T-orders in MaxEnt Arto Anttila (Stanford University) and Giorgio - PowerPoint PPT Presentation

T-orders in MaxEnt Arto Anttila (Stanford University) and Giorgio Magri (CNRS) Society for Computation in Linguistics Salt Lake City | January 4-7, 2018 A. Anttila and G. Magri T-orders in MaxEnt SCiL 2018 1 / 48

Introduction A. Anttila and G. Magri T-orders in MaxEnt SCiL 2018 2 / 48

Introduction Formal results 1 Formal results 2 Phonological applications 1 Phonological applications 2 � A good linguistic theory should neither under-generate (does not miss any attested pattern) nor over-generate (does not predict any “unattestable” pattern) A. Anttila and G. Magri T-orders in MaxEnt SCiL 2018 3 / 48

Introduction Formal results 1 Formal results 2 Phonological applications 1 Phonological applications 2 � A good linguistic theory should neither under-generate (does not miss any attested pattern) nor over-generate (does not predict any “unattestable” pattern) � Rich literature argues that Max Entropy (ME) is rich enough to avoid under-generation [Zuraw and Hayes 2017] A. Anttila and G. Magri T-orders in MaxEnt SCiL 2018 3 / 48

Introduction Formal results 1 Formal results 2 Phonological applications 1 Phonological applications 2 � A good linguistic theory should neither under-generate (does not miss any attested pattern) nor over-generate (does not predict any “unattestable” pattern) � Rich literature argues that Max Entropy (ME) is rich enough to avoid under-generation [Zuraw and Hayes 2017] � But does ME over-generate? A. Anttila and G. Magri T-orders in MaxEnt SCiL 2018 3 / 48

Introduction Formal results 1 Formal results 2 Phonological applications 1 Phonological applications 2 � A good linguistic theory should neither under-generate (does not miss any attested pattern) nor over-generate (does not predict any “unattestable” pattern) � Rich literature argues that Max Entropy (ME) is rich enough to avoid under-generation [Zuraw and Hayes 2017] � But does ME over-generate? � Over-generation is “easy” to investigate for categorical theories such as HG: the typology is usually finite and can be exhaustively listed A. Anttila and G. Magri T-orders in MaxEnt SCiL 2018 3 / 48

Introduction Formal results 1 Formal results 2 Phonological applications 1 Phonological applications 2 � A good linguistic theory should neither under-generate (does not miss any attested pattern) nor over-generate (does not predict any “unattestable” pattern) � Rich literature argues that Max Entropy (ME) is rich enough to avoid under-generation [Zuraw and Hayes 2017] � But does ME over-generate? � Over-generation is “easy” to investigate for categorical theories such as HG: the typology is usually finite and can be exhaustively listed � The situation is very different for probabilistic theories such as ME: the typology consists of an infinite number of probability distributions which therefore cannot be exhaustively listed A. Anttila and G. Magri T-orders in MaxEnt SCiL 2018 3 / 48

Introduction Formal results 1 Formal results 2 Phonological applications 1 Phonological applications 2 � A natural way around this problem is to enumerate not the individual grammars/distributions in the typology, but the corresponding set of predicted implicational universals A. Anttila and G. Magri T-orders in MaxEnt SCiL 2018 4 / 48

Introduction Formal results 1 Formal results 2 Phonological applications 1 Phonological applications 2 � A natural way around this problem is to enumerate not the individual grammars/distributions in the typology, but the corresponding set of predicted implicational universals � An implicational universal is an implication [Greenberg 1963] → � P − P which holds whenever every language with property P has property � P A. Anttila and G. Magri T-orders in MaxEnt SCiL 2018 4 / 48

Introduction Formal results 1 Formal results 2 Phonological applications 1 Phonological applications 2 � A natural way around this problem is to enumerate not the individual grammars/distributions in the typology, but the corresponding set of predicted implicational universals � An implicational universal is an implication [Greenberg 1963] → � P − P which holds whenever every language with property P has property � P � The idea is that a phonological theory over-generates provided it generates so many languages/grammars/distributions that implicational universals become very hard to satisfy (they involve universal quantification) A. Anttila and G. Magri T-orders in MaxEnt SCiL 2018 4 / 48

Introduction Formal results 1 Formal results 2 Phonological applications 1 Phonological applications 2 � A natural way around this problem is to enumerate not the individual grammars/distributions in the typology, but the corresponding set of predicted implicational universals � An implicational universal is an implication [Greenberg 1963] → � P − P which holds whenever every language with property P has property � P � The idea is that a phonological theory over-generates provided it generates so many languages/grammars/distributions that implicational universals become very hard to satisfy (they involve universal quantification) � And the phonological theory thus fails to predict many implicational universals that seem like they should hold of natural language phonology A. Anttila and G. Magri T-orders in MaxEnt SCiL 2018 4 / 48

Introduction Formal results 1 Formal results 2 Phonological applications 1 Phonological applications 2 � Consider a typology T of categorical phonological grammars, construed as mappings from URs to SRs A. Anttila and G. Magri T-orders in MaxEnt SCiL 2018 5 / 48

Introduction Formal results 1 Formal results 2 Phonological applications 1 Phonological applications 2 � Consider a typology T of categorical phonological grammars, construed as mappings from URs to SRs � Within this framework, the simplest antecedent property P is the property of mapping a certain UR x to a certain SR y : ( x , y ) A. Anttila and G. Magri T-orders in MaxEnt SCiL 2018 5 / 48

Introduction Formal results 1 Formal results 2 Phonological applications 1 Phonological applications 2 � Consider a typology T of categorical phonological grammars, construed as mappings from URs to SRs � Within this framework, the simplest antecedent property P is the property of mapping a certain UR x to a certain SR y : ( x , y ) � Analogously, the simplest consequent property � P is the property of mapping a certain UR � x to a certain SR � y : ( � x , � y ) A. Anttila and G. Magri T-orders in MaxEnt SCiL 2018 5 / 48

Introduction Formal results 1 Formal results 2 Phonological applications 1 Phonological applications 2 � Consider a typology T of categorical phonological grammars, construed as mappings from URs to SRs � Within this framework, the simplest antecedent property P is the property of mapping a certain UR x to a certain SR y : ( x , y ) � Analogously, the simplest consequent property � P is the property of mapping a certain UR � x to a certain SR � y : ( � x , � y ) � We consider the simplest implicational universal T ( x , y ) → ( � x , � y ) holds provided each grammar in T which maps x to y also maps � x to � y A. Anttila and G. Magri T-orders in MaxEnt SCiL 2018 5 / 48

Introduction Formal results 1 Formal results 2 Phonological applications 1 Phonological applications 2 � Consider a typology T of categorical phonological grammars, construed as mappings from URs to SRs � Within this framework, the simplest antecedent property P is the property of mapping a certain UR x to a certain SR y : ( x , y ) � Analogously, the simplest consequent property � P is the property of mapping a certain UR � x to a certain SR � y : ( � x , � y ) � We consider the simplest implicational universal T ( x , y ) → ( � x , � y ) holds provided each grammar in T which maps x to y also maps � x to � y T → is a partial order called the T-order induced by T [Anttila and Andrus 2006] � A. Anttila and G. Magri T-orders in MaxEnt SCiL 2018 5 / 48

Introduction Formal results 1 Formal results 2 Phonological applications 1 Phonological applications 2 � Consider a typology T of categorical phonological grammars, construed as mappings from URs to SRs � Within this framework, the simplest antecedent property P is the property of mapping a certain UR x to a certain SR y : ( x , y ) � Analogously, the simplest consequent property � P is the property of mapping a certain UR � x to a certain SR � y : ( � x , � y ) � We consider the simplest implicational universal T ( x , y ) → ( � x , � y ) holds provided each grammar in T which maps x to y also maps � x to � y T → is a partial order called the T-order induced by T [Anttila and Andrus 2006] � � For instance, any dialect of English which deletes t / d before V, also does before C: (/ cost.us /, [ cos.us ]) − → (/ cost.me /, [ cos.me ]) A. Anttila and G. Magri T-orders in MaxEnt SCiL 2018 5 / 48

Introduction Formal results 1 Formal results 2 Phonological applications 1 Phonological applications 2 � Implicational universals can also be statistical: variable t / d deletion is more frequent before C than V [Guy 1991; Kiparsky 1993; Coetzee 2004] A. Anttila and G. Magri T-orders in MaxEnt SCiL 2018 6 / 48