There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

What is modal logic

The aim of this paper is to summarize and analyze some results obtained in 2000-2001 about decidable and undecidable fragments of various first-order temporal logics, give some applications in the field of knowledge representation and reasoning, and attract the attention of the 'temporal community' to a number of interesting open problems.

Monodic fragments of first-order temporal logics: 2000-2001 A.D

Classification is one of the most researched questions in machine learning and data mining. A wide range of real problems have been stated as classification problems, for example credit scoring, bankruptcy prediction, medical diagnosis, pattern recognition, text categorization, software quality assessment, and many more. The use of evolutionary algorithms for training classifiers has been studied in the past few decades. Genetic programming (GP) is a flexible and powerful evolutionary technique with some features that can be very valuable and suitable for the evolution of classifiers. This paper surveys existing literature about the application of genetic programming to classification, to show the different ways in which this evolutionary algorithm can help in the construction of accurate and reliable classifiers.

A Survey on the Application of Genetic Programming to Classification

Qualitative spatial reasoning using constraint calculi

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Relation Algebras by Games

Metro railway safety: An analysis of accident precursors

A boolean algebra is shown to be completely representable if and only if it is atomic, whereas it is shown that neither the class of completely representable relation algebras nor the class of completely representable cylindric algebras of any fixed dimension (at least 3) are elementary.

Complete representations in algebraic logic

Fatalities due to railway accidents occur rarely and some railways identify risks from potential accident precursors. By lowering precursor frequency, the probability of more serious incidents and accidents may be reduced, following the idea of a reverse pyramid between precursors, top events, injuries and deaths. To assist in reducing such risks, a new safety maturity model (SMM) is proposed which aims to address not only the behavioural and/or attitudinal culture, but also technical, operational and methodological elements and actual achievements in terms of safety outcomes.This paper outlines the results of precursor analysis from 18 CoMET and Nova railways, all but two of which are metro (subway) operations, the other two being commuter railways. One of the commuter railways has mixed traffic including freight and long distance passenger trains, while four of the metro railways share lines with longer distance railways.The paper analyses precursors, top events, injuries and deaths as well as safety maturity and their relationships both to each other and to incidents and accidents for the set of the major global metro railways. The 27 precursors analysed, for the period 2002-2009, fall into six categories: human performance; technical failures; passengers; fires; malicious action and management action.To assess safety maturity, a model was developed based upon literature and metro experience. A questionnaire assessed the following safety maturity criteria for each metro: publication of safety reports; periodicity of safety monitoring; prioritisation of safety related incidents; efforts to mitigate risks and avoid incidents; description of safety procedures and monitoring of residual risks. The responses of each metro were scored to determine its aggregate safety maturity level.Statistical analysis indicates a positive correlation between injuries and top events as well as between injuries and precursors. The safety maturity score is correlated with injuries but not with precursors, top events or fatalities. Using these results, this paper proposes a number of measures to improve metro railways safety in each precursor category.

Metro Railway Safety: An Analysis of Accident Precursors

We consider the problem of finding and classifying representations in algebraic logic. This is approached by letting two players build a representation using a game. Homogeneous and universal representations are characterized according to the outcome of certain games. The Lyndon conditions defining representable relation algebras (for the finite case) and a similar schema for cylindric algebras are derived. Finte relation algebras with homogeneous representations are characterized by first order formulas. Equivalence games are defined, and are used to establish whether an algebra is ω-categorical. We have a simple proof that the perfect extension of a representable relation algebra is completely representable.An important open problem from algebraic logic is addressed by devising another two-player game, and using it to derive equational axiomatisations for the classes of all representable relation algebras and representable cylindric algebras.Other instances of this approach are looked at, and include the step by step method.

Robin Hirsch

Papers

Relation Algebras by Games

Metro railway safety: An analysis of accident precursors

Complete representations in algebraic logic

Metro Railway Safety: An Analysis of Accident Precursors

Step by step – Building representations in algebraic logic