Well-Nestedness Properly Subsumes Strict Derivational Minimalism

Abstract

Minimalist grammars (MGs) constitute a mildly contextsensitive formalism when being equipped with a particular locality condition (LC), the shortest move condition. In this format MGs define the same class of derivable string languages as multiple context-free grammars (MCFGs). Adding another LC to MGs, the specifier island condition (SPIC), results in a proper subclass of derivable languages. It is rather straightforward to see this class is embedded within the class of languages derivable by some well-nested MCFG (MCFGwn). In this paper we show that the embedding is even proper. We partially do so adapting the methods used in [13] to characterize the separation of MCFGwnlanguages from MCFG-languages by means of a "simple copying" theorem. The separation of strict derivational minimalism from well-nested MCFGs is then characterized by means of a "simple reverse copying" theorem. Since for MGs, well-nestedness seems to be a rather ad hoc restriction, whereas for MCFGs, this holds regarding the SPIC, our result may suggest we are concerned here with a structural difference between MGs and MCFGs which cannot immediately be overcome in a non-stipulated manner. This work has essentially been carried out within the joint research project "Open Problems on Multiple Context-Free Grammars" funded by the

Distributional Learning of Context-Free and Multiple Context-Free Grammars

“…First, note that the strings themselves are enough to infer the "movement" structure but only when there is a fairly explicit clue in at least some of the strings that exhibit this structure. Secondly, wellnestedness (Kuhlmann and Möhl, 2007;Kanazawa et al, 2011) seems to make things a lot simpler; this tends to support Kanazawa et al (2011)'s arguments for well-nestedness as a condition on mildly contextsensitive language formalisms to go with the parsing e ciency arguments (Gómez-Rodríguez et al, 2010) and the corpus based arguments of, among others, Kuhlmann and Nivre (2006). Note that for example MIX (Kanazawa and Salvati, 2012) is not in the class of languages defined; the strong learning classes are much more restricted in linguistically significant ways that the weak learning algorithms considered in Hao (2019).…”

“…If we restrict the functions to these sets then we define a normal form for the class of well-nested MCFGs of dimension 2; in the sense that for every language generated by a well-nested MCFG of dimension 2, there is a grammar in this class that generates the same language, that uses only productions with functions in these sets, as can be demonstrated using standard techniques (e.g. Kanazawa et al (2011)), adapted from the standard approaches for converting CFGs into Chomsky normal form. Indeed although we allow in this paper productions of rank greater than 2, restricting productions to those of rank 2 does not change the set of languages generated as these well-nested grammars can be binarised.…”

“…For example if we have the string aabb, then we know that there must be two occurrences of the anchoring production in any derivation of this string but we don't know which pairs of a and b "match". We will state this problem more formally in section 3, but what is necessary is some way of restricting the distribution of the substring in some way, and we will present a method that works with well-nested MCFGs (Kanazawa et al, 2011), Moreover the additional power of the formalism introduces new sorts of structural indeterminacy of the derivation trees which need to be handled carefully. This is the first strong learning algorithm for these sorts of grammars and the goal of this paper is not to provide a complete solution to the problem but rather to identify the key di culties and get an understanding of some of the ways in which these di culties can be overcome.…”

Two Models of Minimalist, Incremental Syntactic Analysis

“…MG[+SpIC] and variants have been studied in a series of papers (Gärtner & Michaelis, ; Kanazawa, Michaelis, Salvati, & Yoshinaka, ; Kobele & Michaelis, ; Michaelis, ; Michaelis, ; Stabler, ). Recently, Kobele and Michaelis () show that blocking extraction from specifiers formed by merge reduces expressive power, while prohibiting only extractions from inside specifiers formed by move does not.…”

Chapter 5. Combinatory Categorial Grammar

“…Salvati suggests that the languages characterized by the well-nested subset of MCFG, MCFG WN might formally correspond to the set of MCS languages, and shows that TAG is weakly in MCFG WN , while Kanazawa and Salvati (2012) show that MIX is not in MCFL WN . However, the MCFGs to which Stabler's MG corresponds are known to be non-well-nested (Boston et al, 2010), (although Kanazawa et al, 2011 show that the addition of a further Specifier Island Contraint to MG restricts them to a subset of MCFG WN ).…”