A 'natural logic' inference system using the Lambek calculus

Journal of Logic, Language and Information 15 (3):273-295 (2006)
  Copy   BIBTEX

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.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,252

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Modal logic as metalogic.Kosta Došen - 1992 - Journal of Logic, Language and Information 1 (3):173-201.
A note on the proof theory the λII-calculus.David J. Pym - 1995 - Studia Logica 54 (2):199 - 230.
Multimodal linguistic inference.Michael Moortgat - 1996 - Journal of Logic, Language and Information 5 (3-4):349-385.
On the logic of β -pregroups.Aleksandra Kiślak-Malinowska - 2007 - Studia Logica 87 (2-3):323 - 342.
Syntactic calculus with dependent types.Aarne Ranta - 1998 - Journal of Logic, Language and Information 7 (4):413-431.
The Lambek calculus enriched with additional connectives.Makoto Kanazawa - 1992 - Journal of Logic, Language and Information 1 (2):141-171.

Analytics

Added to PP
2009-01-28

Downloads
75 (#213,716)

6 months
8 (#303,628)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Nissim Francez
Technion, Israel Institute of Technology

References found in this work

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.

View all 13 references / Add more references