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European Workshop on Logics in Artificial Intelligence

JELIA 1990: Logics in AI pp 97–120Cite as

Action logic and pure induction

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 478))

Abstract

In Floyd-Hoare logic, programs are dynamic while assertions are static (hold at states). In action logic the two notions become one, with programs viewed as on-the-fly assertions whose truth is evaluated along intervals instead of at states. Action logic is an equational theory ACT conservatively extending the equational theory REG of regular expressions with operations preimplication a→b (had a then b) and postimplication b←a (b if-ever a). Unlike REG, ACT is finitely based, makes a* reflexive transitive closure, and has an equivalent Hilbert system. The crucial axiom is that of pure induction, (a→a)* = a→a.

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, 94305, Stanford, CA

    Vaughan Pratt

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  1. Vaughan Pratt
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J. van Eijck

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© 1991 Springer-Verlag Berlin Heidelberg

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Pratt, V. (1991). Action logic and pure induction. In: van Eijck, J. (eds) Logics in AI. JELIA 1990. Lecture Notes in Computer Science, vol 478. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0018436

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  • DOI: https://doi.org/10.1007/BFb0018436

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53686-4

  • Online ISBN: 978-3-540-46982-7

  • eBook Packages: Springer Book Archive

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