T. S. E. Maibaum

Temporal theories as modularisation units for concurrent system specification

In this paper, we bring together the use of temporal logic for specifying concurrent systems, in the tradition initiated by A. Pnueli, and the use of tools from category theory as a means for structuring specifications as combinations of theories in the style developed by R. Burstall and J. Goguen. As a result, we obtain a framework in which systems of interconnected components can be described by assembling the specifications of their components around a diagram, using theory morphisms to specify how the components interact. This view of temporal theories as specification units naturally brings modularity to the description and analysis of systems. Moreover, it becomes possible to import into the area of formal development of reactive systems the wide body of specification techniques that have been defined for structuring specifications independently of the underlying logic, and that have been applied with great success in the area of Abstract Data Types. Finally, as a discipline of design, we use the object-oriented paradigm according to which components keep private data and interact by sharing actions, with a view towards providing formal tools for the specification of concurrent objects.

Categorical semantics of parallel program design

Abstract We formalise, using Category Theory, modularisation techniques for parallel and distributed systems based on the notion of superposition, showing that parallel program design obeys the “universal laws” formulated by Goguen for General Systems Theory, as well as other algebraic properties of modularity formulated for Specification Theory. The resulting categorical formalisation unifies the different notions of superposition that have been proposed in the literature and clarifies their algebraic properties with respect to modularisation. It also suggests ways of extending or revising existing languages in order to provide higher levels of reusability, modularity and incrementality in system design.

Sharing Actions and Attributes in Modal Action Logic

Distributed systems may be specified in Structured Modal Action Logic by decomposing them into agents which interact by sharing attributes (memory) as well as actions.

Describing, Structuring and Implementing Objects

The popularity of the notion of object for structuring (the specification of) systems has not been accompanied by the necessary formalisation of the concepts and constructions involved. We have a well developed theory of abstract data types that explains how to structure specifications based on the notion of value, but objects involve imperative notions such as those of action and state which are not well captured in an applicative way. In this paper, we focus on the development of an alternative framework to support systems design based on the concept of object. We provide a notion of object signature around which we define the notion of locality (encapsulation). We adopt a deontic action logic for the description of objects. We define the notion of morphism between object descriptions, and show how these notions can be used to combine object descriptions and, in this way, define the behaviour of societies of interacting objects. And, finally, we show by means of an example how object descriptions may be reified by implementing descriptions of objects at one level (of abstraction) in terms of object descriptions at the level below.

Temporal Reasoning over Deontic Specifications

Starting from a deontic specification modelling the behaviour of a system, we show how it is possible to reason about the temporal properties of the normative behaviours of that system. In particular, we show how safety and liveness properties can be derived, respectively, from permission and obligation structures. A formal relationship is thus established between the recently proposed deontic accounts of behaviour, that are more actionoriented, and the already traditional and successful property-oriented frameworks based on temporal logics.

A generalized approach to formal languages

A generalization of ranked alphabets, many-sorted alphabets, is studied. The concepts of finite automaton, regular, recognizable, equational, and context free languages are generalized to sets over these new alphabets. It is shown that the derivation trees of a context free set are always characterized by some recognizable set over a related many-sorted alphabet. Previous theory is drawn as a special case of these results and new results are advanced. A number of suggestions about language theory are made.

Interconnecting formalisms: supporting modularity, reuse and incrementality

The necessity to deal simultaneously with different formalisms seems to be intrinsic to the discipline of Software Engineering, particularly in relation to modularity, reusability and incremental ity. In order to accommodate this diversity of formalisms, some authors have proposed the adoption of a common semantic domain for the different specification languages, and their transla tion into a common style of predicate logic. In this paper, we suggest that an alternative approach may be taken where the different modelling approaches are formalised individually in a common mathematical framework – Category Theory, and relationships are established between them using functors. Several examples are adduced to support this view and the generality of the approach is illustrated by formalising reusability as a property of a functor relating two such formalisms.

Towards electronic contract performance

An increasing volume of research in e-commerce is concerned with the development of tools and environments to support various aspects of business-to-business electronic contract formation and performance. This paper is mainly concerned with the latter and takes up the suggestion that automated execution of an agreement between (at least) two parties can be effected through a central control mechanism (a so-called e-marketplace). We revisit modal action logic to model an agreement as a state-based system and specify acceptable and unacceptable states of a business transaction. Unacceptable states result from violations of contractual obligations or prohibitions and call for appropriate recovery mechanisms to be specified, so that they can be enforced by the central control mechanism. We comment on the relations between contract violations and the concepts of fault tolerance and recovery arising in the broader distributed systems context, on the one hand, and contrary-to-duty structures from the (theoretical) deontic logic perspective, on the other.

Software certification: is there a case against safety cases?

Safety cases have become popular, even mandated, in a number of jurisdictions that develop products that have to be safe. Prior to their use in software certification, safety cases were already in use in domains like aviation, military applications, and the nuclear industry. Argument based methodologies/approaches have recently become the cornerstone for structuring justification and evidence to support safety claims. We believe that the safety case methodology is useful for the software certification domain, but needs to be tailored, more clearly defined, and more appropriately structured in analogy with regulatory regimes in classical engineering disciplines. This paper presents a number of reasons as to why current approaches to safety cases do not satisfy essential attributes for an effective software certification process and proposes improvements based on lessons learned from other engineering disciplines. In particular, the safety case approach lacks the highly prescriptive and domain specific nature that can be seen in other engineering specialities, in terms of engineering and analysis methods to be applied in generating the relevant evidence. Safety case approaches and corresponding methods should aim to achieve the levels of precision and effectiveness of engineering methods underpinning regulatory regimes in other engineering disciplines.

A temporal logic approach to the specification of reconfigurable component-based systems

We propose a formal specification language for dynamically reconfigurable component-based systems, based on temporal logic. The main aim of the language is to allow one to specify behaviours of component-based systems declaratively, with special emphasis on behaviours in which the architectural structure of the system changes dynamically. Due to the semantics and organisation of our language, it is straightforward to hierarchically build reconfigurable systems in terms of subsystems and basic component parts, and reason about them within the language. Despite its expressive power, the language is rather simple.