The program composition approach can be fruitfully applied to combine general logic programs, that is, logic programs possibly containing negative premises. We show how the introduction of a basic set of (meta-level) composition operations over general programs increases the knowledge representation capabilities of logic programming for non-monotonic reasoning. Examples of modular programming, hierarchical reasoning, constraints and rules with exceptions will be illustrated. The semantics of programs and program compositions is dened in terms of three-valued logic by extending the three-valued semantics for logic programs proposed by Fitting [16]. A computational interpretation of program compositions is formalised by means of an equivalence preserving syntactic transformation of arbitrary program compositions into standard general programs. 1 Introduction It is becoming more and more evident that the activity of building software is moving from writing lines of code in some program...

Compositionality of programs is an important concern in knowledge representation and software development. In the context of Logic Programming, up till now, the issue has mostly been studied for definite programs only. Here, we study compositionality in the context of normal open logic programming. This is a very expressive logic for knowledge representation of uncertainty and incomplete knowledge on concepts and on problem domain, in which the compositionality issue turns up very naturally. The semantics of the logic is a generalisation (allowing non-Herbrand interpretations) of the well-founded semantics. We provide a number of results which offer different sufficient conditions under which the models of the composition of two theories can be related to the intersection of the models of the composing theories. In particular, under these conditions, logical consequence will be preserved under composition. Keywords : Logic Programming, Knowledge representation. CR Subject Classific...

ion) Given two normal programs P1 and P2, the following three facts are equivalent: (i) Sem(P 1) = Sem(P 2) (ii) For every program P , Sem(P [ P 1) = Sem(P [ P 2) (iii) For every program P , MP[P1 = MP[P2 . Proof. It is enough to prove that (iii) implies (i), because the other implications are direct consequences of lemma 3.1 and theorem 5.1. Let us suppose that there exists a model A in Mod(; ;) such that F 1(A) 6= F 2(A), where F1 = Sem(P 1) and F2 = Sem(P 2). Then, we will show that there exists a program P such that MP[P1 6= MP[P2 . Let j 2 IN be the least layer such that F 1(A) + j 6= F 2(A) + j or F 1(A) j 6= F 2(A) j . Then we can consider two cases. First, if there exists the given level k 2 IN , and F 1(A) + j 6= F 2(A) + j , for some j < k, then F 1(B) 6= F 2(B) for all models B 2 Mod(; ;) such that A + j = B + i and A j 1 = B i 1 for some layer i. This is the case for the model B such that, for all i 2 IN : B + i = A + j B i = A j 1 In any other cas...

. Most modern computing systems consist of large numbers of software components that interact with each other. Correspondingly, the capability of re-using and composing existing software components is of primary importance in this scenario. In this paper we analyse the role of renaming as a key ingredient of component-based programming. More precisely, a meta-level renaming operation is introduced in the context of a logic-based program composition setting which features a number of other composition operations over general logic programs, that is, logic programs possibly containing negative premises. Several examples are presented to illustrate the increased knowledge representation capabilities of logic programming for non-monotonic reasoning. The semantics of programs and program compositions is dened in terms of three-valued logic by extending the three-valued semantics for logic programs proposed by Fitting [10]. A computational interpretation of program composition...

In this paper we propose a new operational semantics, called BCN, which is sound and complete with respect to Clark-Kunen's completion for the unrestricted class of Normal Logic Programs. BCN is based on constructive negation and can be seen as an operational semantics for the class of Normal Constraint Logic Programs (NCLP) over the Herbrand universe. The main features of BCN making it a useful operational mechanism are twofold: First, BCN improves the existing proposals because it is more amenable to a practical implementation. The point is that, instead of computing subsidiary trees, the process of constructing answers for negative goals is reduced to a simple symbolic manipulation plus a constraint satisfaction checking process. Essentially, our approach exploits the definition of negative literals in the completion to interpret the constructive negation meta-rule. Second, the way in which BCN is defined makes it an extensible scheme to NCLP over arbitrary constraint domains. 1

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This paper studies a semantics of multiple logic programs, and synthesizes a program having such a collective semantics. More precisely, the following two problems are considered: given two logic programs P1 and P2, which have the collections of answer sets AS(P1) andAS(P2), respectively; (i) find a program Q which has the set of answer sets such that AS(Q) =AS(P1)∪AS(P2); (ii) find a program R which has the set of answer sets such that AS(R) =AS(P1) ∩AS(P2). A program Q satisfying the condition (i) is called generous coordination of P1 and P2; andRsatisfying (ii) is called rigorous coordination of P1 and P2. Generous coordination retains all of the answer sets of each program, but permits the introduction of additional answer sets of the other program. By contrast, rigorous coordination forces each program to give up some answer sets, but the result remains within the original answer sets for each program. Coordination provides a program that reflects the meaning of two or more programs. We provide methods for constructing these two types of coordination and address its application to logic-based multi-agent systems.

Abstract. This paper studies compositional semantics of nonmonotonic logic programs. We suppose the answer set semantics of extended disjunctive programs and consider the following problem. Given two programs P1 and P2, which have the sets of answer sets AS(P1) and AS(P2), respectively; find a program Q which has answer sets as minimal sets S ∪T for S from AS(P1) and T from AS(P2). The program Q combines answer sets of P1 and P2, and provides a compositional semantics of two programs. Such program composition has application to coordinating knowledge bases in multi-agent environments. We provide methods for computing program composition and discuss their properties. 1

Modular programs are built as a combination of separate modules, which may be developed and verified separately. Therefore, in order to reason over such programs, compositionality plays a crucial role: the semantics of the whole program must be obtainable as a simple function from the semantics of its individual modules. In the field of logic programming, the need for a compositional semantics has been long recognized, however, while for definite (i.e. negation-free) logic programs a few such semantics have been proposes, in the literature of normal logic programs (programs which employ the negation operator), compositionality has received scarce attention. This is mainly due to the fact that normal programs typically have a nonmonotonic behavior, which is difficult to fit in a compositional framework. Here we propose a declarative compositional semantics for general logic programs. First, a compositional semantics for first-order modules is presented and proven correct wrt the set of ...

In this paper we study the semantics of normal open programs. In particular, we consider normal open logic programs in full generality, without some usual restrictions considered in previous approaches: in our case, se, 4 is dened allowing to close some, but not necessarily all, open predicates. In this context, two semantic denitions are presented: Q P; denes the semantics of P as a certain set of formula (from a given domain) which are logic consequences of the completion of P : This semantics is shown to be compositional and fully abstract with respect to 30599 The second semantics, FQ (P ), easier to compute than Q P; , is dened as the least xpoint of an immediate consequence continuous operator associated to P . This semantics is only proved to be weakly compositional and fully abstract. 1 Introduction The full applicability of program analysis tools largely depends on the possibility of being able to decompose large programs into units that could be analized...