Varieties of crossing dependencies: structure dependence and mild context sensitivity

Abstract

Four different kinds of grammars that can define crossing dependencies in human language are compared here: (i) context sensitive rewrite grammars with rules that depend on context, (ii) matching grammars with constraints that filter the generative structure of the language, (iii) copying grammars which can copy structures of unbounded size, and (iv) generating grammars in which crossing dependencies are generated from a finite lexical basis. Context sensitive rewrite grammars are syntactically, semantically and computationally unattractive. Generating grammars have a collection of nice properties that ensure they define only "mildly context sensitive" languages, and Joshi has proposed that human languages have those properties too. But for certain distinctive kinds of crossing dependencies in human languages, copying or matching analyses predominate. Some results relevant to the viability of mildly context sensitive analyses and some open questions are reviewed.

Regular and polyregular theories of reduplication

“…Computational perspectives on reduplication, and copying more generally, have centered around the complexity of the "copy language", which is the set of totally reduplicated strings: {ww | w ∈ Σ*}, which is not a regular language since there is no bound on the reduplicant size (Culy 1985), nor is it a context-free language for the same reason. Instead, more advanced types of acceptors are needed, such as context-sensitive grammars (Seki et al 1991;Albro 2000;Stabler 2004 for those with a goal to better understand natural language -to better understand the different kinds of string-to-string functions and their properties. This paper takes a small step in that direction.…”

Processing of nested and cross-serial dependencies: an automaton perspective on SRN behaviour

“…An example of this is found in Dutch (Huybregts 1976;Bresnan, Kaplan, Peters, and Zaenen 1982): (2) In this case, the first noun phrase ik is semantically dependent on the first verb zag, the second noun phrase Cecilia on the second verb helpen, and so on. Although not as prominent as in Dutch, English also shows constructions that can be taken to involve cross-serial dependencies: in VPellipsis, a verb phrase that is omitted is understood to be an in-order copy of a verb phrase that occurred earlier (Stabler 2004). Such a copying relationship can be represented as a cross-serial dependency.…”

Computationelle Neurolinguistik

“…Die oben genannten Ansätze haben allerdings den Nachteil, dass sie hauptsächlich von kontextfreien Beschreibungen natürlicher Sprache ausgehen (Carstensen et al 2010, Hopcroft & Ullman 1994, während in der theoretischen Linguistik der Nachweis erbracht worden ist, dass natürliche Sprachen zur Klasse der sogenannten gemäßigt kontextsensitiven Sprachen gehören (Shieber 1985, Stabler 2004. Daher werden in jüngerer Zeit mächtigere Grammatik-Formalismen, wie z.…”