Authors
Nissim Francez
Technion, Israel Institute of Technology
Abstract
This paper develops an inference system for natural language within the ‘Natural Logic’ paradigm as advocated by van Benthem, Sánchez and others. The system that we propose is based on the Lambek calculus and works directly on the Curry-Howard counterparts for syntactic representations of natural language, with no intermediate translation to logical formulae. The Lambek -based system we propose extends the system by Fyodorov et~al., which is based on the Ajdukiewicz/Bar-Hillel calculus Bar Hillel,. This enables the system to deal with new kinds of inferences, involving relative clauses, non-constituent coordination, and meaning postulates that involve complex expressions. Basing the system on the Lambek calculus leads to problems with non-normalized proof terms, which are treated by using normalization axioms.
Keywords Natural logic  Inference  Lambek calculus  Normalization
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DOI 10.1007/s10849-006-9018-x
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References found in this work BETA

Completeness in the Theory of Types.Leon Henkin - 1950 - Journal of Symbolic Logic 15 (2):81-91.
The Mathematics of Sentence Structure.Joachim Lambek - 1958 - Journal of Symbolic Logic 65 (3):154-170.
Language and Information.Yehoshua Bar-Hillel - 1965 - Journal of Symbolic Logic 30 (3):382-385.
Completeness in the Theory of Types.Leon Henkin - 1950 - Journal of Symbolic Logic 16 (1):72-73.

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Citations of this work BETA

Inclusion and Exclusion in Natural Language.Thomas F. Icard - 2012 - Studia Logica 100 (4):705-725.
An Analytic Tableau System for Natural Logic.Reinhard Muskens - 2010 - In Maria Aloni, H. Bastiaanse, T. De Jager & Katrin Schulz (eds.), Logic, Language and Meaning. Springer. pp. 104-113.

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