The success of automated reasoning techniques over large natural-language texts heavily relies on a fine-grained analysis of natural language assumptions. While there is a common agreement that the analysis should be hyperintensional, most of the automatic reasoning systems are still based on an intensional logic, at the best. In this paper we introduce the TIL-Script language, which is a computational variant of Pavel Tichý's Transparent Intensional Logic (TIL). TIL is a hyperintensional, typed lambda calculus of partial functions. Hyperintensional, because the TIL terms are interpreted as denoting procedures rather than their products, which are partial functions-in-extension. Thus, in our stratified ontology we have got procedures, their products, i.e. functions-in-extensions, or even procedures of a lower order, as well as functional values. These procedures are rigorously defined as TIL constructions. With constructions of constructions, constructions of functions, functions, and functional values in our stratified ontology, we need to keep track of the traffic between multiple logical strata. The ramified type hierarchy does just that. The type of first order objects includes all objects that are not constructions. The type of second-order objects includes constructions of first-order objects. The type of third-order objects includes constructions of first- or second-order objects. And so on, ad infinitum. The goal of this paper is to introduce the algorithm of type control over the results of logical analysis of natural-language expressions, i.e., checking whether the analysis results in a type-theoretically coherent procedure assigned to the expression as its meaning.
IOS Press, Inc.
6751 Tepper Drive
Clifton, VA 20124
Tel.: +1 703 830 6300
Fax: +1 703 830 2300 email@example.com
(Corporate matters and books only) IOS Press c/o Accucoms US, Inc.
For North America Sales and Customer Service
West Point Commons
Lansdale PA 19446
Tel.: +1 866 855 8967
Fax: +1 215 660 5042 firstname.lastname@example.org