Negative Indefinites

Abstract

Recent theoretical results on adversarial multi-class classification showed a similarity to the multi-marginal formulation of Wasserstein-barycenter in optimal transport. Unfortunately, both problems suffer from the curse of dimension, making it hard to exploit the nice linear program structure of the problems for numerical calculations. We investigate how ideas from Genetic Column Generation for multi-marginal optimal transport can be used to overcome the curse of dimension in computing the minimal adversarial risk in multi-class classification.

The Rich Agreement Hypothesis Rehabilitated

“…More generally, the idea that negation is obligatorily (rather than optionally) base-generated higher than TP-adjoining adverbs is strongly at odds with the basic characteristic of negation in Germanic, where sentential negation may always take scope from a position at least as low as vP (i.e., in a vP adjunct position). This characteristic of Germanic is fully in line with the idea that in order to express sentential negation, the negative marker should be able to at least outscope vP (see Acquaviva 1997, Zeijlstra 2004, Penka 2010. (Recall that in Icelandic and Ä lvdalen Swedish as well, negation can appear in a high position, but the low vP-adjoined position is also always available.)…”

“…In order to express sentential negation, a negative marker must outscope vP, but nothing forbids it from being generated in a higher position and taking scope from there (see Acquaviva 1997, Zeijlstra 2004, Penka 2010. Evidence for this semantic flexibility comes from the fact that negation in Ä lvdalen Swedish can be optionally base-generated in an even higher position, preceding the subject, as shown in (22).…”

“…As is well-known, one of the differences between Russian and the Scandinavian languages is that the negative marker in Russian occupies some head position Neg 0 in the clausal spine. In Scandinavian, on the other hand, negation is phrasal and does not occupy a head position in the clausal spine; rather, sentential negation is an adverb that in its lowest position adjoins to vP (for extensive discussion, see Zeijlstra 2004, Penka 2010. Since it is a requirement for sentential negation that at least the entire vP must be in the scope of a negative operator, the template of Russian negative clauses must minimally contain NegP Ͼ vP.…”

Negative Concord in Western Armenian

“…There are a few different approaches as to how to account for the distribution of NC cross-lingusitically. Some of the recent literature that includes discussion and analysis of n-words are: Ladusaw (1992), Giannakidou (2000), Herburger (2001), de Swart andSag (2002), Watanabe (2004), Zeijlstra (2004Zeijlstra ( , 2008 and Penka (2007) and references within each of them. All of these approaches fail to take into account a certain aspect of the data available in the literature.…”

“…This operator is only inserted as a last resort (Zeijlstra 2004:246). For more details, examples and applications consult Zeijlstra (2004Zeijlstra ( , 2008 and Penka (2007).…”