### A completeness theorem for two-parameter stochastic processes

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This paper has three parts. First, we study and characterize amenable and extremely amenable topological semigroups in terms of invariant measures using integral logic. We prove definability of some properties of a topological semigroup such as amenability and the fixed point on compacta property. Second, we define types and develop local stability in the framework of integral logic. For a stable formula ϕ, we prove definability of all complete ϕ-types over models and deduce from this the fundamental...

Logic and Probability, as theories, have been developed quite independently and, with a few exceptions (like Boole's), have largely ignored each other. And nevertheless they share a lot of similarities, as well a considerable common ground. The exploration of the shared concepts and their mathematical treatment and unification is here attempted following the lead of illustrious researchers (Reichenbach, Carnap, Popper, Gaifman, Scott & Krauss, Fenstad, Miller, David Lewis, Stalnaker, Hintikka...

A degree of probabilistic dependence is introduced in the classical logic using the Frank family of $t$-norms known from fuzzy logics. In the quantum logic a degree of quantum dependence is added corresponding to the level of noncompatibility. Further, in the case of the fuzzy logic with $P$-states, (resp. $T$-states) the consideration turned out to be fully analogous to (resp. considerably different from) the classical situation.