Specifications of conceptualisations (ontologies) are often employed for representing reality, both in knowledge representation and software engineering. While languages offer sophisticated constructs and rigorous semantics for building conceptual entities, no attention is paid to the relationship between such entities and the world they intend to represent. This paper studies such a relationship and provides empirical evidences in favour of two main hypotheses: (1) conceptualisations are insufficient to fully represent the specifics of reality; (2) languages (both representation and design-oriented) are general representations of (classes of) systems in the world, and they can be characterised as scientific theories. The first hypothesis establishes a problem for which we propose a solution based on the explicit elaboration of statements claiming the similarity (in some respects and to certain degrees of accuracy) between conceptual entities and real-world systems of interest. The second hypothesis constitutes a new perspective for understanding languages, whose advantages to representation and design are discussed in detail.

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.

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