Gregory M. Kobele

Formalizing Mirror Theory

Mirror theory is a theory of (morpho-) syntax introduced in (Brody, 1997). Here I present a formalization of the theory, and study some of its language theoretic properties.

Evaluating the Complexity of Optimality Theory

Idsardi (2006) claims that Optimality Theory (OT; Prince and Smolensky 1993, 2004) is in general computationally intractable on the basis of a proof adapted from Eisner 1997a. We take issue with this conclusion on two grounds. First, the intractability result holds only in cases where the constraint set is not fixed in advance (contra usual definitions of OT), and second, the result crucially depends on a particular representation of OT grammars. We show that there is an alternative representation of OT grammars that allows for efficient computation of optimal surface forms and provides deeper insight into the sources of complexity of OT. We conclude that it is a mistake to reject OT on the grounds that it is computationally intractable.

Importing montagovian dynamics into minimalism

Minimalist analyses typically treat quantifier scope interactions as being due to movement, thereby bringing constraints thereupon into the purview of the grammar. Here we adapt De Grootes continuation-based presentation of dynamic semantics to minimalist grammars. This allows for a simple and simply typed compositional interpretation scheme for minimalism.

The Learning and Emergence of Mildly Context Sensitive Languages

This paper describes a framework for studies of the adaptive acquisition and evolution of language, with the following components: language learning begins by associating words with cognitively salient representations (“grounding”); the sentences of each language are determined by properties of lexical items, and so only these need to be transmitted by learning; the learnable languages allow multiple agreements, multiple crossing agreements, and reduplication, as mildly context sensitive and human languages do; infinitely many different languages are learnable; many of the learnable languages include infinitely many sentences; in each language, inferential processes can be defined over succinct representations of the derivations themselves; the languages can be extended by innovative responses to communicative demands. Preliminary analytic results and a robotic implementation are described.

Without remnant movement, MGs are context-free

Minimalist grammars offer a formal perspective on a popular linguistic theory, and are comparable in weak generative capacity to other mildly context sensitive formalism. Minimalist grammars allow for the straightforward definition of so-called remnant movement constructions, which have found use in many linguistic analyses. It has been conjectured that the ability to generate this kind of configuration is crucial to the super-context-free expressivity of minimalist grammars. This conjecture is here proven.

Memory Resource Allocation in Top-Down Minimalist Parsing

This paper provides a linking theory between the minimalist grammar formalism and off-line behavioural data. We examine the transient stack states of a top-down parser for Minimalist Grammars as it analyzes embedded sentences in English, Dutch and German. We find that the number of time steps that a derivation tree node persist on the parser’s stack derives the observed contrasts in English center embedding, and the difference between German and Dutch embedding. This particular stack occupancy measure formalizes the leading idea of “memory burden” in a way that links predictive, incremental parsing to specific syntactic analyses.

The Failure of the Strong Pumping Lemma for Multiple Context-Free Languages

Seki et al. (Theor. Comput. Sci. 88(2):191–229, 1991) showed that every m-multiple context-free language L is weakly 2m-iterative in the sense that either L is finite or L contains a subset of the form

Deriving Reconstruction Asymmetries

\{ u_{0} w_{1}^{i} u_{1} \cdots w_{2m}^{i} u_{2m} \mid i \in \mathbb {N}\}

Quantification in German

, where w1⋯w2n≠ε. Whether every m-multiple context-free language L is 2m-iterative, that is to say, whether all but finitely many elements z of L can be written as z=u0w1u1⋯w2mu2m with w1⋯w2m≠ε and

Disentangling notions of specifier impenetrability: late adjunction, islands, and expressive power

\{ u_{0} w_{1}^{i} u_{1} \cdots w_{2m}^{i} u_{2m} \mid i \in \mathbb {N}\} \subseteq L