Modellings for belief change: Prioritization and entrenchment*

7. Introduction LI, Representation of beliefs OUR MODEL OF belief wil l be a simple one. A belief is represented by a sentence in some (regimented) language. Research done in Art if icial Intelligence has recently lead to a revival of the logic of belief. It was felt that a clear distinction should be drawn between the explicit and the implicit beliefs of a reasoner [15, 19]. The former ones are those that the reasoner would assent to i f asked and for which he has some kind of independent warrant. The latter ones are those that follow, by some specified logic, from the set of explicit beliefs. We distinguish a belief base, the set of explicit beliefs, from a belief set. A belief set is closed under logical consequences, it is a theory in the logician's sense. In general, we conceive of belief sets as generated by belief bases. Let us say that H is a belief base for the belief set K if and only i f K is the set of all logical consequences o f / / , i.e., i f K= Cn{H). We must make a decision what to count as a belief state. A belief state is that kind of thing, pre-theoretically understood, which is changed when we change our beliefs. A s we cannot read off from a belief set K which beliefs in it are the explicit ones, a belief state cannot be just a belief set. Should we say that a belief state is modelled by a belief base HI O f course, we then have no problem in generating the full belief set, provided we have fixed an