Formal program synthesis is concerned with deriving programs that are (formally) correct wrt their specifications, and is therefore of crucial importance to formal development of verifiably correct software. Declarative paradigms such as logic programming are particularly suitable for program synthesis, and we have formulated a formal approach to synthesising standard logic programs. Our approach is object-oriented in the sense that it allows the synthesis of modular, reusable, and hence maintainable programs. In this paper, we propose a formal approach to synthesising constraint logic programs based on our current work. We will show that this approach can be used to synthesise modular and reusable CLP programs. An integral part of this paper is the introduction of an abstract semantics to reason about the synthesis of CLP programs. 1 Introduction Program synthesis is concerned with deriving programs that are correct wrt their specifications. A formal approach to synthesis guarantees ...

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...

Abstract. In this paper general mechanisms and syntactic restrictions are explored in order to specify and merge rule bases in the Semantic Web. Rule bases are expressed by extended logic programs having two forms of negation, namely strong (or explicit) and weak (also known as default negation or negation-as-failure). The proposed mechanisms are defined by very simple modular program transformations, and integrate both open and closed world reasoning. These program transformations are shown to be appropriate for the two major semantics for extended logic programs: answer set semantics and well-founded semantics with explicit negation. Moreover, the results obtained by both semantics are compared. 1

Given two context-free grammars (CFGs), G 1 and G 2 , the language generated by the union of the grammars is not the union of the languages generated by each grammar: L(G 1 [ G 2 ) 6= L(G 1 ) [ L(G 2 ). In order to account for modularity of grammars, another way of defining the meaning of grammars is needed. This paper adapts results from the semantics of logic programming languages to CFGs. We discuss alternative approaches for defining the denotation of a grammar, culminating in one which we show to be both compositional and fullyabstract. We then show how grammar modules can be defined such that their semantics retains these desirable properties. 1 Introduction This paper provides the mathematical infrastructure required for defining modules in context-free grammars (CFGs). Our departure point is the belief that any advances in grammar engineering must be preceded by a more theoretical work, concentrating on the semantics of grammars. This view reflects the situation in logic pr...

. Quality software must be reusable, extensible, and reliable. Object-oriented programming purports to achieve these attributes by the use of classes and inheritance (informally). In this paper, we show how our existing approach to deductive synthesis of logic programs can serve as the basis for an object-oriented methodology for formal program development that achieves reusability, extensibility and correctness (formally). 1 Introduction Object-oriented programming is very much seen as the standard bearer of the software industry nowadays, because it purports to achieve the key attributes of any quality software: reusability , extensibility , and reliability (see e.g. [12, 13]). Object-oriented programming achieves reusability and extensibility by using a class as the basic modular unit, and a mechanism called inheritance to define new classes from existing ones. Reliability results from the ability to monitor assertions and invariants contained in classes. However, at present, th...

Abstract. In this paper we develop a declarative language for modular answer set programming (ASP). Our language allows to declaratively state how one ASP module can import processed answer sets from another ASP module. We define the syntax and semantics of our language and illustrate its applicability by modeling the ACC tournament scheduling problem. Besides the elegance of developing declarative programs in a modular manner, our illustration shows that a problem that is not timely solvable when done in a monolithic way, but becomes solvable when done in a modular way. 1

In what sense is a grammar the union of its rules? This paper adapts the notion of composition, well developed in the context of programming languages, to the domain of linguistic ibrmalisms. We study alternative definitions tbr the semantics of such formalisms, suggesting a denotational semantics that we show to be compositional and fully-abstract. This facilitates a clear, mathematically sound way for defining grammar modularity.

Abstract. Recently, enabling modularity aspects in Answer Set Programming (ASP) has gained increasing interest to ease the composition of program parts to an overall program. In this paper, we focus on modular nonmonotonic logic programs (MLP) under the answer set semantics, whose modules may have contextually dependent input provided by other modules. Moreover, (mutually) recursive module calls are allowed. We define a model-theoretic semantics for this extended setting, show that many desired properties of ordinary logic programming generalize to our modular ASP, and determine the computational complexity of the new formalism. We investigate the relationship of modular programs to disjunctive logic programs with well-defined input/output interface (DLP-functions) and show that they can be embedded into MLPs.

The Herbrand model H of a definite logic program P is an initial model among the class of all the models of P , interpreting P as an initial theory. Such a theory proves (computes) only positive literals (atoms) in P , so it does not deal with negation. In this paper, we introduce isoinitial models of logic programs. We show that isoinitial semantics deals with negation, and works in a uniform way for definite and normal logic programs. Moreover, the lack of an isoinitial model signals the absence of information. Thus it also provides a unifying semantics for closed and open logic programs. Keywords: Semantics, isoinitial models, negation 1 Introduction The intended model of a standard (Horn clause) logic program P is its Herbrand model H. It interprets P under the Closed World Assumption [11]. Considering the class of all the models of P , H interprets P as an initial (Horn) theory [5]. A distinguishing feature of an initial theory P is that, in general, it proves (computes) only p...

In this paper we study the replacement transformation for Constraint Logic Programming modules. We define new applicability conditions that guarantee the correctness of the operation also wrt module's composition: under these conditions, the original and the transformed modules have the same observable properties also when they are composed with other modules. The applicability conditions are not bound to a specific notion of observable. Here we consider three distinct such notions. Two are operational and are based on the computed constraints; the third is the algebraic one based on the least model. We show that our transformation method can be applied in any of these distinct contexts, thus providing a parametric approach. 1 Introduction Constraint Logic Programming (CLP for short) is a powerful declarative programming paradigm in which constraints are primitive elements and the computation is specified by a logical inference rule. CLP has already been successfully employed in many ...