Modellings for Belief Change: Base Contraction, Multiple Contraction, and Epistemic Entrenchment

1 . I n t r o d u c t i o n 1.1. R e p r e s e n t a t i o n o f b e l i e f s Our mode l of bel ief will be a s imple one. A belief is r ep resen ted by a sentence in some ( reg imented) language. Research done in Art i f ic ial Inte l l igence has recen t ly l ead to a revival of the logic of belief. I t was felt t h a t a c lear d i s t inc t ion should be d rawn be tween the explicit and the implicit beliefs of a reasoner [14, 18]. The former ones are those t h a t the reasoner would assent to if asked and for which he has some k ind of i n d e p e n d e n t war ran t . The l a t t e r ones are those t h a t follow, by some specif ied logic, from the set of expl ic i t beliefs. We d i s t ingu i sh a belief base, the set of expl ic i t beliefs, f rom a belief set. A bel ief set is closed unde r logical consequences, i t is a theory in t he logic ian ' s sense. In general , we conceive of bel ief sets as gene ra t ed by bel ief bases. Let us say t h a t H is a belief base for the belief set K if and only if K is the set of all logical consequences of H , i.e., if K = Cn(H). We mus t make a decision wha t to count as a belief state. A bel ief s t a t e is t h a t k ind of th ing , p re theo re t i ca l ly unde r s tood , t h a t is changed when we change our beliefs. As we canno t read off from a bel ief set K which beliefs in it are t he expl ic i t ones, a bel ief s t a t e canno t be ju s t a bel ief set. Should we then say t h a t a bel ief s t a t e is mode l l ed by a bel ief base H ? Of course, we t hen have no p rob l e m in gene ra t ing the full be l ief set, p rov ided we have fixed an a p p r o p r i a t e logic Cn. So eve ry th ing