The starting point of the paper is the (well-known)observation that the “classical” Rough Set Theory as introduced by PAWLAK is equivalent to the S5 Propositional Modal Logic where the reachability relation is an equivalence relation. By replacing this equivalence relation by an arbitrary binary relation (satisfying certain properties, for instance, reflexivity and transitivity) we shall obtain...

In this paper S, X denote non empty sets and R denotes a binary relation on X. We consider orthorelational structures, extensions of relational structure and ComplStr, as systems 〈 a carrier, an internal relation, a complement operation 〉, where the carrier is a set, the internal relation is a binary relation on the carrier, and the complement operation is a unary operation on the carrier. Let ...

The relationship between bilevel optimization and multiobjective optimization has been studied by several authors and there have been repeated attempts to establish a link between the two. We unify the results from the literature and generalize them for bilevel multiobjective optimization. We formulate sufficient conditions for an arbitrary binary relation to guarantee equality between the effi...

Total path length, or search cost, for a rooted tree is defined as the sum of all root-to-node distances. Let Tn be the total path length for a random recursive tree of order n. Mahmoud (1991) showed that Wn := (Tn − E[Tn])/n converges almost surely and in L2 to a nondegenerate limiting random variable W . Here we give recurrence relations for the moments of Wn and of W and show that Wn converg...

We study the discrete approximation to solutions of first-order system arising from applying the trapezoidal rule to a second-order scalar ordinary differential equation. In the trapezoidal rule the finite difference approximation are Dyk = (zk + zk−1)/2, Dzk = ( fk + fk−1)/2, for k = 1, 2, .., n, and tk = kh for k = 0, ..., n, 0 = G ( (y0, yn), (z0 + z1)/2, (zn−1 + zn)/2) ) , where fi ≡ f (ti,...

Bouttier, Di Francesco and Guitter introduced a method for solving certain classes of algebraic recurrence relations arising the context of embedded trees and map enumeration. The aim of this note is to apply this method to three problems. First, we discuss a general family of embedded binary trees, trying to unify and summarize several enumeration results for binary tree families, and also to ...

This paper presents a novel approach to the problem of finding all subgraph isomorphisms of a (pattern) graph into another (target) graph. A relational formulation of the problem, combined with a representation of relations and graphs by Boolean functions, allows to handle the combinatorial explosion in the case of small pattern graphs and large target graphs by using Binary Decision Diagrams (...

This paper defines a selection problem which selects an appropriate object from a set that is specified by parameters. We discuss inductive learning of selection problems and give a method combining inductive logic programming (ILP) and Bayesian learning. It induces a binary relation comparing likelihood of objects being selected. Our methods estimate probability of each choice by evaluating va...

A Chu space is a binary relation =| from a set A to an antiset X defined as a set which transforms via converse functions. Chu spaces admit a great many interpretations by virtue of realizing all small concrete categories and most large ones arising in mathematical and computational practice. Of particular interest for computer science is their interpretation as computational processes, which t...

The semantic binary engine is a database management system built on the principles of the Semantic Binary Data Model (Rishe, 1992). A semantic binary database is a set of facts about objects. Objects belong to categories, are connected by relations, and may have attributes. The concept of an object is at the core of the data model and it is crucial to have efficient algorithms that allow the se...