Any hereditarily finite set S can be represented as a finite pointed graph –dubbed membership graph– whose nodes denote elements of the transitive closure of {S} and whose edges model the membership relation. Membership graphs must be hyper-extensional –nodes are pairwise not bisimilar– and bisimilar nodes represent the same hereditarily finite set. It is worth to notice that the removal of eve...

We consider an extension of the guarded fragment in which one can guard quanti ers using the transitive closure of some binary relations. The obtained logic captures the guarded fragment with transitive guards, and in fact extends its expressive power non-trivially, preserving the complexity: we prove that its satis ability problem is 2Exptime-

There are two central themes to research involving applications of probabilistic methods to partially ordered sets. The first of these can be described as the study of random partially ordered sets. Among the specific models which have been studied are: random labelled posets; random t-dimensional posets; and the transitive closure of random graphs. A second theme concentrates on the adaptation...

We prove that the cyclic closure of the permutation class avoiding the pattern k(k− 1) . . . 21 is finitely based. The minimal length of a minimal permutation is 2k − 1 and these basis permutations are enumerated by (2k− 1).ck where ck is the kth Catalan number. We also define lift operations and give similar results. Finally, we consider the toric closure of a class and we propose some open pr...

Suppose that R is a two-dimensional normal standard-graded domain over a finite field. We prove that there exists a uniform Frobenius test exponent b for the class of homogeneous ideals in R generated by at most n elements. This means that for every ideal I in this class we have that f b ∈ I [p ] if and only if f ∈ I . This gives in particular a finite test for the Frobenius closure. On the oth...

Westudy abstract decision problems by introducing an extended dominance relation with respect to a set of alternatives. This extension is in between the traditional dominance relation as formulated by Von Neumann and Morgenstern (Theory of games and economic behavior, Princeton University Press, Princeton, 1944) and the transitive closure of it. Subsequently, stable sets are defined and studied...

Fuzzy operators are an essential tool in many fields and the operation of composition is often needed. In general, composition is not a commutative operation. However, it is very useful to have operators for which the order of composition does not affect the result. In this paper, we analyze when permutability appears. That is, when the order of application of the operators does not change the ...

Let G be a primitive permutation group on a finite set ft, and, for k ^ 2, let G be the Ar-closure of G, that is, the largest subgroup of Sym (ft) preserving all the G-invariant ^-relations on ft. Suppose that G<H^ G and G and H have different socles. It is shown that k ^ 5 and the groups G and H are classified explicitly.

This paper introduces the concept of fuzzy neutrosophic equivalence relations and discuss some of their properties. define fuzzy neutrosophic transitive closure and investigate their properties.

A (hereditarily finite) set/hyperset S can be completely depicted by a (finite pointed) graph GS—dubbed its membership graph— in which every node represents an element of the transitive closure of {S} and every arc represents a membership relation holding between its source and its target. In a membership graph different nodes must have different sets of successors and, more generally, if the g...