David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Logic, Language and Information 7 (4):413-431 (1998)
The aim of this study is to look at the the syntactic calculus of Bar-Hillel and Lambek, including semantic interpretation, from the point of view of constructive type theory. The syntactic calculus is given a formalization that makes it possible to implement it in a type-theoretical proof editor. Such an implementation combines formal syntax and formal semantics, and makes the type-theoretical tools of automatic and interactive reasoning available in grammar.In the formalization, the use of the dependent types of constructive type theory is essential. Dependent types are already needed in the semantics of ordinary Lambek calculus. But they also suggest some natural extensions of the calculus, which are applied to the treatment of morphosyntactic dependencies and to an analysis of selectional restrictions. Finally, directed dependent function types are introduced, corresponding to the types of constructive type theory.
|Keywords||Constructive type theory Lambek calculus proof editors|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Twan Laan & Rob Nederpelt (1996). A Modern Elaboration of the Ramified Theory of Types. Studia Logica 57 (2-3):243 - 278.
Maria Bulińska (2009). On the Complexity of Nonassociative Lambek Calculus with Unit. Studia Logica 93 (1):1 - 14.
Sean A. Fulop (2005). Semantic Bootstrapping of Type-Logical Grammar. Journal of Logic, Language and Information 14 (1):49-86.
David J. Pym (1995). A Note on the Proof Theory the λII-Calculus. Studia Logica 54 (2):199 - 230.
Maria Bulińska (2005). The Pentus Theorem for Lambek Calculus with Simple Nonlogical Axioms. Studia Logica 81 (1):43 - 59.
Added to index2009-01-28
Total downloads7 ( #172,414 of 1,096,179 )
Recent downloads (6 months)1 ( #218,857 of 1,096,179 )
How can I increase my downloads?