Reasoning Under Inconsistency: The Forgotten Connective
Sébastien Konieczny, Jérôme Lang, Pierre Marquis · 2005
In many frameworks for reasoning under inconsistency, it is implicitly assumed that the formulae from the belief base are connected using a weak form of conjunction. When it is consistent, a belief base B = {ϕ1,..., ϕn}, where the ϕi are propositional formulae, is logically equivalent to the base {ϕ1 ∧... ∧ ϕn}. However, when it is not consistent, both bases typically lead to different conclusions. This illustrates the fact that the comma used in base B has to be considered as an additional, genuine connective, and not as a simple conjunction. In this work we define and investigate a propositional framework with such a “comma connective”. We give it a semantics and show how it generalizes several approaches for reasoning from inconsistent beliefs. 1