2007/01/01 by Hans Rott, Rott, Hans
Computer Science · #Bayesian Modeling and Causal Inference #Topic Modeling #AI-based Problem Solving and Planning
paper · doi:10.4230/dagsemproc.07351.22
The idea of two-dimensional belief change operators is that a belief state is transformed by an input sentence A in such a way that A gets accepted with at least the strength or certainty of a sentence B (the reference sentence). The input of such a transformation may alternatively be conceived as `B leq A' [`B less-than-or-equal-to A']. This notation makes explicit that the process induced is basically one of doxastic preference change. The principal case of two-dimensional belief change obtains when B is a prior belief which is more strongly accepted than both A and eg A, but the non-principal cases are interesting in their own right. Various two-dimensional revision operators were studied by Cantwell (1997, `raising' and `lowering'), Fermé and Rott (2003, `revision by comparison'), and Rott (2007, `bounded revision'). Special choices of a fixed input sentence A or a fixed reference sentence B lead to some well-known unary oparators of belief change: `irrevocable' (aka `radical') revision, `severe withdrawal' (aka `mild contraction'), `natural' (aka `conservative') and `lexicographic' (aka `moderate') revision. The talk gives a survey of several variants of two-dimensional belief change and their representations. I argue that two-dimensional belief change operators offer an interesting qualitative model with an expressive power between (all too poor) unary operators and (all too demanding) quantitative models of belief change.