Proof-theoretic Analysis of Rationality for Strategic Games with Arbitrary Strategy Sets

In the context of strategic games, we provide an axiomatic proof of the statement Common knowledge of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies. Rationality here means playing only strategies one believes to be best responses. This involves looking at two formal languages. One is first-order, and is used to formalise optimality conditions, like avoiding strictly dominated strategies, or playing a best response. The other is a modal fixpoint language with expressions for optimality, rationality and belief. Fixpoints are used to form expressions for common belief and for iterated elimination of non-optimal strategies.Comment: 16 pages, Proc. 11th International Workshop on Computational Logic in Multi-Agent Systems (CLIMA XI). To appea

The Invisible Thin Red Line

The aim of this paper is to argue that the adoption of an unrestricted principle of bivalence is compatible with a metaphysics that (i) denies that the future is real, (ii) adopts nomological indeterminism, and (iii) exploits a branching structure to provide a semantics for future contingent claims. To this end, we elaborate what we call Flow Fragmentalism, a view inspired by Kit Fine (2005)’s non-standard tense realism, according to which reality is divided up into maximally coherent collections of tensed facts. In this way, we show how to reconcile a genuinely A-theoretic branching-time model with the idea that there is a branch corresponding to the thin red line, that is, the branch that will turn out to be the actual future history of the world

Blue and Red Cathodoluminescent Emission of Y2O3:Eu Phosphor Studied as a Function of Temperature in a Transmission Electron Microscope

Combined EELS, CL and STEM imaging are used to characterize and study Y2O3:Eu to confirm the variation in CL properties and photo-luminescent properties observed. The synthetic procedures used have facilitated this material to manifest a strong blue emission at low temperature with the expected red emission dominating at room temperature

On the Complexity of Searching in Trees: Average-case Minimization

We focus on the average-case analysis: A function w : V -> Z+ is given which defines the likelihood for a node to be the one marked, and we want the strategy that minimizes the expected number of queries. Prior to this paper, very little was known about this natural question and the complexity of the problem had remained so far an open question. We close this question and prove that the above tree search problem is NP-complete even for the class of trees with diameter at most 4. This results in a complete characterization of the complexity of the problem with respect to the diameter size. In fact, for diameter not larger than 3 the problem can be shown to be polynomially solvable using a dynamic programming approach. In addition we prove that the problem is NP-complete even for the class of trees of maximum degree at most 16. To the best of our knowledge, the only known result in this direction is that the tree search problem is solvable in O(|V| log|V|) time for trees with degree at most 2 (paths). We match the above complexity results with a tight algorithmic analysis. We first show that a natural greedy algorithm attains a 2-approximation. Furthermore, for the bounded degree instances, we show that any optimal strategy (i.e., one that minimizes the expected number of queries) performs at most O(\Delta(T) (log |V| + log w(T))) queries in the worst case, where w(T) is the sum of the likelihoods of the nodes of T and \Delta(T) is the maximum degree of T. We combine this result with a non-trivial exponential time algorithm to provide an FPTAS for trees with bounded degree

Helping education undergraduates to use appropriate criteria for evaluating accounts of motivation

The aim of the study was to compare students in a control group with those in a treatment group with respect to evaluative comments on psychological accounts of motivation. The treatment group systematically scrutinized the nature and interpretation of evidence that supported different accounts, and the assumptions, logic, coherence and clarity of accounts. Content analysis of 74 scripts (using three categories) showed that the control group students made more assertions than either evidential or evaluative points, whereas the treatment group used evaluative statements as often as they used assertion. The findings provide support for privileging activities that develop understanding of how knowledge might be contested, and suggest a need for further research on pedagogies to serve this end. The idea is considered that such understanding has a pivotal role in the development of critical thinking

Social presence in the 21st Century: an adjustment to the Community of Inquiry framework

The Community of Inquiry framework, originally proposed by Garrison, Anderson and Archer (2000) identifies teaching, social and cognitive presences as central to a successful online educational experience. This article presents the findings of a study conducted in Uruguay between 2007 and 2010. The research aimed to establish the role of cognitive, social and teaching presences in the professional development of 40 English language teachers on Continuous Professional Development (CPD) programmes delivered in blended learning settings. The findings suggest that teaching presence and cognitive presence have themselves 'become social'. The research points to social presence as a major lever for engagement, sense-making and peer support. Based on the patterns identified in the study, this article puts forward an adjustment to the Community of Inquiry framework, which shows social presence as more prominent within the teaching and cognitive constructs than the original version of the framework suggests

Current and future management of non-tuberculous mycobacterial pulmonary disease (NTM-PD) in the UK

A rising number of non-tuberculous mycobacterial (NTM) isolates are being identified in UK clinical practice. There are many uncertainties around the management of non-tuberculous mycobacterial pulmonary disease (NTM-PD), including its epidemiology, diagnosis, treatment and prevention. Regional variations in how patients with NTM-PD are managed reflects the lack of standardised pathways in the UK. Service optimisation and multidisciplinary working can improve the quality of care for patients with NTM-PD, including (1) better identification of patients at risk of NTM-PD and modification of risk factors where applicable; (2) standardisation of reference laboratory testing to offer clinicians access to accurate and prompt information on NTM species and drug sensitivities; (3) development of recognised specialist NTM nursing care; (4) standardisation of NTM-PD imaging strategies for monitoring of treatment and disease progression; (5) establishment of a hub-and-spoke model of care, including clear referral and management pathways, dedicated NTM-PD multidisciplinary teams, and long-term patient follow-up; (6) formation of clinical networks to link experts who manage diseases associated with NTM; (7) enabling patients to access relevant support groups that can provide information and support for their condition; and (8) development of NTM research groups to allow patient participation in clinical trials and to facilitate professional education