This is a well-developed scholarly website (at Indiana University) devoted to a couple of projects that were also of special importance to Peirce: first, the graphical representation of inference structures and processes, and, second, the thesis that mathematical reasoning and deduction in general involve appeal to the observation of diagrammatic figures ("iconic" representations, in Peirce's terminology) and cannot be reduced to purely symbolic (i.e. rule-governed) transformations. You will want to pay special attention to Jon Barwise and his work in particular, as he is the leading figure in this, but may find it worthwhile to follow out the interests of all of his associates and students as well.
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