This paper describes a preliminary effort in identifying many different types of relations among words in Thai sentences based on dependency grammar. The relation is represented as a triple containing the pair of words and their relation. So far, the current representation contains 35 grammatical relations. The dependencies are all binary relations. That is, a grammatical relation holds between...

Rough relation algebras arise from Pawlak’s information systems by considering as object ordered pairs on a fixed set X . Thus, the subsets to be approximated are binary relations over X , and hence, we have at our disposal not only the set theoretic operations, but also the relational operators ; , ̆ , and the identity relation 1′. In the present paper, which is a continuation of [6], we furth...

The notion of rough sets is generalized by using an arbitrary binary relation on attribute values in information systems, instead of the trivial equality relation. The relation, not necessarily equivalence, between objects are defined in terms of relationships between attribute values. The adoption of other types of relations enables us to define various classes of rough set models. This study ...

A concept (or Galois) lattice is built on a binary relation; this relation can be represented by a bipartite graph. We explain how we can use the graph tool of clique minimal separator decomposition to decompose some bipartite graphs into subgraphs in linear time; each subgraph corresponds to a subrelation. We show that the lattices of these subrelations easily yield the lattice of the global r...

We use a relational characterization of binary direct sums to model sequences within the relation-algebraic manipulation and prototyping system RelView in a simple way. As an application we formally derive a RelView program for computing equivalence classes of an equivalence relation, where we combine relation-algebraic calculations with the so-called Dijkstra-Gries program development method. ...

Rough relation algebras arise from Pawlak’s information systems by considering as object ordered pairs on a fixed set X . Thus, the subsets to be approximated are binary relations over X , and hence, we have at our disposal not only the set theoretic operations, but also the relational operators ; , ̆ , and the identity relation 1′. In the present paper, which is a continuation of [6], we furth...

In this paper, we describe a relation between the embedding degree of an elliptic curve over a prime field Fp and the inertial degree of the primes above p in a certain ring class field. From this relation, we conclude that the embedding degree divides the class number of a group of binary quadratic forms of a fixed discriminant.

ly, taking a step amounts to applying a function, and going step by step corresponds to applying functions one after the other. This is captured by the operation of composing functions. Composing the functions f and g means that first f is applied to some argument, x, to produce f .x/, and then g is applied to that result to produce g.f .x//. Definition 4.3.1. For functions f W A ! B and g W B ...

Formal Concept Analysis (FCA) provides an account of classification based on a binary relation between two sets. These two sets contain the objects and attributes (or properties) under consideration. In this paper I propose a generalization of formal concept analysis based on binary relations between hypergraphs, and more generally between pre-orders. A binary relation between any two sets alre...