Four different kinds of grammars that can define crossing dependencies in human language are compared here: (1) "context sensitive rewrite" grammars with rules that depend on context; (2) "matching" grammars with constraints that filter the generative structure of the language; (3) "copying" grammars which can copy structures of unbounded size;…

We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. We show that although these sentences are known to have a diagrammatic expression (in the form of the Gergonne…