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    Real-time and Probabilistic Temporal Logics: An Overview

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    Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have been introduced for the formal specification of real-time and complex systems, an up to date comprehensive analysis of these logics does not exist in the literature. In this paper we analyse real-time and probabilistic temporal logics which have been widely used in this field. We extrapolate the notions of decidability, axiomatizability, expressiveness, model checking, etc. for each logic analysed. We also provide a comparison of features of the temporal logics discussed

    Some remarks on modified power entropy

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    The aim of this note is to point out some observations concerning modified power entropy of Z\Z- and N\N-actions. First, we provide an elementary example showing that this quantity is sensitive to transient dynamics, and therefore does not satisfy a variational principle. Further, we show that modified power entropy is not suitable to detect the break of equicontinuity which takes place during the transition from almost periodic to almost automorphic minimal systems. In this respect, it differs from power entropy and amorphic complexity, which are two further topological invariants for zero entropy systems (`slow entropies'). Finally, we construct an example of an irregular Toeplitz flow with zero modified power entropy.Comment: 17 pages, to appear in AMS Contemporary Mathematics serie

    Governance for sustainability: learning from VSM practice

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    Purpose – While there is some agreement on the usefulness of systems and complexity approaches to tackle the sustainability challenges facing the organisations and governments in the twenty-first century, less is clear regarding the way such approaches can inspire new ways of governance for sustainability. The purpose of this paper is to progress ongoing research using the Viable System Model (VSM) as a meta-language to facilitate long-term sustainability in business, communities and societies, using the “Methodology to support self-transformation”, by focusing on ways of learning about governance for sustainability. Design/methodology/approach – It summarises core self-governance challenges for long-term sustainability, and the organisational capabilities required to face them, at the “Framework for Assessing Sustainable Governance”. This tool is then used to analyse capabilities for governance for sustainability at three real situations where the mentioned Methodology inspired bottom up processes of self-organisation. It analyses the transformations decided from each organisation, in terms of capabilities for sustainable governance, using the suggested Framework. Findings – Core technical lessons learned from using the framework are discussed, include the usefulness of using a unified language and tool when studying governance for sustainability in differing types and scales of case study organisations. Research limitations/implications – As with other exploratory research, it reckons the convenience for further development and testing of the proposed tools to improve their reliability and robustness. Practical implications – A final conclusion suggests that the suggested tools offer a useful heuristic path to learn about governance for sustainability, from a VSM perspective; the learning from each organisational self-transformation regarding governance for sustainability is insightful for policy and strategy design and evaluation; in particular the possibility of comparing situations from different scales and types of organisations. Originality/value – There is very little coherence in the governance literature and the field of governance for sustainability is an emerging field. This piece of exploratory research is valuable as it presents an effective tool to learn about governance for sustainability, based in the “Methodology for Self-Transformation”; and offers reflexions on applications of the methodology and the tool, that contribute to clarify the meaning of governance for sustainability in practice, in organisations from different scales and types
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