25 Oct 2013, 2pm-4pm, Oak Hall 408
The revision theory is a general theory of circular definitions. We give a brief history and overview of the revision theory. We motivate extending the revision theory with a new unary operator, and show how to modify the basic framework of the revision theory to accommodate it. We provide some examples to show how the extended theory works. A modification of the calculus C_0 from The Revision Theory of Truth is sound and complete with respect to one notion of validity for the revision theory. This permits us to demonstrate how the addition of the operator strengthens the calculus.
There is a stronger notion of validity for which the calculus is merely sound. In the basic revision theory, completeness can be regained by restricting to a certain class of definitions, the finite definitions. These are definitions for which the revision process is, in a sense, over in finitely many steps. In the modified theory, the notion of finiteness needs to be refined, but the new notion retains many of the nice properties of the old one. We sketch how to obtain completeness for definitions that are finite in the new sense.
Time permitting, we will also make connections to a modal logic and sketch a proof of a Solovay-style completeness theorem.
Relevant background material: Gupta and Belnap 1993 “The Revision Theory of Truth”, chapter 4 sections 1-4, chapter 5B