Notes on Neighbourhood Logic

UNU/IIST UNU/IIST enables developing countries to attain self-reliance in software technology by: (i) their own development of high integrity computing systems, (ii) highest level postgraduate university teaching, (iii) international level research, and, through the above, (iv) use of as sophisticated software as reasonable. UNU/IIST contributes through: (a) advanced, joint industry-university advanced development projects in which rigorous techniques supported by semantics-based tools are applied in case studies to large scale software developments , (b) own and joint university and academy institute research in which new techniques for application domain and computing platform modelling, requirements capture, software engineering and programming are being investigated, (c) advanced, postgraduate and post-doctoral level courses which typically teach Design Cal-culi oriented software development techniques, (d) events panels, task forces, workshops and symposia], and (e) dissemination. Application-wise, the advanced development projects presently focus on software to support large-scale infrastructure systems such as transport systems (railways, airlines, air traac, etc.), manufacturing industries, telecommunications , etc., and are thus aligned with UN and International Aid System concerns. UNU/IIST is a leading research centre in the area of Duration Calculi, i.e. techniques applicable to real-time, reactive, hybrid & safety critical systems. The research projects parallel and support the advanced development projects. At present, the technical focus of UNU/IIST in all of the above is on applying, teaching, researching, and disseminating Design Calculi oriented techniques and tools for trustworthy software development. UNU/IIST currently emphasises techniques that permit proper development steps and interfaces. UNU/IIST also endeavours to promulgate sound project and product management principles. UNU/IIST's primary dissemination strategy is to act as a clearing house for reports from research and technology centres in industrial countries to industries and academic institutions in developing countries. At present more than 200 institutions worldwide contribute to UNU/IIST's report collection while UNU/IIST at the same time subscribes to more than 125 international scientiic and technical journals. Information on reports received (and produced) and on journal articles is to be disseminated regularly to developing country centres | which are then free to order a reasonable number of report and article copies from UNU/IIST. Abstract In 1996, Zhou Chaochen and Michael Hansen proposed a rst order interval logic called Neighbourhood Logic (NL) in view of specifying liveness and fairness of computing systems and also deening notions of real analysis in terms of expanding modalities introduced therein. This paper serves as a reference manual of NL. It contains proofs of various …