Saturday, April 19, 2008

Visualizing accessibility

In Kripke frames, the accessibility relation can be represented nicely in a diagram. For S4, the accessibility relations form nice trees. For S5 the accessibility relation is still easily diagrammed. This is one of the nice things about working with Kripke frames.

Recently I've been studying Routley-Meyer frames for relevance logic a bit. These are frames with a three place accessibility relation. (Actually, I am coming at these via Dunn's generalization of them, gaggles.) I sort of have an idea of what the relation is, but this understanding is based primarily on thinking about through the Routley-Meyer semantic clause for evaluating the relevance logic conditional. I wasn't able to come up with a nice way of diagramming these frames and Dunn's book didn't have any either. Are there any nice diagrammatic representations of the ternary accessibility relations?

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