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Logics of Phonological Reasoning

Graf, Thomas

Abstract Inspired by Kracht (2003) and Potts and Pullum (2002), who use tools from mathematical logic in their investigation of phonological theories, I develop an extendable modal logic over string structures, which in turn is used to formalize a specific phonological theory, Government Phonology. Building on this logical foundation, I compare Government Phonology to SPE and arrive at the surprising result that Government Phonology corresponds to a very weak fragment of SPE yet can attain the latter’s full expressivity by extending the power of feature spreading. I then exhibit two attested phonological phenomena that require moving beyond the power of standard Government Phonology: n-retroflexion in Sanskrit and primary stress assignment in Creek and Cairene Arabic. I further identify several other axes along which Government Phonology can be generalized, moving us towards a parametric metatheory of phonology.

These results are of interest to linguists as they (i) establish a lower bound on the power every descriptively adequate phonological theory has to make available, (ii) tell us how this power can be measured in a precise way, and (iii) show how different phonological proposals are related to each other, thus complementing the well-established empirical methods of theory comparison. Computational phonologists, on the other hand, will appreciate the explicit formalization of a subregular theory of phonology and the (implicit) demonstration that the majority of empirical phenomena does not need full finite-state expressivity.

Most of the results reported herein can also be found in a series of papers of mine from 2010. This thesis, however, vastly exceeds them in terms of clarity, exhaustiveness and preciseness, thanks to the lack of page restrictions.

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@MastersThesis{Graf10Thesis,
  author    = {Graf, Thomas},
  title     = {Logics of Phonological Reasoning},
  year      = {2010},
  school    = {University of California, Los Angeles},
  url       = {http://thomasgraf.net/doc/papers/LogicsOfPhonologicalReasoning.pdf}
}

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