The Logic and Metaphysics Workshop will meet on February 4th from 4:15-6:15 in room 7314 of the CUNY Graduate Center for a talk by Melvin Fitting (CUNY).
Title: Bilattices and Strict Tolerant Logics
Abstract: Strict/tolerant logic is a formally defined logic that has the same consequence relation as classical logic, though it differs from classical logic at the metaconsequence level. Specifically, it does not satisfy a cut rule. It has been recommended for use in work on theories of truth because it avoids some objectionable features arising from the use of classical logic. Here we are not interested in applications, but in the formal details themselves. We show that a wide range of logics have strict/tolerant counterparts, with the same consequence relations but differing at the metaconsequence level. Among these logics are Kleene’s K3, Priest’s LP, and first degree entailment, FDE. The primary tool we use is the bilattice. But it is more than a tool, it seems to be the natural home for this kind of investigation.