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Natural Logic for Natural Language

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Logic, Language, and Computation (TbiLLC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4363))

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Abstract

For a cognitive account of reasoning it is useful to factor out the syntactic aspect — the aspect that has to do with pattern matching and simple substitution — from the rest. The calculus of monotonicity, alias the calculus of natural logic, does precisely this, for it is a calculus of appropriate substitutions at marked positions in syntactic structures. We first introduce the semantic and the syntactic sides of monotonicity reasoning or ‘natural logic’, and propose an improvement to the syntactic monotonicity calculus, in the form of an improved algorithm for monotonicity marking. Next, we focus on the role of monotonicity in syllogistic reasoning. In particular, we show how the syllogistic inference rules (for traditional syllogistics, but also for a broader class of quantifiers) can be decomposed in a monotonicity component, an argument swap component, and an existential import component. Finally, we connect the decomposition of syllogistics to the doctrine of distribution.

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Authors and Affiliations

  1. CWI, Amsterdam and Uil-OTS, Utrecht University,  

    Jan van Eijck

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  1. Jan van Eijck
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Balder D. ten Cate Henk W. Zeevat

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© 2007 Springer-Verlag Berlin Heidelberg

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van Eijck, J. (2007). Natural Logic for Natural Language. In: ten Cate, B.D., Zeevat, H.W. (eds) Logic, Language, and Computation. TbiLLC 2005. Lecture Notes in Computer Science(), vol 4363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75144-1_16

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  • DOI: https://doi.org/10.1007/978-3-540-75144-1_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75143-4

  • Online ISBN: 978-3-540-75144-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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