Geometry

The Mother of All Tableaux - Order, Equivalence, and Geometry in the Large-scale Structure of Optimality Theory - Nazarré Merchant

Nazarré Merchant [+-]
Eckerd College, St Petersburg, Florida
Nazarré Merchant is an associate professor of mathematics at Eckerd College in St. Petersburg, Florida, and has a Ph.D. in linguistics from Rutgers University.
Alan Prince [+-]
Independent Scholar
Alan Prince has worked on prosody, prosodic morphology, cognitive science of language, and Optimality Theory while teaching at several universities in the United States.

Description

We conclude with a discussion of the remarkably well-behaved geometry of OT typologies, which gives a concrete sense to the notion of the Border Point Pair from which the MOAT derives. We show how a typology is represented on the permutohedron, a well-studied figure where each vertex corresponds to a linear order. We then show this representation reduces to the typohedron, a structure in which each vertex represents an entire grammar, leading to a visually accessible representation of the overall structure of a typology. We complete the discussion by offering proofs of several striking results announced by Jason Riggle, showing that when distance is defined between linear orders, grammars are convex regions analogous to disks and balls in the familiar Euclidean world.

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Citation

Merchant, Nazarré; Prince, Alan. Geometry. The Mother of All Tableaux - Order, Equivalence, and Geometry in the Large-scale Structure of Optimality Theory. Equinox eBooks Publishing, United Kingdom. p. Jun 2023. ISBN 9781781798997. https://www.equinoxpub.com/home/view-chapter/?id=38360. Date accessed: 30 Jan 2023 doi: 10.1558/equinox.38360. Jun 2023

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