On Admissible Consensuses

Abstract

Consensus-finding is a ubiquitous paradigm in both A.I. and everyday life. Recently, a computational approach to consensus-finding has been introduced in the standard clausal Boolean logic framework. It captures non-contradictory fragments of the information conveyed by different agents such that these fragments do not logically conflict with any of the agents. This kind of consensuses concerns open-minded agents: On one side, these agents accept to drop their own information that contradicts other agents. On the other side, they can accept any information from another agent provided that this latter information does not contradict them. In this study, it is shown that a family of consensuses might not actually be endorsed by these open-minded agents, due to the usual ad-hoc logical representation of knowledge and well-known paradoxes linked to material implication. Accordingly, we trim the set of consensuses by filtering out these undesirable consensuses and keep so-called admissible consensuses, only. A computational approach that is based on the SAT technologies and that delivers one maximal admissible consensus is then investigated.