Consequence Relations

Abstract

In this chapter we will describe the formalism of consequence relations that will serve as a logical basis for our approach to nonmonotonic reasoning and belief change. We are not intending, however, to give a comprehensive theory of consequence relations. Rather, the following exposition can be seen as a compendium of notions and results that will be used in what follows. In fact, due to this biased description, a lot of the notions described below, such as semi-classicality, groundedness and base-generation, will be quite new and unusual in a general theory of consequence relations. We will show, in particular, that Scott consequence relations is a powerful formalism that allows a concise logical description of many interesting concepts outside their traditional range of applications. Actually, the results of this chapter will also show that common descriptions of consequence relations still only scratch the surface of this notion. And subsequent applications will demonstrate that it is worth being studied in depth.