This paper provides an overview of how the Event-B language and verification method can be used to model and reason about system behaviour. Formal modelling and reasoning help to increase understanding and reduce defects in requirements specification. Sets and relations play a key role in modelling as do operators on these structures. Precise definitions and rules are provided in order to help ...

Previous research has suggested that parents' aspirations for their children's academic attainment can have a positive influence on children's actual academic performance. Possible negative effects of parental overaspiration, however, have found little attention in the psychological literature. Employing a dual-change score model with longitudinal data from a representative sample of German sch...

The notion of a rough set, developed by Pawlak [10], is an important tool to describe situation of incomplete or partially unknown information. In this article, which is essentially the continuation of [6], we try to give the characterization of approximation operators in terms of ordinary properties of underlying relations (some of them, as serial and mediate relations, were not available in t...

The aim of this paper is to give the non-specialist reader a comprehensible and intuitive introduction to multiview relations. It focusses on the geometric interpretation of the di erent image relationships, but also presents a concise mathematical formalism which allows to derive the algebraic expressions explicitly in an elementary and uniform manner. Special attention has been paid both to t...

The method in mathematical logic invented by Schönfinkelf and developed in detail by Curry | is important in that it completely eliminates the variable from the formal presuppositions of logic and mathematics. Constructed according to Schönfinkel's scheme the primitive language of mathematical logic consists only of a few constants; variables, if wanted as a convenience, are introduced afterwar...

Bipolarity is an important feature of spatial information, involved in the expression of preferences and constraints about spatial positioning or in pairs of opposite spatial relations such as left and right. Another important feature is imprecision which has to be taken into account to model vagueness, inherent to many spatial relations (as for instance vague expressions such as close to, to t...

Logic1 GLARF relations are generated from treebank and parses for English, Chinese and Japanese. We focus on evaluation of system output for both input types, often allowing for multiple correct answers.

We present and discuss a simple semantic approach to force step-indexed logical relations to be transitive.

We investigatea simple form of parametricity, based on adding \abstract" copies of pre-existing types. Connections are made with the Reynolds-Ma theory of parametricity by logical relations, with the theory of parametricity via dinaturality, and with the categorical notion of equivalence.

We argue that uncomputability and classical scepticism are both re ections of inductive underdetermination, so that Church's thesis and Hume's problem ought to receive equal emphasis in a balanced approach to the philosophy of induction. As an illustration of such an approach, we investigate how uncomputable the predictions of a hypothesis can be if the hypothesis is to be reliably investigated...