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

Published online by Cambridge University Press:  01 December 2008

JOSÉ M. CAÑETE-VALDEÓN
JOSÉ M. CAÑETE-VALDEÓN*
Affiliation:
Departamento de Lenguajes y Sistemas Informáticos, Universidad de Sevilla, ETS de Ingeniería Informática, Avenida de la Reina Mercedes S/N, Sevilla 41012, Spain Email: jmcv@us.es
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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.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 18 , Issue 6 , December 2008 , pp. 1017 - 1030
Copyright
Copyright © Cambridge University Press 2008

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References

Cañete-Valdeón, J. M. (2006) A Theory of Languages and Design Methods in Software Engineering, Ph.D. thesis, Universidad de Sevilla.Google Scholar
Giere, R. N. (1985) Constructive realism. In: Churchland, P. and Hooker, C. (eds.) Images of Science, University of Chicago Press.Google Scholar
Giere, R. N. (1988) Explaining Science: A Cognitive Approach, University of Chicago Press.Google Scholar
Giere, R. N. (1999) Science without Laws, University of Chicago Press.Google Scholar
Giere, R. N. (2004) How models are used to represent reality. Philos. Sci. 71 742–752.CrossRefGoogle Scholar
Giere, R. N. (2006) Scientific Perspectivism, University of Chicago Press.Google Scholar
Goguen, J. A. and Malcolm, G. (1996) Algebraic Semantics of Imperative Programs, MIT Press.Google Scholar
Gosling, J., Joy, B., Steele, G. and Bracha, G. (2005) The Java Language Specification, 3rd edition, The Java Series, Addison-Wesley.Google Scholar
Hennessy, J. and Patterson, D. A. (2003) Computer Architecture: A Quantitative Approach, 3rd edition, Morgan Kaufmann Publishers.Google Scholar
Hoare, C. A. R. (1969) An axiomatic basis for computer programming. Commun. ACM 12 (10)576–580, 583.Google Scholar
Hoare, C. A. R. (1985) Communicating Sequential Processes, Prentice-Hall International Series in Computer Science.Google Scholar
Jackson, M. A. (2001) Problem Frames: Analyzing and Structuring Software Development Problems, Addison-Wesley, ACM Press.Google Scholar
Mosses, P. D. (ed.) (2004) CASL Reference Manual. Springer-Verlag Lecture Notes in Computer Science 2960.Google Scholar
OMG (2000) Unified Modeling Language specification 1.3. Tech. Rep. formal/00-03-01.Google Scholar
Reggio, G., Astesiano, E. and Choppy, C. (1999) CASL-LTL: A CASL extension for dynamic reactive systems – summary. Tech. Rep. DISI-TR-99-34, DISI.Google Scholar
Reggio, G., Cerioli, M. and Astesiano, E. (2000) An algebraic semantics of UML supporting its multiview approach. In: Heylen, D., Nijholt, A. and Scollo, G. (eds.) Proc. AMiLP 2000, Twente Workshop on Language Technology number 16.Google Scholar
Suppe, F. (ed.) (1974) The Structure of Scientific Theories, University of Illinois Press.Google Scholar
Watt, D. A. (1991) Programming Language Syntax and Semantics, Prentice Hall International Series in Computer Science.Google Scholar