Does MaxEnt Overgenerate? Implicational Universals in Maximum Entropy Grammar

Abstract

A good linguistic theory should neither undergenerate (i.e., it should not miss any attested patterns) nor overgenerate (i.e., it should not predict any “unattestable” patterns). We investigate the question of overgeneration in Maximum Entropy Grammar (ME) in the context of basic syllabification (Prince and Smolensky 2004) and obstruent voicing (Lombardi 1999), using the theory’s T-order as a measure of typological strength. We find that ME has non-trivial T-orders, but compared to OT and HG, they are relatively sparse and sometimes linguistically counterintuitive. The fact that many reasonable implicational universals fail under ME suggests that the theory overgenerates, at least in the two phonological examples we examine. More generally, our results serve as a reminder that linguistic theories should be evaluated in terms of both descriptive fit and explanatory depth. A good theory succeeds on both fronts: we want a flexible theory that best fits the data, but we also want an informative theory that excludes unnatural patterns and derives the correct implicational universals.

Equiprobable mappings in weighted constraint grammars

“…Our characterization of ME and SHG equiprobability in sections 4-5 rests on some results from Anttila and Magri (2018;A&M) recalled here.…”

“…The proof of the SHG result is analogous and it is omitted for reasons of space (see the longer version of this paper available on the authors' websites). Our discussion rests on some earlier results on uniform SHG and ME probability inequalities from Anttila and Magri (2018), recalled in Section 3.…”

Paradoxes of MaxEnt markedness

“…In this paper, we have focused on implications of the form (y, y) → ( y, y) that compare the faithful realizations of two phonological forms y and y. Building on Anttila & Magri (2018), we have said that this implication (y, y) → ( y, y) is a universal of a typology of probabilistic phonological grammars provided the probability of the faithful realization of the antecedent form y is never larger than the probability of the faithful realization of the consequent form y and this probability inequality holds uniformly for every single grammar in the typology. The implicational universal (y, y) → ( y, y) thus defined intuitively captures the generalization that the antecedent form y is more marked than the consequent form y.…”

“…To capture such statistical generalizations, Anttila & Magri (2018) say that the implication (x, y) → ( x, y) is a universal of a probabilistic typology provided the probability of the consequent mapping ( x, y) is at least as large as the probability of the antecedent mapping (x, y) and this probability inequality holds UNIFORMLY for any grammar in the typology, as stated in (2). Condition ( 1) is a special case of condition (2), when categorical grammars are construed as probabilistic grammars that assign probabilities equal to zero and one.…”

“…New tools are needed to analyze ME probabilistic typologies-that is, to do probabilistic ME phonology with the same theoretical ambition that has characterized categorical phonology in the past seventy years. Anttila & Magri (2018) introduce UNIFORM PROBABILITY INEQUALITIES as a new tool for probabilistic typological analysis. The idea is to study a typology of probabilistic grammars by characterizing cases where one phonological mapping has a probability smaller than another mapping and this probability inequality holds uniformly for every grammar in the typology.…”