Conditionals and theory change

revisions, expansions, and additions

Hans Rott

pp. 91-113

in: Synthese 81 (1), 1989.

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 (‘additions’) are to be equated with logical expansions. If negated or ‘might’ conditionals are interpreted on the basis of ‘autoepistemic omniscience’, or if autoepistemic modalities (Moore) are admitted, even more severe triviality results ensue. It is argued that additions cannot be philosophically construed as ‘parasitic’ (Levi) on expansions. In conclusion I outline somed logical consequences of the fact that we must not expect ‘monotonic’ revisions in languages including conditionals.