Belief revision by sets of sentences

Evolution of crystal morphologies to equilibrium by surface diffusion with anisotropic surface free energy in three dimensions

“…Here, we use the approach of allowing jumps in the surface orientation across the unstable directions similar to the cases of 1D surface [6,7,20] in the computation. For 1D surfaces the corresponding evolution equation is unstable for certain surface orientations regardless of surface curvature [6,7,20]. As shown in Section 3, the evolution equation for 2D surfaces is less likely to be unstable since the principal directions of surface curvature also play a role in stability.…”

“…There are studies of the evolution of two-dimensional (2D) crystals with one-dimensional (1D) surfaces [6][7][8][9]. Although there are similarities between the cases of 2D and 3D crystals, due to the extra dimension in 3D crystals, there exist phenomena and properties that are not exhibited in models for 2D crystals as we will show.…”

“…Researchers Refs. [6][7][8][9] have studied steady-state (or equilibrium) crystal shapes obtained through surface diffusion with anisotropic surface free energies. These steady state crystal shapes are equilibrium solutions of the evolution equations and called ECS here.…”

Rational evaluation in belief revision

“…In Zhang (1996), Zhang proposed a new kind of multiple contraction called general contraction, denoted by K F. It was renamed as set contraction in Zhang and Foo (2001) by Zhang and Foo to avoid confusion with other multiple contractions. The main difference between set contraction and other contractions is that it does not specify any information to be discarded.…”

Properties of Iterated Multiple Belief Revision

“…Applying logical constraint on the mapping to make it to be an epistemic entrenchment ordering has been also exploited in [17] [18]. However, the ordering we use here should be differentiated from the ways to map possible worlds to ordinals [16] or to map Spohn's system of spheres to ordinals [15] since the underlying ontologies are significantly different even though they might be interconvertible.…”