A split-combination approach to merging knowledge bases in possibilistic logic

In this paper, we propose an adaptive approach to merging possibilistic knowledge bases that deploys multiple operators instead of a single operator in the merging process. The merging approach consists of two steps: one is called the splitting step and the other is called the combination step. The splitting step splits each knowledge base into two subbases and then in the second step, different classes of subbases are combined using different operators. Our approach is applied to knowledge bases which are self-consistent and the result of merging is also a consistent knowledge base. Two operators are proposed based on two different splitting methods. Both operators result in a possibilistic knowledge base which contains more information than that obtained by the t-conorm (such as the maximum) based merging methods. In the flat case, one of the operators provides a good alternative to syntax-based merging operators in classical logic.

Interpolation formula between very low and intermediate-to-high damping Kramers escape rates for single-domain ferromagnetic particles

It is shown that the Mel'nikov-Meshkov formalism for bridging the very low damping (VLD) and intermediate-to-high damping (IHD) Kramers escape rates as a function of the dissipation parameter for mechanical particles may be extended to the rotational Brownian motion of magnetic dipole moments of single-domain ferromagnetic particles in nonaxially symmetric potentials of the magnetocrystalline anisotropy so that both regimes of damping, occur. The procedure is illustrated by considering the particular nonaxially symmetric problem of superparamagnetic particles possessing uniaxial anisotropy subject to an external uniform field applied at an angle to the easy axis of magnetization. Here the Mel'nikov-Meshkov treatment is found to be in good agreement with an exact calculation of the smallest eigenvalue of Brown's Fokker-Planck equation, provided the external field is large enough to ensure significant departure from axial symmetry, so that the VLD and IHD formulas for escape rates of magnetic dipoles for nonaxially symmetric potentials are valid.