Mario Ornaghi

A software component model and its preliminary formalisation

A software component model should define what components are, and how they can be composed. That is, it should define a theory of components and their composition. Current software component models tend to use objects or port-connector type architectural units as components, with method calls and port-to-port connections as composition mechanisms. However, these models do not provide a proper composition theory, in particular for key underlying concepts such as encapsulation and compositionality. In this paper, we outline our notion of these concepts, and give a preliminary formalisation of a software component model that embodies these concepts.

An Abstract Formalization of Correct Schemas for Program Synthesis

Program schemas should capture not only structured program design principles, but also domain knowledge, both of which are of crucial importance for hierarchical program synthesis. However, most researchers represent schemas as purely syntactic constructs, which can provide only a program template, but not the domain knowledge. In this paper, we take a semantic approach and show that a schema S consists of a syntactic part, namely a template T, and a semantic part. Template T is formalized as an open (first-order) logic program in the context of the problem domain, characterized as a first-order axiomatization, called a specification frameworkF, which is the semantic part. F endows the schema S with a formal semantics, and enables us to define and reason about its correctness. Naturally, correct schemas can be used to guide the synthesis of correct programs.

A constructive approach to testing model transformations

This paper concerns a formal encoding of the Object Management Groups Complete Meta-Object Facility (CMOF) in order to provide a more trustworthy software development lifecycle for Model Driven Architecture (MDA). We show how a form of constructive logic can be used to provide a uniform semantics of metamodels, model transformation specifications, model transformations and black-box transformation tests. A models instantiation of a metamodel within the MOF is treated using the logics realizability relationship, a kind of type inhabitation relationship that is expressive enough to characterize constraint conformance between terms and types. These notions enable us to formalize the notion of a correct model instantiation of a metamodel with constraints. We then adapt previous work on snapshot generation to generate input models from source metamodel specification with the purpose of testing model transformations.

Some results on intermediate constructive logics.

Some techniques for the study of intermediate constructive logics are illustrated. In particular a general characterization is given of maximal constructive logics from which a new proof of the maximality of MV (Med- vedevs logic of finite problems ) can be obtained. Some semantical notions are also introduced, allowing a new characterization of MV, from which a new proof of a conjecture of Friedmans and a new family of principles valid in MV can be extracted.

An improved refutation system for intuitionistic predicate logic

In this paper a refutation calculus for intuitionistic predicate logic is presented where the necessity of duplicating formulas to which rules are applied is analyzed. In line with the semantics of intuitionistic logic in terms of Kripke models a new signFCbeside the SignsT andF is added which reduces the size of the proofs and the involved nondeterminism. The resulting calculus is proved to be correct and complete. An extension of it for Kuroda logic is given.

On Correct Program Schemas

We present our work on the representation and correctness of program schemas, in the context of logic program synthesis. Whereas most researchers represent schemas purely syntactically as higher-order expressions, we shall express a schema as an open first-order theory that axiomatises a problem domain, called a specification framework, containing an open program that represents the template of the schema. We will show that using our approach we can define a meaningful notion of correctness for schemas, viz. that correct program schemas can be expressed as parametric specification frameworks containing templates that are steadfast, i.e. programs that are always correct provided their open relations are computed correctly.

OOD Frameworks in Component-Based Software - Development in Computational Logic

Current Object-oriented Design (OOD) methodologies tend to focus on objects as the unit of reuse, but it is increasingly recognised that frameworks, or groups of interacting objects, are a better unit of reuse. Thus, in next-generation Component-based Development (CBD) methodologies, we can expect components to be frameworks rather than objects. In this paper, we describe a preliminary attempt at a formal semantics for OOD frameworks in CBD in computational logic.

Correct-schema-guided synthesis of steadfast programs

It can be argued that for (semi-)automated software development, program schemas are indispensable, since they capture not only structured program design principles but also domain knowledge, both of which are of crucial importance for hierarchical program synthesis. Most researchers represent schemas purely syntactically (as higher-order expressions). This means that the knowledge captured by a schema is not formalised. We take a semantic approach and show that a schema can be formalised as an open (first-order) logical theory that contains an open logic program. By using a special kind of correctness for open programs, called steadfastness, we can define and reason about the correctness of schemas. We also show how to use correct schemas to synthesise steadfast programs.

Refutation Systems for Propositional Modal Logics

Now we are working on extensions to first order modal logics and to modal logics with intuitionistic basis. A comparison with the work of Wallen [Wal] is planned.

Generalized Tableau Systems for Intemediate Propositional Logics

Given an intermediate propositional logic L (obtained by adding to intuitionistic logic INT a single axiom-scheme), a pseudo tableau system for L can be given starting from any intuitionistic tableau system and adding a rule which allows to insert in any line of a proof table suitable T-signed instances of the axiom-scheme. In this paper we study some sufficient conditions from which, given a well formed formula H, the search for these instances can be restricted to a suitable finite set of formulae related to H. We illustrate our techniques by means of some known logics, namely, the logic D of Dummett, the logics PR k (k≥1) of Nagata, the logics FIN m (m≥1), the logics G n (n≥1) of Gabbay and de Jongh, and the logic KP of Kreisel and Putnam