A 'natural logic' inference system using the Lambek calculus

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
Categories (categorize this paper)
DOI 10.1007/s10849-006-9018-x
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 25,100
Through your library
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.
Completeness in the Theory of Types.Leon Henkin - 1950 - Journal of Symbolic Logic 15 (2):81-91.
Order-Based Inference in Natural Logic.Yaroslav Fyodorov, Yoad Winter & Nissim Francez - 2003 - Logic Journal of the IGPL 11 (4):385-416.

View all 6 references / Add more references

Citations of this work BETA
Inclusion and Exclusion in Natural Language.Thomas F. Icard - 2012 - Studia Logica 100 (4):705-725.

Add more citations

Similar books and articles
Modal Logic as Metalogic.Kosta Došen - 1992 - Journal of Logic, Language and Information 1 (3):173-201.
The Lambek Calculus Enriched with Additional Connectives.Makoto Kanazawa - 1992 - Journal of Logic, Language and Information 1 (2):141-171.
Syntactic Calculus with Dependent Types.Aarne Ranta - 1998 - Journal of Logic, Language and Information 7 (4):413-431.
On the Logic of Β -Pregroups.Aleksandra Kiślak-Malinowska - 2007 - Studia Logica 87 (2-3):323 - 342.
Multimodal Linguistic Inference.Michael Moortgat - 1996 - Journal of Logic, Language and Information 5 (3-4):349-385.
A Note on the Proof Theory the λII-Calculus.David J. Pym - 1995 - Studia Logica 54 (2):199 - 230.

Monthly downloads

Added to index

2009-01-28

Total downloads

33 ( #147,893 of 2,132,897 )

Recent downloads (6 months)

1 ( #388,047 of 2,132,897 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums