Alexandre Madeira

Encoding Hybridised Institutions into First Order Logic

A ‘hybridization’ of a logic, referred to as the base logic , consists of developing the characteristic features of hybrid logic on top of the respective base logic, both at the level of syntax (i.e. modalities, nominals, etc.) and of the semantics (i.e. possible worlds). By ‘hybridized institutions’ we mean the result of this process when logics are treated abstractly as institutions (in the sense of the institution theory of Goguen and Burstall). This work develops encodings of hybridized institutions into (many-sorted) first-order logic (abbreviated

Hybrid specification of reactive systems: an institutional approach

\mathcal{FOL}

Hybridisation at Work

) as a ‘hybridization’ process of abstract encodings of institutions into

Refinement via Interpretation

\mathcal{FOL}

Refinement in hybridised institutions

, which may be seen as an abstraction of the well-known standard translation of modal logic into

Refinement by Interpretation in a General Setting

\mathcal{FOL}

Proof theory for hybrid(ised) logics

. The concept of encoding employed by our work is that of comorphism from institution theory, which is a rather comprehensive concept of encoding as it features encodings both of the syntax and of the semantics of logics/institutions. Moreover, we consider the so-called theoroidal version of comorphisms that encode signatures to theories, a feature that accommodates a wide range of concrete applications. Our theory is also general enough to accommodate various constraints on the possible worlds semantics as well a wide variety of quantifications. We also provide pragmatic sufficient conditions for the conservativity of the encodings to be preserved through the hybridization process, which provides the possibility to shift a formal verification process from the hybridized institution to

A Coalgebraic Perspective on Logical Interpretations

\mathcal{FOL}

Dynamic Logic with Binders and Its Application to the Development of Reactive Systems

.

THE ROLE OF LOGICAL INTERPRETATIONS IN PROGRAM DEVELOPMENT

This paper introduces a rigorous methodology for requirements specification of systems that react to external stimulus by evolving through different operational modes. In each mode different functionalities are provided. Starting from a classical state-machine specification, the envisaged methodology interprets each state as a different mode of operation endowed with an algebraic specification of the corresponding functionality. Specifications are given in an expressive variant of hybrid logic which is, at a later stage, translated into first-order logic to bring into scene suitable tool support. The papers main contribution is to provide rigorous foundations for the method, framing specification logics as institutions and the translation process as a comorphism between them.