There are various logic-based approaches to modelling concurrent programming. The use of logic for system development concerns both the specification step and the study of the operational aspects (through proof analysis and construction) of such development. This means that we have to consider different logical systems for different uses of logic. Moreover, we can also consider concurrency from both points of view: we want to reason and to specify systems where some concurrency aspects are involved, but also to have some operational interpretation of concurrency within logic (focusing on the concept of proof). For this purpose, it seems clear that we have to identify and to study, on the one hand, the role and the treatment of objects (representation, inheritance, modularity, communication, and so on) in this context, and, on the other hand, the interaction of work on proofs and concurrency with the Object-Oriented Programming paradigm.

The ECOOP’96 workshop on ‘Proof Theory of Concurrent Object-Oriented Programming’ took place in Linz, Austria, in July 1996. Its objective was to provide an integrated forum for the presentation of research and the exchange of ideas and experiences in the topics concerned with proofs, concurrency and object-oriented programming (specification, proof development, and so on). The call for papers for this Special Issue of Mathematical Structures in Computer Science can be considered to have been a natural scientific continuation of the workshop.

The papers selected for this Special Issue address some of the topics discussed in the workshop. They present different alternative frameworks that are effectively based on a proof-theoretic approach. They illustrate, from different points of view, the interest, potentialities and difficulties of dealing with such an approach in the design of object-based concurrent systems.