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Formulas-as-types for a hierarchy of sublogics of intuitionistic propositional logic

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Nonclassical Logics and Information Processing (All-Berlin 1990)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 619))

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Abstract

This paper contains a detailed presentation of Howard's [1969] ‘forrrmlas-as-types notion of construction’ for fragments of various subsystems of intuitionistic propositional logic. Buszkowski's [1987, 1988] distinction between two kinds of lambda-abstractors is taken up and suitable fragments of typed terms are singled out (cf. also [van Benthem 1986], [Buszkowski 1987]). The relationship between cut-elimination and normalization of terms is dealt with. Amongst other things, it is shown that in certain cases in which applications of the (cut)-rule can be eliminated from an implicational fragment of the logics considered, cut-elimination and normalization of terms wrt β-reduction are homomorphic images of each other.

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References

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Authors and Affiliations

  1. Institut für Philosophie, LWI, Freie Universität Berlin, Habelschwerdter Allee 30, D-1000, Berlin 33, Germany

    Heinrich Wansing

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  1. Heinrich Wansing
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David Pearce Heinrich Wansing

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© 1992 Springer-Verlag Berlin Heidelberg

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Wansing, H. (1992). Formulas-as-types for a hierarchy of sublogics of intuitionistic propositional logic. In: Pearce, D., Wansing, H. (eds) Nonclassical Logics and Information Processing. All-Berlin 1990. Lecture Notes in Computer Science, vol 619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0031928

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  • DOI: https://doi.org/10.1007/BFb0031928

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55745-6

  • Online ISBN: 978-3-540-47280-3

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