Paraconsistent Logics in Argumentation Systems

Abstract

This thesis is about argumentation theory and the problems that can arise when two contradicting conclusions are obtained during an argument. These conclusions can be taken as premises for falsum from which everything can be derived (in non-paraconsistent logics). This is a problem since for every sentence phi, an argument can be constructed which takes falsum as a premise and concludes with phi.

The instantiation is examined of the ASPIC+ framework with paraconsistent logics for the strict inference rules in order to prevent the system from becoming trivial in case of an inconsistency. For the paraconsistent Da Costa's C omega system, the Logic of Paradox, the logic W and the relevant logic R, it is examined whether the closure and consistency postulates are satis?fied. These postulates impose relevant requirements on any extension of an argumentation framework. It is shown that the ?first two logics do not satisfy these postulates. The relevant logic R is also not applicable since this logic is non monotonic. However, the rationality postulates are satisfied for the logic W . For this, the ASPIC* framework is introduced.

Furthermore, the generation of arguments of which the strict rules are non-minimal can be seen as an efficiency problem. It is investigated whether these unnecessary subarguments can be removed without affecting the conclusions of the extensions. Like for the ASPIC+ framework, the obtained extensions, when conflict-free is defined in terms of defeat or attack free, are compared for minimal ASPIC* frameworks and minimal ASPIC+ frameworks. It turns out that these extensions are the same for both definitions.