{'fraction_non_alphanumeric': 0.027777777777777776, 'fraction_numerical': 0.009081196581196582, 'mean_word_length': 5.201986754966887, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
1 On the complexity of natural language

This dissertation makes three main contributions. First, I show how to assign meanings (model-theoretic objects) to sentences in a way that takes advantage of the inductive structure minimalist grammars assign to the sentences they generate. In other words, I show how to associate a compositional semantics with minimalist grammars. To show that this is more than a mathematical exercise, I provide grammar fragments for English and the west african language Yoruba, and show how the developed semantics assigns reasonable truth conditions to the expressions of these fragments. Second, I present a formalization of the recently influential copy theory of movement [Chomsky, 1995, Nunes, 2004], and show that such an extension to the minimalist grammar formalism does not increase its expressive power too much (i.e. all languages definable by minimalist grammars with copying are parallel multiple context-free languages (PMCFLs [Seki et al., 1991]), and are thus strictly contained in P, the languages recognizable in polynomial time on a deterministic turing machine). Finally, using original data elicited from a native speaker of Yoruba, I argue that natural languages, regardless of the syntactic theory one uses to describe them, require more in the way of abstract computational resources for their description than standardly assumed [Joshi, 1985]. Thus I motivate the increase in expressive power obtained by adding copying to minimalist grammars, by arguing that no grammar formalism without the ability to describe languages like {a n : n ∈ N} (a language generable by minimalist grammars with copying but not without) is empirically adequate. This final contribution is the most significant, telling us the most about the phenomenon of natural language. For this reason, I focus solely upon it in the space remaining.