My PhD thesis Logical Specification of Finite-State Transductions for Natural Language Processing (available from http://www.ling.ohio-state.edu/~nvail/papers) concerns linguistic knowledge representation with finite-state automata. I investigate how automata representing string-to-string mappings (such underlying-to-surface phonological mappings, orthography-to-phonology conversion, partial parsing functions, etc.) can be specified using a logical language. The logic makes the specification easier to reason about and more amenable to rigorous proof. Meanwhile, formulas of the logic can be automatically converted into efficient automata for computing the functions described. The thesis illustrates the application of the technique to the statement of syllable structure constraints, the finite-state replace operator, and the rule formalisms of two-level morphology. Probabilistic versions of the latter two applications are also given. I am continuing to investigate applications of the techniques developed in my thesis, as well as other finite-state approaches, to natural language problems.
My current research applies computational techniques to the study of language variation and change. In particular, I am interested Information-Theoretic approaches to dialectometry and to the investigation of regular sound change vs. lexical diffusion. I have participated in generating funding for this work (see Research Grants above) and applied it to Bulgarian dialect data as part of a dialectometry research project involving the universities of Tübigen, Groningen, and Sofia. I am currently working on applying it to the mainland Germanic Scandinavian languages in collaboration with Charlotte Gooskens of the University of Groningen.
I have also published theoretical work on the syntax of resumptive pronouns, particularly in Modern Hebrew and Irish, as well as on the semantics of plural noun phrases. My primary theoretical interest is in constraint-based grammar, particularly HPSG.