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Logic-Based Formalisms

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Modeling Time in Computing

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Abstract

In this chapter, we discuss logic-based formalism as descriptive notations that allow users to provide and analyze system models in terms of their properties. We discuss and compare various types of temporal logic with respect to their expressive power, their relation to transition systems, and the features of the assumed underlying time domain. We also present other logic-based formalisms that entertain an explicit notion of time without using the modal operators typical of temporal logics, and we introduce probabilistic logic-based models that assign probabilities to events and can therefore express requirements on the probability of certain system evolutions to occur. The chapter concludes with a brief review of the tools supporting the analysis techniques associated with the formalism.

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Notes

  1. 1.

    A function is analytic at a given point if it possesses derivatives of all orders and agrees with its Taylor series about that point. It is piecewise analytic if it is analytic over finitely many contiguous (open) intervals.

  2. 2.

    Presburger arithmetic is the first-order theory of the natural numbers with only addition.

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Authors and Affiliations

  1. Department of Computer Science, Zürich, Switzerland

    Carlo A. Furia

  2. Dipartimento di Elettronica e Informazione, Politecnico di Milano, Milan, Italy

    Dino Mandrioli, Angelo Morzenti & Matteo Rossi

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  1. Carlo A. Furia
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  3. Angelo Morzenti
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Furia, C.A., Mandrioli, D., Morzenti, A., Rossi, M. (2012). Logic-Based Formalisms. In: Modeling Time in Computing. Monographs in Theoretical Computer Science. An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32332-4_9

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