Formal theories of mental representation have receded from the importance they had in the early days of cognitive science. I argue that such theories are crucial in any mental domain, not just for their own sake, but to guide experimental inquiry, as well as to integrate the domain into the mind as a whole. To illustrate the criteria of adequacy…

We introduce a computational theory of situated language understanding in which the meaning of words and utterances depends on the physical environment and the goals and plans of communication partners. According to the theory, concepts that ground linguistic meaning are neither internal nor external to language users, but instead span the…

Theories of natural language syntax often characterize grammatical knowledge as a form of abstract computation. This paper argues that such a characterization is correct, and that fundamental properties of grammar can and should be understood in terms of restrictions on the complexity of possible grammatical computation, when defined in terms of…

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…