A Case of Fibroma of the Ovary.*

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Using Proof-Planning to Investigate the Structure of Proof in Non-Standard Analysis

Centre for Intelligent Systems and their Applicationsaward number 99303126This thesis presents an investigation into the structure of proof in non-standard analysis using proof-planning. The theory of non-standard analysis, developed by Robinson in the 1960s, offers a more algebraic way of looking at proof in analysis. Proof-planning is a technique for reasoning about proof at the meta-level. In this thesis, we use it to encapsulate the patterns of reasoning that occur in non-standard analysis proofs. We first introduce in detail the mathematical theory and the proof-planning architecture. We then present our research methodology, describe the formal framework, which includes an axiomatisation, and develop suitable evaluation criteria. We then present our development of proof-plans for theorems involving limits, continuity and differentiation. We then explain how proof-planning applies to theorems which combine induction and non-standard analysis. Finally we give a detailed evaluation of the results obtained by combining the two attractive approaches of proof-planning and non-standard analysis, and draw conclusions from the work

The Search for Computational Intelligence

We define and explore in simulation several rules for the local evolution of generative rules for 1D and 2D cellular automata. Our implementation uses strategies from conceptual blending. We discuss potential applications to modelling social dynamics.Comment: 8 pages. Submitted to Social Aspects of Cognition and Computing symposium at AISB 201

ASP, amalgamation, and the conceptual blending workflow

We present a framework for conceptual blending – a concept invention method that is advocated in cognitive science as a fundamental, and uniquely human engine for creative thinking. Herein, we employ the search capabilities of ASP to find commonalities among input concepts as part of the blending process, and we show how our approach fits within a generalised conceptual blending workflow. Specifically, we orchestrate ASP with imperative Python programming, to query external tools for theorem proving and colimit computation. We exemplify our approach with an example of creativity in mathematics. © Springer International Publishing Switzerland 2015.This work is supported by the 7th Framework Programme for Research of the European Commission funded COINVENT project (FET-Open grant number: 611553). M. Eppe is supported by the German Academic Exchange ServicePeer Reviewe

Proof planning Non-standard Analysis

This paper presents work carried out in the Clam proof-planner (Richardson et al. 00) on automating mathematical proofs using induction and non-standard analysis. The central idea is to show that the proofs we present are well-suited to proof-planning, due to their shared common structure. The theorems presented in this paper belong to standard analysis, and have been proved using induction and techniques from non-standard analysis. We rst give an overview of the proof-planning paradigm, giving a brief exposition of rippling as a heuristic for guiding rewriting. We then present the basic notions of non-standard analysis and explain our axiomatisation. We then go on to explain the theorems we intend to prove and sketch their proofs. Finally we show the parts of the proofs which have been planned automatically in Clam and draw some conclusions from the work completed so fa

Automating Event-B invariant proofs by rippling and proof patching

This work is supported by EPSRC grants EP/H024204/1, EP/E005713/1, EP/M018407/1 and EP/J001058/1.The use of formal method techniques can contribute to the production of more reliable and dependable systems. However, a common bottleneck for industrial adoption of such techniques is the needs for interactive proofs. We use a popular formal method, called Event-B, as our working domain, and set invariant preservation (INV) proofs as targets, because INV proofs can account for a significant proportion of the proofs requiring human interactions. We apply an inductive theorem proving technique, called rippling, for Event-B INV proofs. Rippling automates proofs using meta-level guidance. The guidance is in particular useful to develop proof patches to recover failed proof attempts. We are interested in the case when a missing lemma is required. We combine a scheme-based theory-exploration system, called IsaScheme [MRMDB10], with rippling to develop a proof patch via lemma discovery. We also develop two new proof patches to unfold operator definitions and to suggest case-splits, respectively. The combined use of rippling with these three proof patches as a proof method significantly improves the proof automation for our evaluation set.Publisher PDFPeer reviewe

Health and wellbeing outcomes of programs for Indigenous Australians that include strategies to enable the expression of cultural identities: a systematic review

Indigenous people have long maintained that strong cultural identities are critical to health and wellbeing. The purpose of this systematic review is to examine whether interventions that entail strategies to enable expression of cultural identities for Australian Indigenous peoples are associated with measurable improvements in health and wellbeing. Peer-reviewed articles that reported quantitatively expressed health and wellbeing outcomes involving Indigenous Australian participants only were included. The cultural intervention component was defined and assessed by Indigenous researchers on the team. A narrative analysis was conducted. The protocol was registered on PROSPERO (CRD42015027387). Thirteen articles describing eleven studies were identified, including one randomised control trial (RCT), one cluster RCT and two studies with non-randomised controls. Other studies reported on case series or cross-sectional studies. All except two studies described multiple intervention strategies. Eight studies showed significant improvement in at least one psychosocial, behavioural or clinical measure, with two showing a positive direction of effect and one showing no improvement. Publication bias may discourage researchers to report negative findings of these interventions. Although studies vary in quality, this review provides evidence that interventions that include opportunities for expression of cultural identities can have beneficial effects for Australian Indigenous peoples