This paper deals with two kinds of fuzzy implications: QL and Dishkant implications. That is, those defined through the expressions $I(x,y)=S\left(N\right(x),T(x,y\left)\right)$ and $I(x,y)=S\left(T\right(N\left(x\right),N\left(y\right)),y)$ respectively, where $T$ is a t-norm, $S$ is a t-conorm and $N$ is a strong negation. Special attention is due to the relation between both kinds of implications. In the continuous case, the study of these implications is focused in some of their properties (mainly the contrapositive symmetry and the exchange principle). Finally, the case of non continuous t-norms...

Some probabilistic inference rules which can be compared with the inference rules of preferential logic are given and it will be shown how they work in graphical models, allowing qualitative plausible reasoning in Bayesian networks.

In this article, using mostly Pervin [9], Kunzi [6], [8], [7], Williams [11] and Bourbaki [3] works, we formalize in Mizar [2] the notions of quasiuniform space, semi-uniform space and locally uniform space. We define the topology induced by a quasi-uniform space. Finally we formalize from the sets of the form ((X Ω) × X) ∪ (X × Ω), the Csaszar-Pervin quasi-uniform space induced by a topological space.