Inherently Weighted Constraints Gašper Beguš Harvard University begus@fas.harvard.edu AMP 2016 University of Southern California Oct 22-24, 2016 Outline Discussion of phonological typology yields two main proposals: the analytic bias (AB) and channel bias (CB) approach (Moreton 2008). his paper introduces a new constraint interaction architecture, Inherently Weighted Constraints (IWC), which models both the inluences of AB and CB and provides grounds for disambiguating the two. At the same time, the IWC model is shown to solve several long-standing problems within the OT approach: derivation of unnatural processes and Too Many / Too Few Solutions problem. Introduction A new division of naturalness ▶ Natural: phonetically motivated ▶ Unmotivated: lack phonetic motivations ▶ Unnatural: operate against universal phonetic tendencies Post-nasal devoicing (Hyman 2001, Solé et al. 2010, Coetzee and Pretorius 2010) Sh. /χʊ-m-bɔ ́ n-á/ → [χʊmpɔ ́ ná] /χʊ-m-dʊʒ-a/ → [χʊntʊʒa] Gradient phonotactic restrictions ▶ Inter-vocalic devoicing (Burkhardt 2014) ▶ Post-nasal devoicing/post-consonantal voicing (Adelaar 1977, Nazarov 2008) Problem in OT: overgeneration and undergeneration Undergeneration: unnatural processes predicted impossible if we admit only phonetically grounded constraints into Cॵॴ Overgeneration: Too Many / Too Few Solutions problem (Steriade 2001) uestion : What factors inluence phonological typology? AB or CB? (Moreton 2008) Historical probabilities A new model for explaining unnatural phenomena: २lॻॸॸ९ॴ७ ॶॸॵ३५ॹॹ a. A set of segments enters complementary distribution b. A sound change occurs that operates on the changed/unchanged subset of those segments c. Another sound change occurs that blurs the original complementary distribution Two trajectories that yield unnatural processes (all sound changes in the blurring process are natural, trajectories atested) २lॻॸॸ९ॴ७ ३y३l५ B > C/Z B > A C > B २lॻॸॸ९ॴ७ ३८१९ॴ B > C/X C > D D > A Minimal Sound Change Requirement (MSCR) Minimally three sound changes have to operate in combination for an unnatural process to arise. Minimally two sound changes have to operate in combination for an unmotivated process to arise. How do we get the unnatural B > A / X? With one single natural sound change, it is impossible, because B > A / X is by deinition unnatural. However, B > A / X is also impossible with two natural sound changes. Why? We know that A and B difer in one feature only. For a B > A / X sound change to arise, therefore, we irst need B to change into something other than A (it cannot change to A directly because such sound change is unnatural). So, let B change to C, where B and C difer in one feature, but a diferent feature from the one that separates A and B. From this point, it is still impossible for an unnatural sound change to arise without a third sound change: C cannot develop directly to A, since the two segments difer in two features: feature F1, which distinguishes A and B, and feature F2, which distinguishes B and C. By deinition, two sound changes are required in order to change two features; hence it follows that at least three sound changes must take place in order for an unnatural process to arise. MSCR translates directly into typology: processes that require more sound changes will be less frequent We can calculate historical probabilities of processes (Fussell et al. 1976, Eid 2011) P(T 1 )= ∫ t 0 f 1 t 1 dt 1 × ∫ t t 1 f 2 t 2 dt 2 × ∫ t t 2 f 3 t 3 dt 3 × ... × ∫ t t n−1 f n t n dt n where f i = λ i e −λ i t Or P(T 1 )= P(A 1 )P(A 2 )...P(A n ) n! Historical probability of a process equals the probability of all possible trajectories that lead to it P(Alt)= P(T 1 ∪ T 2 ∪ T 3 ∪ ... ∪ T n ) Unrestricted Cॵॴ Unmotivated markedness constraints already in Cॵॴ All constraints should be admited to Cॵॴ regardless of phonetic substance Without the unnatural *ND, we cannot derive post-nasal devoicing in Tswana and Shekgalagari /nd/ *ND *I४५ॴॺ-IO(voi) a. [nd] *! ☞ b. [nt] * Unnatural gradient phonotactics impossible to derive without unnatural constraints. Harmony (in HG) can be transformed to percentages, but given richness of the base, we cannot derive a system in which the unnatural element is more frequent a) w(I४५ॴॺ-IO(voi)) > w(*T#): P([T#]) = P([D#]) = .5 b) w(*T#) > w(I४५ॴॺ-IO(voi)): P([T#]) > P([D#]) Problem: unrestricted Cॵॴ has no predictive power Analytic bias Learning afects typology Structurally complex alternations are more difuclt to learn For equally complex alternations, opposing results reported (Moreton and Pater 2012) Wilson (2006), Do and Albright (2016) report signiicant diferences in learnability when structural complexity is controlled for Both AB and CB afect typology (Moreton 2008) Most model still exclude one of the two: no proposals that would model both A New Proposal All constraints into Cॵॴ But we have to encode that some processes are rare or non-existent A new proposal: Iॴ८५ॸ५ॴॺly W५९७८ॺ५४ Cॵॴॹॺॸ१९ॴॺॹ Constraints have Inherent Weights: weighted on a scale with means ( μ ) and variance (σ 2 ) he model crucially difers from that of Boersma and Hayes (2001), Wilson (2006), White (2013): IWC is a formal model of typology, modeling both AB and CB Inherently Weighted Constraints -2 0 2 4 0.0 0.1 0.2 0.3 0.4 Max IdIO(nas) IdIO(voi) *NT *D# Generates unnatural processes, but encodes that they are rare. Also, a solution to Too Many / Too Few Solutions problem: he probability P(*D# ≫ I४५ॴॺ-IO(voi)) will be considerably greater than P(*D# ≫ I४५ॴॺ-IO(nas)), which captures the generalization that devoicing is by far the most common repair strategy for *D#. On the other hand, the diference in probabilities between P(*NT ≫ I४५ॴॺ-IO(voi)) and P(*NT ≫ I४५ॴॺ-IO(nas)) will be smaller due to higher variance of *NT, therefore *NT is predicted to have more repair strategies. IWC Division of Labor Hypothesis Analytical bias determines variance (σ 2 ) of IW, channel bias determines the means ( μ ). When we control for the input data, or in other words, force constraints to have equal mean diferences, we get information about the variance of constraints (learnability or AB) When we examine processes that are equally learnable (tested on the basis of artiicial grammar learning experiments), we get information about the distances in means Compatible with MaxEnt (Wilson 2006 employs variance to encode learning bias) Conclusions he paper proposes a new constraint interaction architecture: IWC. he new model of phonological typology admits both inluences of AB and CB. I propose a new model of typology within the CB: the number of sound changes required and their relative probabilities determine historical probabilities of processes. IWC models both inluences: historical probabilities determine mean diference between constraints, AB determines variance. IWC provides ground for disambiguating the diferent inluences on phonological typology and solves several long-standing problems of the OT/HG family of theoretical models. References Adelaar, W. F. 1977. Tarma uechua: grammar, texts, dictionary. Lisse: he Peter de Ridder Press. • Boersma, P., and Hayes, B. 2001. Empirical tests of the gradual learning algorithm. Linguistic inquiry, 32(1), 45-86. • Burkhardt, Jürgen. 2014. he reconstruction of the phonology of Proto-Berawan. Ph.D. Dissertation, Goethe University Frankfurt. • Coetzee, A. W. and Pretorius, R. 2010. Phonetically grounded phonology and sound change: he case of Tswana labial plosives. JPh, 38(3), 404-421. • Eid, M. 2011. A general analytical solution for the occurrence probability of a sequence of ordered events following Poisson stochastic processes. Reliability: heory & Applications 6(2): 21-32. • Fussell, J., E. Aber, and R. Rahl. 1976. On the quantitative analysis of priority-AND failure logic. 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Learning phonology with substantive bias: An experimental and computational study of velar palatalization. Cog Sci, 30(5), 945-982. * I would like to thank Kevin Ryan for his useful comments. All mistakes are my own. Gašper Beguš (Harvard University | begus@fas.harvard.edu) Inherently Weighted Constraints Annual Meeting on Phonology, University of Southern California, October 23, 2016