We introduce the notion of a dice model as a framework for describing a class of probabilistic relations. We investigate the transitivity of the probabilistic relation generated by a dice model and prove that it is a special type of cycle-transitivity that is situated between moderate stochastic transitivity or product-transitivity on the one side, and Lukasiewicz-transitivity on the other side. Finally, it is shown that any probabilistic relation with rational elements on a three-dimensional space of alternatives which possesses this particular (...) type of cycle-transitivity, can be represented by a dice model. The same does not hold in higher dimensions. (shrink)

We introduce two extreme methods to pairwisely compare ordered lists of the same length, viz. the comonotonic and the countermonotonic comparison method, and show that these methods are, respectively, related to the copula T M (the minimum operator) and the Ł ukasiewicz copula T L used to join marginal cumulative distribution functions into bivariate cumulative distribution functions. Given a collection of ordered lists of the same length, we generate by means of T M and T L two probabilistic relations Q (...) M and Q L and identify their type of transitivity. Finally, it is shown that any probabilistic relation with rational elements on a 3-dimensional space of alternatives which possesses one of these types of transitivity, can be generated by three ordered lists and at least one of the two extreme comparison methods. (shrink)

The Cell Cycle Ontology (CCO) has the aim to provide a 'one stop shop' for scientists interested in the biology of the cell cycle that would like to ask questions from a molecular and/or systems perspective: what are the genes, proteins, and so on involved in the regulation of cell division? How do they interact to produce the effects observed in the regulation of the cell cycle? To answer these questions, the CCO must integrate a large amount of knowledge from (...) diverse sources; the irregularity and incompleteness of this information suggests an ontology can act as the means of this integration. The volatility and continued expansion of biological knowledge means the content and modelling of the CCO will have to be frequently changed and updated. The CCO is generated from the input data automatically once every two months. This makes it easy to change the representation to enable certain queries; incorporate new knowledge; and consistently apply design patterns across the CCO. The automatic process also allows the CCO to be delivered in a variety of representations that suit the needs of various CCO customers and the abilities of existing toolsets. In this paper we present the CCO and its characteristics of utility and flexibility, that, from our perspective, make it a beautiful ontology. (shrink)

ABSTRACT A modal logic interpretation of Dempster-Shafer theory is developed in the framework of multivalued models of modal logic, i.e. models in which in any possible world an arbitrary number (possibly zero) of atomic propositions can be true. Several approaches to conditioning in multivalued models of modal logic are presented.