Every now and then a technology, or set of technologies, comes along that offers a rich set of components that can be combined and recombined to create new products. The arrival of these components then sets off a technology boom as innovators work through the possibilities. This is, of course, an old idea in economic history. Schumpeter (1934), p. 66 refers to “new combinations of productive m...

Verbs like "eat" are special in that they can appear both with a complement (e.g., "John ate ice-cream") and without a complement ("John ate"). How are such verbs with optional complements represented? This fMRI study attempted to provide neurally based constraints for the linguistic theory of the representation of verbs with optional complements. One linguistic approach suggests that the repre...

The present research documents the American English usage frequencies for 136 verbs that occur with noun phrase and tensed sentence complements (e.g., accepted, noun phrase complement: The student knew the answer yesterday, tensed sentence complement: The student knew the answer was correct). This class of verbs has been the focus of numerous empirical studies investigating how syntactic ambigu...

This paper analyzes Kiparsky & Kiparsky’s (1970) observation that there exists a deep correlation between the semantics and the syntax of factive complements in the light of a wide range of (old and new) phenomena : the incompatibility of ECM and that-less complements with factive predicates, weak island effects, the incompatibility of pure propositional complements with verbs that contain aspe...

This paper continues the development of complete fragments of natural language by adding a noun-level complement operator to the basic syllogistic language of All X are Y and Some X are Y : in the fragment of this paper we can also say, for example, Some non-X are Y . We axiomatize this logic of this fragment in two ways: in a direct fashion, allowing the inference of an arbitrary sentence from...

By a regular tessellation, we mean any hyperbolic 3-manifold tessellated by ideal Platonic solids such that the symmetry group acts transitively on oriented flags. A regular tessellation has an invariant we call the cusp modulus. For small cusp modulus, we classify all regular tessellations. For large cusp modulus, we prove that a regular tessellations has to be infinite volume if its fundament...

We study spaces obtained from a complete finite volume complex hyperbolic n-manifold M by removing a compact totally geodesic complex (n−1)-submanifold S . The main result is that the fundamental group of M \S is relatively hyperbolic, relative to fundamental groups of the ends of M \S , and M \S admits a complete finite volume A -regular Riemannian metric of negative sectional curvature. It fo...

We discuss two constructions (long scrambling and ECM verbs) which challenge most syntactic theories (including traditional TAG approaches) since they seem to require exceptional mechanisms and postulates. We argue that these constructions should in fact be analyzed in a similar manner, namely as involving a verb which selects for a " defective " complement. These complements are defective in t...

In this paper we study a number of problems in the context of rational representations of behaviors. In that context, a given proper real rational matrix can represent three behaviors. In the first place it can represent an input-output behavior. Secondly it can represent the kernel behavior of the rational ’differential operator’ associated with the rational matrix. Thirdly, it can represent t...