Infinite arguments and semantics of dialectical proof procedures
Phan Minh Thang, Phan Minh Dũng, Jiraporn Pooksook · Argument & Computation · 2021
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.