Generic "X" valuation adjustment.
A key outcome of this work is that the presentation of our risk capital valuation methodology is sufficiently generalized for application to a wide variety of engineering projects.
We give a complete description of the spaces of continuous and generalized translation- and SO+(p,q -invariant valuations,q -invariantg Hadwiger's classification of Euclidean isometry-invaluationsluations.
In contrast, the situation where the inputs depend on the past history of the processes is harder to address, since a global valuation problem requires to study a generalized BSDE with non-anticipative functionals.
By employing the idea of generalized truth value functions, one can obtain a hierarchy of valuation systems starting with a certain set-theoretic representation of the valuation system for classical logic.
(This is the so-called local (generalized) consequence relation; for the global variant, use valuations vM with vM = T iff for all points x in the model, M⊨x φ.) There is an obvious further adaptation of these definitions if one wants a formulation in terms of determination by ("soundness and completeness with respect to") a class of frames rather than models.
Every (generalized) consequence relation is determined by a class of valuations.
In contrast, this property will typically fail to hold when a valuation problem is global, so that (64) becomes a generalized BSDE.
In this paper we prove the generalized Hyers-Ulam stability of the system defining general Euler-Lagrange quadratic mappings in non-Archimedean fuzzy normed spaces over a field with valuation using the direct and the fixed point methods.
If one continues the construction and applies the idea of generalized truth value functions to Belnap's four truth values, then one obtains further valuation systems which can be represented by various multilattices.
Likewise, in the Kripke-semantical case, any model M and point x therein gives rise to the valuation vMx defined by vMx = T iff M⊨x φ, and the (generalized) consequence relation determined by a class of models is that determined by all such vMx with M in the class.
