The growing use of agent systems and the widespread penetration of the Internet has opened up new possibilities for scientific collaboration. We have been investigating the role for agent systems to aid with collaboration among Experimental High-Energy Physics (EHEP) physicists. A necessary component is an agreed ontology, which must include complex mathematical relations involving such quantit...

Using mathematical morphology on formulas introduced recently by Bloch and Lang (Proceedings of IPMU’2000) we define two new explanatory relations. Their logical behavior is analyzed. The results show that these natural ways for defining preferred explanations are robust because these relations satisfy almost all postulates of explanatory reasoning introduced by Pino-Pérez and Uzcátegui (Artifi...

In 1985, Doignon and Falmagne introduced surmise relations for representing prerequisite relationships between items within a body of information for the assessment of knowledge. Often it is useful to partition such a body of information into sub-collections. As we are primarily interested in psychological applications, we refer to these sub-collections as tests. We extend the concept of surmis...

Rock fragmentation is one of the desired results of rock blasting. So, controlling and predicting it, has direct effects on operational costs of mining. There are different ways that could be used to predict the size distribution of fragmented rocks. Mathematical relations have been widely used in these predictions. From among three proposed mathematical relations, one was selected in this stud...

it is well known fact that binary relations are generalized mathematical functions. contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. some basic operations on functions such as the inverse and composition are applicable to binary relations as well. depending on the domain or range or both are fuzzy value fuzzy set, i...

The basics of set theory are usually copied, directly or indirectly, by computer scientists from introductions to mathematical texts. Often mathematicians are content with special cases when the general case is of no mathematical interest. But sometimes what is of no mathematical interest is of great practical interest in computer science. For example, non-binary relations in mathematics tend t...