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Logical Frameworks

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Handbook of Philosophical Logic

Part of the book series: Handbook of Philosophical Logic ((HALO,volume 9))

Abstract

One way to define a logic is to specify a language and a deductive system. For example, the language of first-order logic consists of the syntactic categories of terms and formulae, and its deductive system establishes which formulae are theorems. Typically we have a specific language in mind for a logic, but some flexibility about the kind of deductive system we use; we are able to select from, e.g., a Hilbert calculus, a sequent calculus, or a natural deduction calculus. A logical framework is an abstract characterization of one of these kinds of deductive system that we can use to formalize particular examples. Thus a logical framework for natural deduction should allow us to formalize natural deduction for a wide range of logics from, e.g., propositional logic to intuitionistic type-theories or classical higher-order logic.

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Author information

Authors and Affiliations

  1. University of Freiburg, Germany

    David Basin

  2. IBM Unternehmensberatung GmbH, Frankfurt, Germany

    Seán Matthews

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  1. David Basin
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Editors and Affiliations

  1. King’ College, London, UK

    D. M. Gabbay

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

    F. Guenthner

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Basin, D., Matthews, S. (2002). Logical Frameworks. In: Gabbay, D.M., Guenthner, F. (eds) Handbook of Philosophical Logic. Handbook of Philosophical Logic, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0464-9_2

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  • DOI: https://doi.org/10.1007/978-94-017-0464-9_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6055-6

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