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Algorithms and Decision Problems: A Crash Course in Recursion Theory

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Handbook of Philosophical Logic

Part of the book series: Handbook of Philosophical Logic ((HALO,volume 1))

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Abstract

At first sight it might seem strange to devote in a handbook of philosophical logic a chapter to algorithms. For, algorithms are traditionally the concern of mathematicians and computer scientists. There is a good reason, however, to treat the material here, because the study of logic presupposes the study of languages, and languages are by nature discrete inductively defined structures of words over an alphabet. Moreover, the derivability relation has strong algorithmic features. In almost any (finitary) logical system, the consequences of a statement can be produced by an algorithm. Hence questions about derivability, and therefore also underivability, ask for an analysis of possible algorithms. In particular, questions about decidability (is there an algorithm that automatically decides if ψ is derivable from φ?) boil down to questions about all algorithms. This explains the interest of the study of algorithms for logicians.

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Authors and Affiliations

  1. Utrecht University, The Netherlands

    Dirk Van Dalen

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  1. Dirk Van Dalen
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  1. King’s College, London, UK

    D. M. Gabbay

  2. Centrum für Informations- und Sprachverarbeitung, Ludwig-Maximilians-Universität München, Germany

    F. Guenthner

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Van Dalen, D. (2001). Algorithms and Decision Problems: A Crash Course in Recursion Theory. In: Gabbay, D.M., Guenthner, F. (eds) Handbook of Philosophical Logic. Handbook of Philosophical Logic, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9833-0_4

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  • DOI: https://doi.org/10.1007/978-94-015-9833-0_4

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