On the Notion of Naturalness in Formal Modeling

Abstract

We investigate what it means for a formal model to be natural using theories from cognitive science and linguistics. Intuitively, naturalness describes that the formal model fits the domain it is modeling – it is not an intrinsic property of the formal model, but a property that is assigned to it by some human interpreter who is making sense of it. Our main observation is that for each formal model, two sense-making processes are possible: First, the process that interprets the formal model as a symbol in the application domain and assigns it a domain concept. Second, the process that interprets the formal model as a symbol in the engineering domain and assigns it a concept describing an engineering view. Naturalness is described as the similarity of these two mental concepts, i.e., the cognitive complexity to map the domain concept to the engineering concept. We discuss these ideas and formalize then using conceptual spaces, a similarity-based concept representation theory based on cognitive semantics.