Rethinking Revision

We sketch a broadening of the Gupta-Belnap notion of a circular or revision theoretic definition into that of a more generalized form incorporating ideas of Kleene’s generalized or higher type recursion . This thereby connects the philosophically motivated, and derived, notion of a circular definition with an older form of definition by recursion using functionals, that is functions of functions, as oracles. We note that Gupta and Belnap’s notion of ‘categorical in L’ can be formulated in at least one of these schemes.