Results 1 
5 of
5
Ellipsis and higherorder unification
 Linguistics and Philosophy
, 1991
"... We present a new method for characterizing the interpretive possibilities generated by elliptical constructions in natural language. Unlike previous analyses, which postulate ambiguity of interpretation or derivation in the full clause source of the ellipsis, our analysis requires no such hidden amb ..."
Abstract

Cited by 109 (1 self)
 Add to MetaCart
We present a new method for characterizing the interpretive possibilities generated by elliptical constructions in natural language. Unlike previous analyses, which postulate ambiguity of interpretation or derivation in the full clause source of the ellipsis, our analysis requires no such hidden ambiguity. Further, the analysis follows relatively directly from an abstract statement of the ellipsis interpretation problem. It predicts correctly a wide range of interactions between ellipsis and other semantic phenomena such as quantifier scope and bound anaphora. Finally, although the analysis itself is stated nonprocedurally, it admits of a direct computational method for generating interpretations. This article is available through the Computation and Language EPrint Archive as cmplg/9503008, and also appears in Linguistics and Philosophy 14(4):399–452. cmplg/9503008 Ellipsis and HigherOrder Unification 1
The Lambda Calculus is Algebraic
 Journal of Functional Programming
, 1996
"... this paper, we point out that the failure of the rule, and the subsequent need for a nonequational class of models, is not due to the lambda calculus itself, but to the way free variables are usually interpreted in these models. An equation M = N between open terms is usually said to be satisfied ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
this paper, we point out that the failure of the rule, and the subsequent need for a nonequational class of models, is not due to the lambda calculus itself, but to the way free variables are usually interpreted in these models. An equation M = N between open terms is usually said to be satisfied in a lambda algebra A if it holds for all substitutions of elements of A for the free variables. We call this the local interpretation, and define M = N to hold
On Coquand's "An Analysis of Girard's Paradox"
"... In his paper "An Analysis of Girard's Paradox" [3], Coquand presents a result of Girard that minimal higherorder logic extended with quantification over types is inconsistent. Using Girard's idea, he shows that some other extensions of minimal higherorder logic, several extensions of the calcul ..."
Abstract
 Add to MetaCart
In his paper "An Analysis of Girard's Paradox" [3], Coquand presents a result of Girard that minimal higherorder logic extended with quantification over types is inconsistent. Using Girard's idea, he shows that some other extensions of minimal higherorder logic, several extensions of the calculus of constructions, and an early calculus of MartinLof with type:type are also inconsistent. He also presents several consistent extensions of minimal higherorder logic and the calculus of constructions. In this paper, I survey relevant background material and present two of Coquand's proofs of inconsistency. 1 Background In this section, I present some material that is relevant for understanding Coquand's results. Readers familiar with this material may wish to skip to section 2 and refer to this section later as necessary. 1.1 Styles of Axiomatization There are two styles commonly used for axiomatizing various logics; the style of natural deduction and the style of Hilbert. Syst...