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Since Boole it is known that probability theory is closely related to logic. According to the axioms of Kolmogorov, probability theory is formulated with a (normalized) probability measure $\mbox …

We denote the category of presheaves on a small category ${\cal C}$ (set-valued functor-category) by $$\widehat{\cal C}:=[{\cal C}^{op},{\bf Set}].$$ Such a category is cartesian closed, i.e. it ha …

The category RefGph of reflexive directed graphs is the functor category $\hat{∆}_1=\mbox{Fun}(∆^◦_1,$Set), where $∆_1$ is the simplex category truncated at level 1. Hence the poset Sub(X) of subob …

We consider the logic of reflexive directed graphs, i.e. the set ${\bf L}_1$ of those propositional formulae $\varphi$ in the variables $p_i$, which are valid in exactly these graphs. It is a proper …

The category RefGph of reflexive directed graphs is the functor category $\hat{∆}_1=\mbox{Fun}(∆^◦_1,$Set), where $∆_1$ is the simplex category truncated at level 1. Hence the poset Sub(X) of subob …