposium on logic programming, pages 152--160, New York. IEEE Computer Society Press.

....of the well founded semantics and of Fitting s semantics, as well as validation results for both of them [13] 15] Since [17] many authors have been interested in giving a compositional semantics for logic programming, especially as a theoretical foundation for a module system. We can cite [24], 5] 7] 6] 4] but all these works are only concerned with definite programs. In the remainder, we use the following notations : ffl The Herbrand base is denoted by HB ; ffl For an atom a 2 HB, Gammaa = a, Gamma:a = a and jaj = j:aj = a. Gammaa is called opposite of a. Let I HB [ ....

R. O'Keefe. Toward an algebra for constructing logic programs. In Symposium on Logic Programming, pages 152--160, Boston, 1985.

....c j . 2 This notion is particularly relevant in the field of program s transformation: in fact we say that a transformation is correct iff it preserves program s equivalence, that is, if it maps programs into equivalent ones. 2.1 Modular CLP Programs Following the original paper of R. O Keefe [17], the approach to modular programming we consider here is based on a meta linguistic programs composition mechanism. This provides a formal background to the usual software engineering techniques for the incremental development of programs. Viewing modularity in terms of meta linguistic operations ....

R. A. O'Keefe. Towards an Algebra for Constructing Logic Programs. In Proc. IEEE Symp. on Logic Programming, pages 152--160, 1985.

....motivation in defining this language comes from the need of structuring facilities to enhance modularity, readability and reusability of logic programs. This problem has been addressed in the literature using many different approaches (like the metalevel approach [6, 8] the algebraic approach [42, 30, 9], and the approach based on use of higher order logic [39, 12] and, in particular, it has been tackled by extending the language of Horn clauses with implications embedded in goals, as proposed in [36, 38, 26, 25] see [11] for a survey of the different approaches) Languages with embedded ....

R. A. O'Keefe. Towards an algebra for constructing logic programs. In Proc. Symp. on Logic Programming, pages 152--160, Boston, 1985.

....by naturally extending the usual notion used for pure logic programs, we say that a query c 2 C is an instance of the query d 2 D iff for any solution fl of c there exists a solution ffi of d such that Cfl j Dffi. 3 Modular CLP Programs Following the original paper of R. O Keefe [31], the approach to modular programming we consider here is based on a meta linguistic program composition mechanism. This provides a formal background to the usual software engineering techniques for the incremental development of programs. Viewing modularity in terms of meta linguistic operations ....

R. A. O'Keefe. Towards an Algebra for Constructing Logic Programs. In Proc. IEEE Symp. on Logic Programming, pages 152--160, 1985.

....accessing and integrating existing sub knowledge bases, and of decomposing a knowledge base into modules . Regarding logic programming environments, these goals have been achieved on a syntactical level, generally without providing a sound declarative semantics of the modularization concepts ( O K85] This situation is quite similar to the interoperability problem in the area of advanced information systems. Although intelligent information systems are expected to cope with the increasing complexity of data and its evaluation, in many cases it will be impossible to move all relevant data ....

R.A. O'Keefe. Towards an algebra for constructing logic programs. In IEEE Symposium on Logic Programming, Boston, USA, July 1985. IEEE Computer Society.

....the aforementioned two dimensions of programming inspired the two orthogonal lines of research the study of modularity has evolved along, over the past ten years. Various proposals have focused primarily on the issue of programming in thelarge. This research was inspired by the work of O Keefe in [86]. His idea was to give a formal account of one of the fundamental principles of the software engineering view of programming: programs should be developed incrementally by defining several units and their interfaces and then by composing those units. This led him to propose an approach to ....

....with few notable exceptions that will be pointed out in the paper, has concentrated primarily on the case of definite programs. 4 2. MODULAR PROGRAMMING AS ALGEBRAIC PROGRAM COMPOSITION We start off our analysis with the study of the algebraic approach to modularity introduced by O Keefe in [86]. As already anticipated, the fundamental idea behind the work of O Keefe is that a logic program should always be understood as part of a system of programs. Having taken this view, he argues that new programs can be designed by combining the components of that system and possibly by defining new ....

[Article contains additional citation context not shown here]

R. O'Keefe. Towards an algebra for constructing logic programs. In J. Cohen and J. Conery, editors, Proceedings of IEEE Symposium on Logic Programming, pages 152--160. IEEE Computer Society Press, 1985.

....software engineering methodology which helps to verify and maintain large applications. In the logic programming field, modularity has received a considerable attention (see for instance [BLM94] and has generated two distinct approaches: the first one is inspired by the work of O Keefe [O K85] and is based on the consideration that Permanent address: D.I.S.I, Universit a di Genova, via Dodecaneso 35, 16146 Genova, Italy. email: sandro disi.unige.it, phone: 39 (0) 10 3536732, fax: 39 (0) 10 3536699. module composition in basically a metalinguistic operation, in which the modular ....

....by any complete theory, is not a source of conflicts. In fact since the manipulations we employ never introduce the symbol = all we have to do is to use a different relation symbol to denote the identity relation. 2 3 A Compositional Semantics Following the original paper of R. O Keefe [O K85] the approach to modular programming we consider here is based on a meta linguistic programs composition mechanism. In this framework, logic programs are seen as elements of an algebra and the composition operation is modeled by an operator on the algebra. Viewing modularity in terms of ....

R. A. O'Keefe. Towards an Algebra for Constructing Logic Programs. In Proc. IEEE Symp. on Logic Programming, pages 152--160, 1985.

....example. In this paper, we consider the problem of defining a semantics for CTRSs which correctly models the operational behaviour of equational logic programs in a compositional way. Our approach shares with the approach in [22,25] the idea of moving from a data level semantics to a function level semantics in order to capture compositionality. We extend the least Herbrand model semantics for CTRSs by considering interpretations which may contain non ground equations. This allows us to model the set of computed answers for ....

....(e.g. 23,26] All these works focus mainly on syntactic conditions to guarantee that the properties of confluence and termination are ensured in the composition, but they do not seek for a compositional semantics, which is the main concern of our work. In the context of (pure) logic programming, [22,25] showed that, if the meaning of a logic program is denoted by the standard immediate consequence operator itself (rather than by its least fixpoint) then such a semantics is compositional for several interesting operators on programs including set union. However, this semantics does not ....

[Article contains additional citation context not shown here]

R. A. O'Keefe. Towards an Algebra for Constructing Logic Programs. In , pages 152--160. IEEE, 1985.

....whole program. For these reasons, modularity has received a considerable attention and, as the recent survey [10] shows, in the last few years several different proposals were introduced for integrating module constructs into logic languages. Here we adhere to the original approach of R. O Keefe [31], and we consider a constraint logic program to be a combination of several separate modules, where different modules are combined together by a simple composition operator Phi. Central to the development of large and efficient applications is now the study of optimization techniques for ....

....that two clauses, in order to be similar, must have exactly the same heads (this will simplify the proofs) 2.1 CLP Modules We now provide a formal background to the usual software engineering techniques for the incremental development of programs. Following the original paper of R. O Keefe [31], the approach to modular programming we consider here is based on a meta linguistic programs composition mechanism. Viewing modularity in terms of meta linguistic operations on programs has several advantages. In fact it leads to the definition of a simple and powerful methodology for structuring ....

R. A. O'Keefe. Towards an Algebra for Constructing Logic Programs. In Proc. IEEE Symp. on Logic Programming, pages 152--160, 1985.

....established software engineering methodology which helps to verify and maintain large applications. In the logic programming field, modularity has received a considerable attention (see for instance [6] and has generated two distinct approaches: the first one is inspired by the work of O Keefe [25] and is based on the consideration that module composition in basically a metalinguistic operation, in which the modular construct should be independent from the logic language being used; the second one originated with the work of Miller [23, 24] and is obtained by using a logical system richer ....

....[27, Theorem 3.3] may be reformulated as follows. Theorem 2.3 Let M be a module in a base language LB . Then, for any allowed formula OE, M [ Delta j= OE iff, for some n, M n ] Delta j= OE Proof: See the Appendix. 2 3 A Compositional Semantics Following the original paper of R. O Keefe [25], the approach to modular programming we consider here is based on a meta linguistic programs composition mechanism. In this framework, logic programs are seen as elements of an algebra and the composition operation is modeled by an operator on the algebra. Viewing modularity in terms of ....

R. A. O'Keefe. Towards an Algebra for Constructing Logic Programs. In Proc. IEEE Symp. on Logic Programming, pages 152--160, 1985.

....computational properties of differential programs and their composition. A preliminary version of this paper appeared in [4] 1 Introduction Program composition has been proposed as a tool for modular logic programming by many authors in the literature. It was first introduced by R. O Keefe in [24]: his goal was to provide a formal account of the software engineering approach to programming that seeks to develop programs incrementally by defining several components, together with their interfaces, and then by composing the components. He formalized this approach by interpreting logic ....

....only the public predicates it defines. However, more sophisticated forms of hiding are clearly desirable. For instance we may want to share the visibility of a predicate among the components of a hierarchy, but hide that predicate from users of the hierarchy. Mechanisms like these are discussed in [24] and [9] and turn out to be useful in several applications. Consider for instance the case of a schema like the following: List Stack Queue This schema could be used, for instance, to implement two abstract modules Stack and Queue that use List as the same implementation module. List ....

R. O'Keefe. Towards an algebra for constructing logic programs. In J. Cohen and J. Conery, editors, Proceedings of IEEE Symposium on Logic Programming, pages 152--160. IEEE Computer Society Press, 1985.

....and conversely, the program itself should be the particular case of a component for a trivial decomposition. These motivations lead us to consider a compositional semantics. A lot of work has been done to give logic programming such a semantics, especially as a foundation for module systems [15] [20] [11] 18] 12] 16] 4] 2] 5] Our choice for the semantics of a component is imposed by the purpose of giving it proof methods which generalize the aforementioned ones for programs. The chosen semantics are precisely defined in section 4. When we only consider definite programs, they look like ....

....[11] 18] 12] 16] 4] 2] 5] Our choice for the semantics of a component is imposed by the purpose of giving it proof methods which generalize the aforementioned ones for programs. The chosen semantics are precisely defined in section 4. When we only consider definite programs, they look like [20] or [11] but they just consider the union operator for it is the only one that matters for our compositional proof methods. 4] defines a semantics in terms of admissible model and [2] in terms of clauses, both for definite programs. Programs with negation are considered by [16] but the purpose is ....

R. O'Keefe. Toward an algebra for constructing logic programs. In Symposium on Logic Programming, pages 152--160, Boston, 1985.

....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 exempli ed by [1, 7, 13, 14], and those that extract composition and scoping mechanisms from an enrichment of the underlying logic, an approach exempli ed by [3, 8, 10] We consider in this paper the implementation of a modularity notion in the language Prolog that arises from following the latter approach [9] Programming ....

Richard O'Keefe. Towards an algebra for constructing logic programs. In J. Cohen and J. Conery, editors, 1985 Symposium on Logic Programming, pages 152160, Boston, Massachusetts, 1985. IEEE Computer Society Press.

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R. A. O'Keefe. Towards an Algebra for Constructing Logic Programs. In Proc. IEEE Symp. on Logic Programming, pp. 152-- 160, 1985.

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