Conditionals and Theory Change: Revisions, Expansions and Additions

Abstract

This paper dwells upon formal models of changes of beliefs, or theories, which are expressed in languages containing a binary conditional connective. After defining the basic concept of a (non-trivial) belief revision model. I present a simple proof of Gärdenfors''s (1986) triviality theorem. I claim that on a proper understanding of this theorem we must give up the thesis that consistent revisions (lsquoadditionsrsquo) are to be equated with logical expansions. If negated or lsquomightrsquo conditionals are interpreted on the basis of lsquoautoepistemic omnisciencersquo, or if autoepistemic modalities (Moore) are admitted, even more severe triviality results ensue. It is argued that additions cannot be philosophically construed as lsquoparasiticrsquo (Levi) on expansions. In conclusion I outline somed logical consequences of the fact that we must not expect lsquomonotonicrsquo revisions in languages including conditionals.