A 'natural logic' inference system using the Lambek calculus

This paper develops an inference system for natural language within the ‘Natural Logic’ paradigm as advocated by van Benthem (1997), Sánchez (1991) 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. (2003), which is based on the Ajdukiewicz/Bar-Hillel (AB) calculus Bar Hillel, (1964). 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
Joachim Lambek (1968). The Mathematics of Sentence Structure. Journal of Symbolic Logic 33 (4):627-628.
Leon Henkin (1950). Completeness in the Theory of Types. Journal of Symbolic Logic 15 (2):81-91.

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