Achievement

The new area of *axiomatic linguistics* developed in this IGERT was expanded in scope through a seminar on Axiomatic Cognitive Science. A central focus was formalizing the link between hypotheses about linguistic representations and the results of psycholinguistics experiments. This involved formalizing the notion of representation, representational similarity, the architecture of mental (e.g., psycholinguistic) processes, the probability of various processing results given the representational similarity structure and the regularities of previous experience, the level of activation required to process information, and much more. Theorems were proven about the predictions of representational hypotheses for functional MRI experiments and for errors produced by brain-damaged patients. The seminar also broke new formal ground in the program through a tutorial on random processes, which are relevant to the theoretical work of a number of trainees but inaccessible to them previously.