Cumulative markedness effects and (non-)linearity in phonotactics

Abstract

This study uses an Artificial Grammar Learning experiment to test for a synchronic relationship between the severity of an individual phonotactic violation and the linearity of its cumulative interaction with other violations, prompted by previous experimental findings (Albright 2012, Breiss (submitted)). We find that as individual phonotactic patterns are made more exceptionful, their interaction moves from linear to super-linear, and argue that this provides evidence for a non-linear relationship between Harmony and probability. We evaluate five contemporary phonological frameworks using this data, and find that those which incorporate such a non-linear relationship -- Maximum Entropy HG and Noisy HG -- are able to capture the super-linear patterns observed significantly better than other frameworks. Further, we demonstrate that a MaxEnt model provided the same training data as experimental participants exhibits similar emergent super-linear cumulativity, and explore the weighting conditions under which MaxEnt models yield sub-linear, linear, and super-linear cumulativity.

A MaxEnt learner for super-additive counting cumulativity

“…Linearity and additivity have both been used in the literature, to refer to types of cumulativity in constraint interaction. According to Breiss & Albright (2022), these terms regard the relationship between the actual probability of doubly-marked structures and the predicted probability of those that is computed by multiplying probabilities of two separate singly-marked structures.…”

“…It was reported that the mere addition of constraint weights often cannot capture the cumulative effect correctly because forms with two marked structures occur even less in natural languages than what grammar predicts by multiplying the probabilities of two separate forms with one marked structure each (Albright 2012;Shih 2017;Breiss & Albright 2022). For example, Albright (2012) showed that some combinations of relatively marked structures are strongly underattested in both Lakhota and English.…”

“…the addition of the conjoined constraint significantly improves the grammar's fit when modeling quantitative natural language patterns. Breiss & Albright (2022), through a series of artificial language experiments, investigated the relationship between the strength of an individual restriction and how it gangs up with other violations. They found that violations are more likely to super-gang up with each other if individual restrictions are weaker, or in other words, have more exceptions.…”

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Whereas most previous studies on (super-)gang effects examined cases where two weaker constraints jointly beat another stronger constraint (Albright 2012;Shih 2017;Breiss & Albright 2022), this paper addresses gang effects that arise from multiple violations of a single constraint, which Jäger & Rosenbach (2006) referred to as counting cumulativity. The super-additive version of counting cumulativity is the focus of this paper; cases where multiple violations of a weaker constraint not only overpower a single violation of a stronger constraint, but also surpass the mere multiplication of the severity of its single violation.

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Rendaku is not blocked by two nasal consonants: A reply to Kim (2022)

“…( In a recent paper, Kim (2022) has proposed a novel generalization about Rendaku: the presence of two nasal consonants in E2-but not that of one nasal consonant-probabilistically lowers the applicability of Rendaku. If this claim is true, it implys that two segments can "gang-up" to block a phonological process, a case which Kim (2022) refers to as "super-additive counting cumulativity" (in addition to Kim 2022, see also Breiss 2020, Breiss & Albright 2022, Jäger & Rosenbach 2006and Kawahara & Breiss 2021 on general discussion on the issues surrounding cumulativity and additivity). In order to account for this pattern, Kim (2022) proposes a modification to MaxEnt Harmonic Grammar (e.g.…”