A relational calculus is a formal system in which relation is the fundamental concept. The simplest relational calculus, that of ordinary binary relations, was introduced by Tarski in [4]. Tarski’s system is essentially an algebra in which the operations are the usual Boolean operations (on sets of ordered pairs) together with the two special operations converse (denoted byq) and composition (d...

In a recent paper Calderbank, Rains, Shor and Sloane [1] described a method of constructing quantum-error-correcting codes from ordinary binary or quaternary codes that are selforthogonal with respect to a certain inner product. We use this relation to show that a class of binary formally self-dual codes defined by symmetric matrices give rise to quantum codes with error-correcting capacity pro...

In this paper we establish the connections between two di7erent extensions of Z4-linearity for binary Hamming spaces. We present both notions – propelinearity and G-linearity – in the context of isometries and group actions, taking the viewpoint of geometrically uniform codes extended to discrete spaces. We show a double inclusion relation: binary G-linear codes are propelinear codes, and trans...

The most prominent proposals of subtyping for asynchronous session types are by Mostrous and Yoshida for binary sessions, by Chen et al. for binary sessions under the assumption that every message emitted is eventually consumed, and by Mostrous et al. for multiparty session types. We prove that, differently from what stated or conjectured in above proposals, all of these three subtyping relatio...

In a recent paper Calderbank, Rains, Shor and Sloane [1] described a method of constructing quantum-error-correcting codes from ordinary binary or quaternary codes that are selforthogonal with respect to a certain inner product. We use this relation to show that a class of binary formally self-dual codes defined by symmetric matrices give rise to quantum codes with error-correcting capacity pro...

Binary relations representable by utility functions with multiplicative error are considered. It is proved that if the error is a power of utility then the underlying binary relation is either an interval order, or a semiorder. Moreover, semiorders can be characterized among interval orders by the magnitude of the power of utility that is used in the form of error function. D 2005 Elsevier B.V....

A novel approach to triclustering of a three-way binary data is proposed. Tricluster is defined in terms of Triadic Formal Concept Analysis as a dense triset of a binary relation Y , describing relationship between objects, attributes and conditions. This definition is a relaxation of a triconcept notion and makes it possible to find all triclusters and triconcepts contained in triclusters of l...

In this article, some results on fixed points under quasicontractions in the framework of metric space endowed with binary relation are proved. Our newly proved improve and extend several noted point theorems existing literature besides their relation-theoretic analogues. We conclude article by constructing an example to affirm efficacy our results.

Different semantic interpretation tasks such as text entailment and question answering require the classification of semantic relations between terms or entities within text. However, in most cases it is not possible to assign a direct semantic relation between entities/terms. This paper proposes an approach for composite semantic relation classification, extending the traditional semantic rela...