We study the ordered set of rough sets determined by relations which are not necessarily reflexive, symmetric, or transitive. We show that for tolerances and transitive binary relations the set of rough sets is not necessarily even a semilattice. We also prove that the set of rough sets determined by a symmetric and transitive binary relation forms a complete Stone lattice. Furthermore, for the...

We present ONTOMS2, an efficient and scalable ONTOlogy Management System with an incremental reasoning. ONTOMS2 stores an OWL document and processes OWL-QL and SPARQL queries. Especially, ONTOMS2 supports SPARQL Update queries with an incremental instance reasoning of inverseOf, symmetric and transitive properties.

It is known that the suspension of a simplicial complex can be realized with only one additional point. Suitable iterations of this construction generate highly symmetric simplicial complexes with various interesting combinatorial and topological properties. In particular, infinitely many non-PL spheres as well as contractible simplicial complexes with a vertex-transitive group of automorphisms...

In this paper, we present a fixed-point theorem in R-complete regular symmetric spaces endowed with locally T-transitive binary relation R using comparison functions that generalizes several relevant existing results. addition, adopt an example to substantiate the genuineness of our newly proved result. Finally, as application main result, establish existence and uniqueness solution periodic bo...

The main aim of this article is to study (v, k, λ)-symmetric designs admitting a flag-transitive and point-primitive automorphism group G whose socle is PSL(3, q). We indeed show that the only possible design satisfying these conditions is a Desarguesian projective plane PG(2, q) and G ⩾ PSL(3, q).

It has been shown that if a (v,k,λ )-symmetric design with λ ≤ 3 admits a flag-transitive automorphism group G which acts primitively on points, then G must be of affine or almost simple type. Here we extend the result to λ = 4.

In this section, we shall introduce a formal definition for the notion of a relation on a set. This is something we often take for granted in elementary algebra courses, but is a fundamental concept in mathematics i.e. the very notion of a function relies upon the definition of a relation. Following this, we shall discuss special types of relations on sets. 1. Binary Relations and Basic Definit...

Abstract I provide an analysis of sentences the form ‘To be F is to G ’ in terms exact truth-maker semantics—an approach that identifies meanings with states world directly responsible for their truth-values. Roughly, argue these hold just case which makes something also it . This hyperintensional and possesses desirable logical modal features. In particular, are reflexive, transitive, symmetri...

It is well known that every alternating and every symmetric group can be generated by two of its substitutions, and that two such generating substitutions can usually be selected in a large number of different ways. Since two operators of order 2 must always generate a dihedral group it is evident that no alternating group can be generated by two of its substitutions of order 2, and that the on...

Symmetric properties of some molecular graphs on the torus are studied. In particular we determine which cubic cyclic Haar graphs are 1-regular, which is equivalent to saying that their line graphs are 1 2-arc-transitive. Although these symmetries make all vertices and all edges indistinguishable , they imply intrinsic chirality of the corresponding molecular graph.