A nice property of the semi naive evaluation of recursive rules is that it does not repeat rule rings in di erent iterations In a recent study W however it was observed that intermediate steps during a rule ring may be repeated in di erent iterations and a notion of the step wise semi naive property and an evaluation with this property were proposed to capture the semi naive prop erty at interm...

Let $\pi$ be a group equipped with an action of second $G$ by automorphisms. We define the equivariant cohomological dimension $\mathsf{cd}\_G(\pi)$, geometric $\mathsf{cat}\_G(\pi)$, and Lusternik–Schnirelmann category $\mathsf{gd}\_G(\pi)$ in terms Bredon dimensions classifying space family subgroups semi-direct product $\pi\rtimes G$ consisting sub-conjugates $G$. When is finite, we extend t...

Pseudo-independent (PI) models are a special class of probabilistic domain model (PDM) where a set of marginally independent domain variables shows collective dependency, a special type of dependency associated with the scope of a set of variables in a probabilistic domain. Due to this property, common probabilistic learning methods based on a single-link lookahead search cannot learn PI models...

Semi-supervised constraint scores, which utilize both pairwise constraints and the local property of the unlabeled data to select features, achieve comparable performance to the supervised feature selection methods. The local property is characterized without considering the pairwise constraints and these two conditions are introduced independently. However, the pairwise constraints and the loc...

We consider a finite set of alternatives A = {a1, a2, . . . , am} evaluated on a family of n criteria F = {g1, g2, . . . , gn}. Let N = {1, 2, . . . , n}. To each criterion gi ∈ F is assigned a positive weight wi. It is supposed wlog that the weights are normalized so that ∑n i=1wi = 1. Let Xi = {gi(a) : a ∈ A} be the set of evaluations of the alternatives on the ith criterion. It is supposed t...

In the context of computational social choice, we study voting methods that assign a set winners to each profile voter preferences. A method satisfies property positive involvement (PI) if for any election in which candidate x would be among winners, adding another who ranks first does not cause lose. Surprisingly, number standard violate this natural property. paper, investigate different ways...

in this paper, we present some inequalities for the co-pi index involving the some topological indices, the number of vertices and edges, and the maximum degree. after that, we give a result for trees. in addition, we give some inequalities for the largest eigenvalue of the co-pi matrix of g.