Abstract
MathIS is a new project that aims to reinvigorate secondary-school mathematics by exploiting insights of the dynamics of algorithmic problem solving. This paper describes the main ideas that underpin the project. In summary, we propose a central role for formal logic, the development of a calculational style of reasoning, the emphasis on the algorithmic nature of mathematics, and the promotion of self-discovery by the students. These ideas are discussed and the case is made, through a number of examples that show the teaching style that we want to introduce, for their relevance in shaping mathematics training for the years to come. In our opinion, the education of software engineers that work effectively with formal methods and mathematical abstractions should start before university and would benefit from the ideas discussed here.

Abstract

Abstract

Abstract
Software connectors are external coordination devices which ensure the flow of data and enforce synchronization constraints within a component's network. The specification of software connectors through which context dependent behaviour is correctly propagated remains an open, non trivial issue in their semantics. This paper, building on previous work by the authors, revisits this problem and introduces a model in which context awareness is suitably handled.

Abstract
Component's QoS constraints cannot be ignored when composing them to build reliable loosely-coupled, distributed systems. Therefore they should be explicitly taken into account in any formal model for component-based development. Such is the purpose of this paper: to extend a calculus of component composition to deal, in an effective way, with QoS constraints. Particular emphasis is put on how the laws that govern composition can be derived, in a calculational, pointfree style, in this new model.

Abstract
Modal logics are successfully used as specification logics for reactive systems. However, they are not expressive enough to refer to individual states and reason about the local behaviour of such systems. This limitation is overcome in hybrid logics which introduce special symbols for naming states in models. Actually, hybrid logics have recently regained interest, resulting in a number of new results and techniques as well as applications to software specification. In this context, the first contribution of this paper is an attempt to 'universalize' the hybridization idea. Following the lines of [15], where a method to modalize arbitrary institutions is presented, the paper introduces a method to hybridize logics at the same institution-independent level. The method extends arbitrary institutions with Kripke semantics (for multi-modalities with arbitrary arities) and hybrid features. This paves the ground for a general result: any encoding (expressed as comorphism) from an arbitrary institution to first order logic (FOL ) determines a comorphism from its hybridization to FOL. This second contribution opens the possibility of effective tool support to specification languages based upon logics with hybrid features. © 2011 Springer-Verlag.