Completeness and Cut-Elimination in the . . .

Completeness and Cut-Elimination in the . . . (2004)

by Mary DeMarco , James Lipton

User correction supplied by mph

Datum	Value	Source
TITLE	Completeness and Cut-Elimination in the . . .	user correction
AUTHOR NAME	Mary DeMarco	user correction
AUTHOR NAME	James Lipton	user correction
AUTHOR AFFIL	Wesleyan University and Technical University of Madrid	user correction
ABSTRACT	In this paper we give a semantic proof of cut-elimination for ICTT. ICTT is an intuitionistic formulation of Church's theory of types defined by Miller, Scedrov, Nadathur and Pfenning in the late 1980s. It is the basis for the *prolog programming language. Our approach, extending techniques of Takahashi, Andrews and tableaux machinery of Fitting, Smullyan, Nerode and Shore, is to prove a completeness theorem for the cut-free fragment, and show, semantically, that cut is a derived rule. The technique used allows us to extract a generalization of the Takahashi-Sch"utte lemma on extending semivaluations in impredicative systems. We strengthen Andrews ' notion of Hintikka sets to intuitionistic logic in a way that also defines tableau-provability for intuitionistic type theory. We develop a corresponding model theory for ICTT and, after giving a completeness theorem without using cut we then show, using cut, how to establish completeness of more conventional term models. Our work	user correction
YEAR	2004	SVM HeaderParse 0.2
CITATIONS	13 found	ParsCit 1.0