Syntax-Prosody in Optimality Theory - Theory and Analyses - Jennifer Bellik
2. Counting Tree Parses
Syntax-Prosody in Optimality Theory - Theory and Analyses - Jennifer Bellik
Edward Shingler [+]
SPOT Project, University of California, Santa Cruz
Jennifer Bellik [+]
University of California, Santa Cruz
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Description
A key component of an OT system is the Gen function, which defines the candidate set for that system. In the domain of syntax-prosody mapping, the candidates are pairs. The goal of this chapter is to develop a deeper understanding of how to construct the outputs in syntax-prosody mapping candidate sets, and of how the number of candidates grows with the addition of terminals. To those ends, this chapter describes the options that the SPOT app makes available for defining Gen, and establishes through mathematical reasoning that SPOT’s Gen functions are generating the correct number of candidates for each set of parameter values. We find that the cardinalities of SPOT’s Gen functions are related to: the powers of two, the Fibonacci sequence, and the super-Catalan or Little Schröder numbers, depending on the parameterization selected.