We consider several ordinal formulations of submodularity, defined for arbitrary binary relations on lattices. Two of these formulations are essentially due to David Kreps (A Representation Theorem for “Preference for Flexibility”, Econometrica, 1979) and one is a weakening of a notion due to Paul Milgrom and Chris Shannon (Monotone Comparative Statics, Econometrica, 1994). We show that any ref...

We study the number and interaction rates of supermassive black holes in galactic bulges as predicted by hierarchical models of galaxy formation in which the spheroidal components of galaxies are formed by mergers. In bright ellipticals, the number of events that can eject a central supermassive binary black hole is large. Central binaries must therefore merge in less than a Hubble time – other...

We discuss an equivalence relation on the set of square binary matrices with the same number of 1’s in each row and each column. Each binary matrix is represented using ordered n-tuples of natural numbers. We give a few starting values of integer sequences related to the discussed problem. The obtained sequences are new and they are not described in the On-Line Encyclopedia of Integer Sequences...

This paper presents a framework to model the semantic representation of binary relations produced by open information extraction systems. For each binary relation, we infer a set of preferred types on the two arguments simultaneously, and generate a ranked list of type pairs which we call schemas. All inferred types are drawn from the Freebase type taxonomy, which are human readable. Our system...

The Strahler number of binary trees has been introduced by hydrogeologists and rediscovered in computer science in relation with some optimization problems. Explicit expressions have been given for the Strahler distribution, i.e. binary trees enumerated by number of vertices and Strahler number. Two other Strahler distributions have been discovered with the logarithmic height of Dyck paths and ...

Rough set theory is an important technique in knowledge discovery in databases. Classical rough set theory proposed by Pawlak is based on equivalence relations, but many interesting and meaningful extensions have been made based on binary relations and coverings, respectively. This paper makes a comparison between covering rough sets and rough sets based on binary relations. This paper also foc...

Binary logical relations do not compose. So we generalise the notion of logical relation to one of lax logical relation, so that binary lax logical relations do compose. We give both a direct generalisation and a corresponding category theoretic formulation. We generalise the Basic Lemma for logical relations to a Basic Lemma for lax logical relations. Finally, we give an axiomatic category the...

Suppose that a binary relation is given on a n-fold Cartesian product. The study of the conditions guaranteeing the existence of n value functions such that the binary relation can be additively represented is known as additive conjoint measurement. In this paper we analyze a related problem: given a partition of a Cartesian product into r ordered categories, what conditions do ensure the repre...

A word on a nite alphabet A is said to be overlap free if it contains no factor of the form xuxux where x is a letter and u a possibly empty word In this paper we study the number un of overlap free binary words of length n which is known to be bounded by a polynomial in n First we describe a bijection between the set of overlap free words and a rational language This yields recurrence relation...

Tarski’s algebra of binary relations is formalised along the lines of the standard textbooks of Maddux and Schmidt and Ströhlein. This includes relation-algebraic concepts such as subidentities, vectors and a domain operation as well as various notions associated to functions. Relation algebras are also expanded by a reflexive transitive closure operation, and they are linked with Kleene algebr...