A recovery operator for non-transitive theories

PAILOS, FEDERICO MATÍAS

Nueva York

Workshop; Logic and Metaphysics Workshop; 2016

Graduate Center, City University of New York

We will present a way to expand non-transitive theories in order to recover cautious versions of Cut. We will show how to do this for ST in a direct way. We will obtain the logic STcon (ST with a consistency operator), and show that it is non-trivial, and also sound and complete with respect to a disjunctive three-side sequent system called LSCcon. The way to do that with ST+ (ST with a transparent truth predicate) is not that straightforward. In order to accomplish our goal, we need to change the self-referential procedure, from a Strong one to a Weak one. We will shown that the resulting theory, ST*, is not only non-trivial, but sound and complete with respect to the proof system LSC.