The powerset operator, P, is compared with other operators of similar type and logical complexity. Namely we examine positive operators whose defining formula has a canonical form containing at most a string of universal quantifiers. We call them ∀-operators. The question we address in this paper is: How is the class of ∀-operators generated? It is shown that every positive ∀-operator Γ such th...

in order to study the relationship between random boolean sets and some explanatory variables, this paper introduces a propagation model. this model can be applied when corresponding poisson process of the boolean model is related to explanatory variables and the random grains are not affected by these variables. an approximation for the likelihood is used to find pseudo-maximum likelihood esti...

It is hard to find nontrivial positive partition relations which hold for many ordinals in ordinary set theory, or even ordinary set theory with the additional assumption of the Generalized Continuum Hypothesis. Erdös, Hajnal and Milner have proved that limit ordinals a < u;"+ satisfy a positive partition relation that can be expressed in graph theoretic terms. In symbols one writes a —► (a, in...

A k-Testable tree set in the Strict sense (k-TS) is essentially defined by a finite set of patterns of "size" k that are permitted to appear in the trees of the tree language. Given a positive sample S of trees over a ranked alphabet, an algorithm is proposed which obtains the smallest k-TS tree set containing S. The proposed algorithm is polynomial on the size of S and identifies the class of ...