Journal of Logic, Language and Information 15 (3):273-295 (2006)
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|
|Categories||categorize this paper)|
References found in this work BETA
The Mathematics of Sentence Structure.Joachim Lambek - 1968 - Journal of Symbolic Logic 33 (4):627-628.
Boolean Semantics for Natural Language.Edward L. Keenan & Leonard M. Faltz - 1987 - Journal of Symbolic Logic 52 (2):554-555.
Order-Based Inference in Natural Logic.Yaroslav Fyodorov, Yoad Winter & Nissim Francez - 2003 - Logic Journal of the IGPL 11 (4):385-416.
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