SPEAKER: Marc Denecker (K.U.Leuven, Belgium)

TITLE: The Approximation Theory and its Unifying Role in Monmonotonic Reasoning

DATE: Thursday, November 8, 2001, 12:30 p.m. - 1:30 p.m; ASB 9898

ABSTRACT:

We present approximation theory, a fixpoint theory of operators in lattices. This theory extends Tarski's least fixpoint theory of monotone operators to the general case of nonmonotone operators. The theory classifies a rich class of fixpoints including Kripke Kleene fixpoints, stable and well-founded fixpoints. Applied on three major nonmonotonic logics, default logic, autoepistemic logic and logic programming, approximation theory describes all the major 2-, 3- and 4-valued semantics that have been proposed for these logics. We will discuss the intuitive meaning of approximation theory, and the differences and equivalences that it establishes between the three logics.