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- Empirically based investigations of type-logical categorial
grammar (TLCG) using a combined Abstract Categorial Grammar/Lambek
calculus foundation with independent λ-calculi for both
prosodic and semantic proof terms and an innovative hybrid
implicational logic (Kubota & Levine 2012; 2013a,b; 2015, 2016a,b;
2017a; in press). We present an application of this hybrid logic to
yield a simple analysis of Gapping as like-category coordination
(Kubota & Levine 2016a), as part of a full-scale unitary treatment
of all major 'non-constituent' coordination phenomena (Kubota &
Levine 2015); other work on the syntax/semantics interface carried
out in our research program appears in Kubota & Levine 2016a,b;
2017a; in press.
- Development of a wide-ranging approach to ellipsis phenomena
employing Hybrid TLCG along the lines of Kubota & Levine 2017a; in press, and
its interaction with the syntax and semantics of extraction.
- Exploration of the role of proof-theoretic semantics, in
particular, Dependent Type Semantics along the lines of Ranta and
Bekki, in providing an empirically adequate formal framework for the
interpretive component of type-logical proof terms; Kubota & Levine
2017b and Kubota, Minishima, Bekki and Levine 2019b illustrate the
application of a particular dependent type formalism to the
notorious 'Geach scope parallelism' problem posed by Right Node
Raising (and other coordination phenomena).
- Syntactic conditions on polarity item distribution; ramifications
of the apparently anomalous entanglement of NPI and auxiliary
properties in the distribution of modal *need*, described in Levine
2013a, and extension of the polarity behavior of *need* (and, more
weakly, *dare*) to the full range of modal auxiliaries as the basis
for a principled account of their scopal interaction with negation
(Kubota and Levine 2019a).
- Fundamental issues in grammatical theory; formal foundations and
well-foundedness of hybrid type logics incorporating both Lambek
and λ-implicational connectives and the possible embedding of
such logics in first-order linear logic with only a single mode of linear
implication, by means of a rich phenoterm subtyping, as per ongoing
work by Chris Worth and Jordan Needle.