Discovering a new class of languages
Sean A. Fulop · 2003
This paper outlines a new approach to specifying formal constraints on grammars and their languages, in pursuit of more far-reaching statements about possible human languages than, e.g., "they are context-free." We propose that possible human languages, conceived as term-labeled tree languages consisting of syntactic word trees annotated by semantic lambda terms, can be said to be syntactically homogeneous and finitely illustratable. These are new properties of term-labeled tree languages which, when used to specify a subset of all languages generated by a large class of multimodal type-logical grammars, yield a new class of languages which cross-cuts the traditional Chomsky hierarchy. A discovery procedure for type-logical lexicons is then outlined, whose range is proven to generate precisely these languages. Our new approach is actually quite old, having roots in ideas of the American Structuralist school.