Knowledge graph embedding (KGE) aims at learning powerful representations to benefit various artificial intelligence applications. Meanwhile, contrastive has been widely leveraged in as an effective mechanism enhance the discriminative capacity of learned representations. However, complex structures KG make it hard construct appropriate pairs. Only a few attempts have integrated strategies with...

Modal logic interpretations of plausibility and belief measures are developed based on the observation that the inverse of the value assignment function in a model of modal logic induces the upper plausibility and lower belief measures of the plausibility and belief measures induced by the accessibility relation, regarded as a multivalued mapping.

Martin Klazar computed the total weight of ordered trees under 12 different notions of weight. The last and perhaps most interesting of these weights, w12, led to a recurrence relation and an identity for which he requested combinatorial explanations. Here we provide such explanations. To do so, we introduce the notion of a “Klazar violator” vertex in an increasing ordered tree and observe that...

This paper is about counting the number of distinct (scattered) subwords occurring in a given word. More precisely, we consider the generalization of the Pascal triangle to binomial coefficients of words and the sequence (S(n))n≥0 counting the number of positive entries on each row. By introducing a convenient tree structure, we provide a recurrence relation for (S(n))n≥0. This leads to a conne...