Nonmonotonic and Paraconsistent Reasoning: From Basic Entailments to Plausible Relations

In this paper we develop frameworks for logical systems which are able to re ect not only nonmonotonic patterns of reasoning, but also paraconsistent reasoning. For this we consider a sequence of generalizations of the pioneering works of Gabbay, Kraus, Lehmann, Magidor and Makinson. Our sequence of frameworks culminates in what we call plausible, nonmonotonic, multiple-conclusion consequence relations (which are based on a given monotonic one). Our study yields intuitive justi cations for conditions that have been proposed in previous frameworks, and also clari es the connections among some of these systems. In addition, we present a general method for constructing plausible nonmonotonic relations. This method is based on a multiple-valued semantics, and on Shoham's idea of preferential models.

• Type: Conference
• Year: 1999
• Where: ECSQARU
• Authors: Ofer Arieli, Arnon Avron
• Keywords: Automated Reasoning, ECSQARU 1999, Multiple-conclusion Consequence Relations, Nonmonotonic Patterns, Plausible Nonmonotonic Relations