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Friday, 5 JanuaryPlenary AddressCalifornia C7:00 – 8:00 PMLanguage Variation and Linguistic InvariantsEdward L. KeenanUniversity of California, Los AngelesI show how to state structural invariants of human language even assuming that grammars of particular languages are structurallydistinct, e.g. have different grammatical categories. Given a grammar G for a set L(G) of expressions, a structure (preserving) map(sm) for G is a bijection from L(G) to L(G) that preserves how expressions are built up. So for h a sm, a rule R derives z from x and yif R derives h(z) from h(x) and h(y). Two expressions have the same structure if one can be mapped to the other by a sm. Aninvariant of G is an expression, a property of expressions, a relation between expressions,...which is mapped to itself (fixed) by allthe sm's. That is, replacing it by anything else changes structure. (To say a sm h fixes a relation R just says xRy if h(x)Rh(y)). Thestructure of G is given by its set of sm's, its symmetry group. Empirically we support that:• The anaphor-antecedent relation is invariant in the languages we have modeled (English, Korean, Toba Batak, and WestGreenlandic). It is (partially) coded by case marking in Korean and voice marking in Toba. Both allow anaphors to asymmetrically c-command their antecedents, structurally distinct from English.• (Provably is a constituent of and c-command, generalized, are invariant relations for all G).• Grammatical formatives, such as case, voice, and applicative affixes, are themselves invariant (fixed by all sm's, notsimply ‘reflections’ of hierarchical structure).• Agreement classes are stable-invariants (fixed by all stable sm's--ones that extend to sm's when new lexical itemsisomorphic to old ones are [iteratively] added to the language). In general, for any category C in a grammar, the property of havingcategory C is a stable invariant.• Theta role assignment is invariant (a function of structure). [This does not imply UTAH, which requires that the functionbe one to one].• Greenberg duality. The class of possible human grammars is closed under word order duals. A G and its dual are notisomorphic but have isomorphic symmetry groups.A Goal of General Linguistics: Classify languages by the symmetry groups of their grammars.Edward L. Keenan is a Distinguished Professor in the Department of Linguistics at UCLA and a member of the American Academyof Arts and Sciences. He has been on faculties in England, Holland, Germany, France, Israel, Madagascar, and New Zealand. He hasco-authored two books: Boolean semantics for natural language, with Leonard Faltz (1985), and Bare grammar: Lectures onlinguistic invariants, with Edward Stabler (2003).67