A valid theory on probabilistic causation

In this paper several definitions of probabilistic causation are considered, and their main drawbacks discussed. Current notions of probabilistic causality have symmetry limitations (e.g. correlation and statistical dependence are symmetric notions). To avoid the symmetry problem, non-reciprocal causality is often defined in terms of dynamic asymmetry. But these notions are likely to consider spurious regularities. In this paper we present a definition of causality that does non have symmetry inconsistences. It is a natural extension of propositional causality in formal logics, and it can be easily analyzed with statistical inference. The modeling problems are also discussed using empirical processes.Causality, Empirical Processes and Classification Theory, 62M30, 62M15, 62G20

Some remarks on locally o-minimal structures (Model theoretic aspects of the notion of independence and dimension)

Locally o-minimal structures are some local adaptation from o-minimal structures. They were treated, e.g. in [1], [2]. We try to characterize types of definably complete locally o-minimal structures. And we argue about the dp-rank of them

Vapnik-Chervonenkis density in some theories without the independence property, I

We recast the problem of calculating Vapnik-Chervonenkis (VC) density into one of counting types, and thereby calculate bounds (often optimal) on the VC density for some weakly o-minimal, weakly quasi-o-minimal, and $P$-minimal theories.Comment: 59