Paris-Nancy Colloquium in Logic and the Philosophy of Mathematics

Kai Wehmeier (UC Irvine)

Titre: Universal Logical Grammar

Résumé : I will present Universal Logical Grammar (ULG), the framework of my ongoing research program, and some results obtained within it. ULG is inspired by Richard Montague’s influential 1970 article “Universal Grammar” (UG) but – unlike Montague’s approach – focuses exclusively on formal-logical languages, thus setting aside, at least for the time being, any ambition to analyze natural languages directly. ULG differs architecturally from UG and its later developments mainly by (a) not requiring interpretations to be compositional and (b) taking syntactic categories to refine, rather than coincide with, the syntactic algebra’s sorts. These architectural innovations make possible substantive new insights regarding the grammatical properties of compositionality and extensionality, and how they are constrained by the consequence relations generated by grammars.