Dialectic Reasoning with Inconsistent Information

TL;DR

This paper introduces a framework for handling logical uncertainty in inconsistent databases by defining 'acceptability' classes for arguments, which help assign linguistic qualifiers to propositions based on their confidence levels.

Contribution

It proposes a novel concept of acceptability for arguments in inconsistent databases, enabling the assignment of linguistic qualifiers to express logical uncertainty.

Findings

Acceptability classes can differentiate arguments based on confidence.

Linguistic qualifiers reflect the degree of logical uncertainty.

Framework generalizes to various criteria for argument acceptability.

Abstract

From an inconsistent database non-trivial arguments may be constructed both for a proposition, and for the contrary of that proposition. Therefore, inconsistency in a logical database causes uncertainty about which conclusions to accept. This kind of uncertainty is called logical uncertainty. We define a concept of "acceptability", which induces a means for differentiating arguments. The more acceptable an argument, the more confident we are in it. A specific interest is to use the acceptability classes to assign linguistic qualifiers to propositions, such that the qualifier assigned to a propositions reflects its logical uncertainty. A more general interest is to understand how classes of acceptability can be defined for arguments constructed from an inconsistent database, and how this notion of acceptability can be devised to reflect different criteria. Whilst concentrating on the aspects of assigning linguistic qualifiers to propositions, we also indicate the more general significance of the notion of acceptability.