On Gupta-Belnap Revision Theories of Truth, Kripkean fixed points, and the next stable set

On Gupta-Belnap Revision Theories of Truth, Kripkean Fixed Points, and The Next Stable Set.

On revision operators

We look at various notions of a class of definability operations that generalise inductive operations, and are characterised as “revision operations”. More particularly we: (i) characterise the revision theoretically definable subsets of a countable acceptable structure; (ii) show that the categorical truth set of Belnap and Gupta’s theory of truth over arithmetic using fully varied revision se...

How Truth Behaves When There's No Vicious Reference

In The Revision Theory of Truth (MIT Press), Gupta and Belnap (1993) claim as an advantage of their approach to truth “its consequence that truth behaves like an ordinary classical concept under certain conditions— conditions that can roughly be characterized as those in which there is no vicious reference in the language.” To clarify this remark, they define Thomason models, nonpathological mo...

Comparing Fixed-Point and Revision Theories of Truth

In response to the liar’s paradox, Kripke developed the fixed-point semantics for languages expressing their own truth concepts. (Martin and Woodruff independently developed this semantics, but not to the same extent as Kripke.) Kripke’s work suggests a number of related fixed-point theories of truth for such languages. Gupta and Belnap develop their revision theory of truth in contrast to the ...

The Guptα - Belnαp Systems S # and S

Anil Gupta and Nuel Belnap's The Revision Theory of Truth presents revision theoretic systems of circular definitions. Part I of the present paper shows that the revision theories S and S* are not axiomatisable. Part II refines this result. Among other things, Part II shows that there is a strong relationship between revision theories and the theory of inductive definitions. This relationship i...