Quantum logics representable as kernels of measures

Lean Kernels in Description Logics

Lean kernels (LKs) are an effective optimization for deriving the causes of unsatisfiability of a propositional formula. Interestingly, no analogous notion exists for explaining consequences of description logic (DL) ontologies. We introduce LKs for DLs using a general notion of consequence-based methods, and provide an algorithm for computing them which incurs in only a linear time overhead. A...

Semigroup Kernels on Measures

We present a family of positive definite kernels on measures, characterized by the fact that the value of the kernel between two measures is a function of their sum. These kernels can be used to derive kernels on structured objects, such as images and texts, by representing these objects as sets of components, such as pixels or words, or more generally as measures on the space of components. Se...

Learning with Kernels in Description Logics

We tackle the problem of statistical learning in the standard knowledge base representations for the Semantic Web which are ultimately expressed in description Logics. Specifically, in our method a kernel functions for the ALCN logic integrates with a support vector machine which enables the usage of statistical learning with reference representations. Experiments where performed in which kerne...

Optimal measures and transition kernels

Probability Measures with Big Kernels

It is shown that in an infinite-dimensional dually separated second category topological vector space X there does not exist a probability measure μ for which the kernel coincides with X. Moreover, we show that in “good” cases the kernel has the full measure if and only if it is finitedimensional. Also, the problem posed by S. Chevet [5, p. 69] is solved by proving that the annihilator of the k...