(Metric) Bisimulation Games and Real-Valued Modal Logics for Coalgebras

Behavioural equivalences can be characterized via bisimulations, modal logics and spoiler-defender games. In this paper we review these three perspectives in a coalgebraic setting, which allows us to generalize from the particular branching type of a transition system. We are interested in qualitative notions (classical bisimulation) as well as quantitative notions (bisimulation metrics). Our first contribution is to introduce a spoiler-defender bisimulation game for coalgebras in the classical case. Second, we introduce such games for the metric case and furthermore define a real-valued modal coalgebraic logic, from which we can derive the strategy of the spoiler. For this logic we show a quantitative version of the Hennessy-Milner theorem

Compositional bisimulation metric reasoning with Probabilistic Process Calculi

We study which standard operators of probabilistic process calculi allow for compositional reasoning with respect to bisimulation metric semantics. We argue that uniform continuity (generalizing the earlier proposed property of non-expansiveness) captures the essential nature of compositional reasoning and allows now also to reason compositionally about recursive processes. We characterize the distance between probabilistic processes composed by standard process algebra operators. Combining these results, we demonstrate how compositional reasoning about systems specified by continuous process algebra operators allows for metric assume-guarantee like performance validation

Generalized labelled Markov processes, coalgebraically

Coalgebras of measurable spaces are of interest in probability theory as a formalization of Labelled Markov Processes (LMPs). We discuss some general facts related to the notions of bisimulation and cocongruence on these systems, providing a faithful characterization of bisimulation on LMPs on generic measurable spaces. This has been used to prove that bisimilarity on single LMPs is an equivalence, without assuming the state space to be analytic. As the second main contribution, we introduce the first specification rule format to define well-behaved composition operators for LMPs. This allows one to define process description languages on LMPs which are always guaranteed to have a fully-abstract semantics

Universal Quantitative Algebra for Fuzzy Relations and Generalised Metric Spaces

We present a generalisation of the theory of quantitative algebras of Mardare, Panangaden and Plotkin where (i) the carriers of quantitative algebras are not restricted to be metric spaces and can be arbitrary fuzzy relations or generalised metric spaces, and (ii) the interpretations of the algebraic operations are not required to be nonexpansive. Our main results include: a novel sound and complete proof system, the proof that free quantitative algebras always exist, the proof of strict monadicity of the induced Free-Forgetful adjunction, the result that all monads (on fuzzy relations) that lift finitary monads (on sets) admit a quantitative equational presentation.Comment: Appendix remove

Automated analysis of free-text comments and dashboard representations in patient experience surveys: a multimethod co-design study

BACKGROUND: Patient experience surveys (PESs) often include informative free-text comments, but with no way of systematically, efficiently and usefully analysing and reporting these. The National Cancer Patient Experience Survey (CPES), used to model the approach reported here, generates > 70,000 free-text comments annually. MAIN AIM: To improve the use and usefulness of PES free-text comments in driving health service changes that improve the patient experience. SECONDARY AIMS: (1) To structure CPES free-text comments using rule-based information retrieval (IR) (‘text engineering’), drawing on health-care domain-specific gazetteers of terms, with in-built transferability to other surveys and conditions; (2) to display the results usefully for health-care professionals, in a digital toolkit dashboard display that drills down to the original free text; (3) to explore the usefulness of interdisciplinary mixed stakeholder co-design and consensus-forming approaches in technology development, ensuring that outputs have meaning for all; and (4) to explore the usefulness of Normalisation Process Theory (NPT) in structuring outputs for implementation and sustainability. DESIGN: A scoping review, rapid review and surveys with stakeholders in health care (patients, carers, health-care providers, commissioners, policy-makers and charities) explored clinical dashboard design/patient experience themes. The findings informed the rules for the draft rule-based IR [developed using half of the 2013 Wales CPES (WCPES) data set] and prototype toolkit dashboards summarising PES data. These were refined following mixed stakeholder, concept-mapping workshops and interviews, which were structured to enable consensus-forming ‘co-design’ work. IR validation used the second half of the WCPES, with comparison against its manual analysis; transferability was tested using further health-care data sets. A discrete choice experiment (DCE) explored which toolkit features were preferred by health-care professionals, with a simple cost–benefit analysis. Structured walk-throughs with NHS managers in Wessex, London and Leeds explored usability and general implementation into practice. KEY OUTCOMES: A taxonomy of ranked PES themes, a checklist of key features recommended for digital clinical toolkits, rule-based IR validation and transferability scores, usability, and goal-oriented, cost–benefit and marketability results. The secondary outputs were a survey, scoping and rapid review findings, and concordance and discordance between stakeholders and methods. RESULTS: (1) The surveys, rapid review and workshops showed that stakeholders differed in their understandings of the patient experience and priorities for change, but that they reached consensus on a shortlist of 19 themes; six were considered to be core; (2) the scoping review and one survey explored the clinical toolkit design, emphasising that such toolkits should be quick and easy to use, and embedded in workflows; the workshop discussions, the DCE and the walk-throughs confirmed this and foregrounded other features to form the toolkit design checklist; and (3) the rule-based IR, developed using noun and verb phrases and lookup gazetteers, was 86% accurate on the WCPES, but needs modification to improve this and to be accurate with other data sets. The DCE and the walk-through suggest that the toolkit would be well accepted, with a favourable cost–benefit ratio, if implemented into practice with appropriate infrastructure support. LIMITATIONS: Small participant numbers and sampling bias across component studies. The scoping review studies mostly used top-down approaches and focused on professional dashboards. The rapid review of themes had limited scope, with no second reviewer. The IR needs further refinement, especially for transferability. New governance restrictions further limit immediate use. CONCLUSIONS: Using a multidisciplinary, mixed stakeholder, use of co-design, proof of concept was shown for an automated display of patient experience free-text comments in a way that could drive health-care improvements in real time. The approach is easily modified for transferable application. FUTURE WORK: Further exploration is needed of implementation into practice, transferable uses and technology development co-design approaches. FUNDING: The National Institute for Health Research Health Services and Delivery Research programme