Alexandre Madeira

In Computer Science stepwise refinement of algebraic specifications is a well-known formal methodology for rigorous program development. This paper illustrates how techniques from Algebraic Logic, in particular that of interpretation, understood as a multifunction that preserves and reflects logical consequence, capture a number of relevant transformations in the context of software design, reuse, and adaptation, difficult to deal with in classical approaches. Examples include data encapsulation and the decomposition of operations into atomic transactions. But if interpretations open such a new research avenue in program refinement, (conceptual) tools are needed to reason about them. In this line, the paper’s main contribution is a study of the correspondence between logical interpretations and morphisms of a particular kind of coalgebras. This opens way to the use of coalgebraic constructions, such as simulation and bisimulation, in the study of interpretations between (abstract) logics

This paper explores a strict relation between two core notions of the semantics of programs and of fuzzy logics: Kleene Algebras and (pseudo) uninorms. It shows that every Kleene algebra induces a pseudo uninorm, and that some pseudo uninorms induce Kleene algebras. This connection establishes a new perspective on the theory of Kleene algebras and provides a way to build (new) Kleene algebras. The latter aspect is potentially useful as a source of formalism to capture and model programs acting with fuzzy behaviours and domains.