Abstract
We present a method for exploring the typologies predicted by Subregular Phonology, in which languages are characterized solely by their computational properties. We refer to our method as the derangement method. The term partial derangement is the combinatorics equivalent of permutation: it is a bijective map where each element of a set is mapped to a (possibly different) member of the same set. In essence, the method calculates the partial derangements of an alphabet and, based on the partially deranged alphabets, translates a “seed” grammar into multiple other grammars with the same computational properties. Because Subregular Phonology characterizes grammars solely by their computational properties, it predicts that if the seed grammar (and its generated language) is included in the typology, then all of the new grammars (and their generated languages) are included as well. The number of possible partial derangements of an alphabet of size n is n!, and this sets an upper limit on the number of distinct new languages yielded from any given alphabet and seed language.
We apply the method to the predictions of Strictly Local (SL) grammars with respect to the typology of stress and accent patterns. In particular, we apply the derangement method to seed SL grammars for Maranungku-type (Tryon 1970) and Wergaia-type (Hercus 1986) stress patterns with two-, three-, six-, and twelve-symbol alphabets. The different alphabets allow us to distinguish between different levels of stress and syllable weight. Derangement of the twelve-symbol SL grammar for the Maranungku-type stress pattern reveals 83,160 unique stress patterns. Derangement of the twelve-symbol SL grammar for the Wergaia-type stress pattern reveals 39,916,800 unique patterns. By contrast, the most thorough database of attested stress patterns at present (Heinz 2007, 2009) contains only 109 distinct stress patterns. The phonological characteristics of the predicted patterns are even more striking, exhibiting a wide range of patterns uncharacteristic of stress in general.
Heinz (2018) has argued that restriction to subregular classes of description like SL grammars is more restrictive than other linguistic frameworks such as Optimality Theory. The arguments for greater restrictiveness, however, rest entirely on examples of patterns that are not generated by subregular classes, without careful examination of the range of patterns that are generated by grammars within the subregular classes. The derangement method reveals how vast this range actually is. The range of stress patterns describable with SL grammars is far less restrictive, in both quantity and quality, than the pattern ranges predicted by the major OT accounts (McCarthy and Prince 1993; Gordon 2002; Hyde 2002, 2016; Alber 2005; Martinez-Paricio and Kager 2015).