On the interpretation of mathematical entities in the formalisation of programming and modelling languages

Abstract

This paper analyses the interpretation of mathematical entities in the formalisations of languages. Four case studies are considered, covering both denotational and axiomatic approaches. We argue that the usual interpretation consists of direct statements about the language concepts and, occasionally, about the real world; some problems of this approach are discussed. Applying results from philosophical studies into the structure of scientific theories, we propose an alternative interpretation of mathematical entities as statements defining constructed concepts, which can be employed in turn as theoretical models of the language concepts and the world. Though this approach requires us to write hypotheses claiming some similarity between the models and the represented subjects, we reason that it is more adequate for formalising certain languages.

Defeasible Argumentation of Software Architectures

“…If RMA is employed for modelling some behavioural view of an architecture, and both the architecture and the real-world domains in the problem context do not completely match these constraints and assumptions, the confidence degree on the model predictions may be reduced. For a more detailed account on the relationship between formal models and software artifacts, the reader may be interested our research on the topic [27]. Figure 6 shows an argumentation scheme, argument from formal model, where formal reasoning is put in the broader context of determining whether an architecture satisfies a certain property.…”