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On the Notion of Naturalness in Formal Modeling

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The Logic of Software. A Tasting Menu of Formal Methods

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13360))

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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.

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Notes

  1. 1.

    We restrict ourselves to the above setting and do not investigate, e.g., epistemological questions. English translations of the features are taken from Kühne [29].

  2. 2.

    We consider Java as being formalized to a sufficient degree to consider it formal.

  3. 3.

    We are sure the interested reader can find situations where the number of axles does change in the lifetime of a car. We assume that this class is written for an application that does not consider any of these situations.

  4. 4.

    Extensions of a simple formalism may be less straightforward than expected, as the study of Quinlan et al. [37] on the use of BNF grammars in practice shows.

  5. 5.

    This is in line with a tradition to describe concepts/categories not by common features, but by distance between instances, following Wittgenstein’s family resemblance [49] and Rosch’ prototype theory [38].

  6. 6.

    I.e., it is not possible to assign a value to an object in one dimension without assigning one in the others.

  7. 7.

    For example, we can assume any programmer to have some knowledge about cars.

  8. 8.

    In the semiotic framework there is no such thing as a model at all without an involved mind, as a model is a sign and a sign needs an interpreter.

  9. 9.

    On the problems of applying the theory of evolution to developments of programming languages we refer to [11].

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Acknowledgement

This work was partially supported by the Research Council of Norway via the SIRIUS Center (237898) and the PeTWIN project (294600). The authors thank Lars Tveito and Michael Lienhardt for feedback on early drafts of this article.

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Authors and Affiliations

  1. University of Oslo, Oslo, Norway

    Eduard Kamburjan

  2. IBM Research, Rio de Janeiro, Brazil

    Sandro Rama Fiorini

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  1. Eduard Kamburjan
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Correspondence to Eduard Kamburjan .

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Editors and Affiliations

  1. Chalmers University of Technology, Gothenburg, Sweden

    Wolfgang Ahrendt

  2. Karlsruhe Institute of Technology, Karlsruhe, Germany

    Bernhard Beckert

  3. TU Darmstadt, Darmstadt, Germany

    Richard Bubel

  4. University of Oslo, Oslo, Norway

    Einar Broch Johnsen

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Kamburjan, E., Fiorini, S.R. (2022). On the Notion of Naturalness in Formal Modeling. In: Ahrendt, W., Beckert, B., Bubel, R., Johnsen, E.B. (eds) The Logic of Software. A Tasting Menu of Formal Methods. Lecture Notes in Computer Science, vol 13360. Springer, Cham. https://doi.org/10.1007/978-3-031-08166-8_13

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  • DOI: https://doi.org/10.1007/978-3-031-08166-8_13

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