Abstract Algebraic Logic Tools in Program Development
Hidden k-logics, as a natural generalization of k-deductive systems, were introduced by Don Pigozzi and Manuel Martins in 2003 to specify object oriented software systems. The use of hidden k-logics unifies the study of several kinds of logics and provides a bridge between abstract algebraic logic (AAL) and specification theory.
In this talk, we discuss a new application of AAL to program development. We present an alternative approach to refinement of algebraic specifications in which signature morphisms are replaced by logic interpretations. Intuitively,an interpretation is a logic translation which preserves meaning. Originally used as a tool for studying equivalent algebraic semantics, this notion has proved to be an effective tool to capture a number of transformations difficult to deal with in classical terms, such as data encapsulation and the decomposition of operations into atomic transactions.