Infinite arguments and semantics of dialectical proof procedures

Abstract

We study the semantics of dialectical proof procedures. As dialectical proof procedures are in general sound but not complete wrt admissibility semantics, a natural question here is whether we could give a more precise semantical characterization of what they compute. Based on a new notion of infinite arguments representing (possibly infinite) loops, we introduce a stricter notion of admissibility, referred to as strict admissibility, and show that dialectical proof procedures are in general sound and complete wrt strict admissibility.