Language and Logic introductory course:
Syntax and Semantics from an Algebraic Perspective.
Developing perspectives from Keenan and Stabler (2003), this class will explore algebraic methods for compositionally defining and comparing various languages (syntax and semantics), with particular attention to various constructions with quantification and binding in the world's languages.
Introduction: Language structure (!=trees) and universals (!=fixed constituent orders). A universal of anaphor binding.
Evans and Levinson (BBS, forthcoming) take Chomskyan linguistics to task for insufficient recognition of the diversity of human languages. This diversity, they claim, renders universal claims few in number and largely trivial in content, whence the monolithic picture of Universal Grammar that generative grammarians present to the CogSci community at large is inaccurate and misleading. Our response to this critique exhibits a novel format of universal generalization that has the mathematical rigor desired (if not always achieved) by a Chomskyan approach, but which incorporates (morpho)syntactic diversity in an essential way. More important than diversity per se is that languages exhibit non-universal structural regularities that speakers must learn. We illustrate this with universal claims concerning anaphora -- one of the areas in which E+L criticize the Chomskyan approach
Example 1: Affixes and structure in Malagasy, without movement.
Example 2: Quantification in 'minimalist grammar', with movement. A 'directly compositional' semantics for a grammar with 'quantifier raising'.
Language similarity 1: Stable automorphisms; perspectives on probabilistic language models.
Language similarity 2: Homomorphic realizations of canonical patterns of predication, modification, and binding.