Formally Real Fields

Summary We extend the algebraic theory of ordered fields [7, 6] in Mizar [1, 2, 3]: we show that every preordering can be extended into an ordering, i.e. that formally real and ordered fields coincide.We further prove some characterizations of formally real fields, in particular the one by Artin and Schreier using sums of squares [4]. In the second part of the article we define absolute values and the square root function [5].Institute of Informatics, Faculty of Mathematics, Physics and Informatics, University of Gdansk Wita Stwosza 57, 80-308 Gdansk, PolandGrzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pak, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261-279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi: 10.1007/978-3-319-20615-8 17.Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191-198, 2015. doi: 10.1007/s10817-015-9345-1.Adam Grabowski, Artur Korniłowicz, and Christoph Schwarzweller. On algebraic hierarchies in mathematical repository of Mizar. In M. Ganzha, L. Maciaszek, and M. Paprzycki, editors, Proceedings of the 2016 Federated Conference on Computer Science and Infor mation Systems (FedCSIS), volume 8 of Annals of Computer Science and Information Systems, pages 363-371, 2016. doi: 10.15439/2016F520.Nathan Jacobson. Lecture Notes in Abstract Algebra, III. Theory of Fields and Galois Theory. Springer-Verlag, 1964.Manfred Knebusch and Claus Scheiderer. Einf¨uhrung in die reelle Algebra. Vieweg-Verlag, 1989.Alexander Prestel. Lectures on Formally Real Fields. Springer-Verlag, 1984.Knut Radbruch. Geordnete K¨orper. Lecture Notes, University of Kaiserslautern, Germany, 1991.Christoph Schwarzweller. The binomial theorem for algebraic structures. Formalized Mathematics, 9(3):559-564, 2001.Christoph Schwarzweller. Ordered rings and fields. Formalized Mathematics, 25(1):63-72, 2017. doi: 10.1515/forma-2017-0006.Christoph Schwarzweller. On roots of polynomials and algebraically closed fields. Formalized Mathematics, 25(3):185-195, 2017. doi: 10.1515/forma-2017-0018.Christoph Schwarzweller and Artur Korniłowicz. Characteristic of rings. Prime fields. Formalized Mathematics, 23(4):333-349, 2015. doi: 10.1515/forma-2015-0027.25424925

On potential cognitive abilities in the machine kingdom

The final publication is available at Springer via http://dx.doi.org/10.1007/s11023-012-9299-6Animals, including humans, are usually judged on what they could become, rather than what they are. Many physical and cognitive abilities in the ‘animal kingdom’ are only acquired (to a given degree) when the subject reaches a certain stage of development, which can be accelerated or spoilt depending on how the environment, training or education is. The term ‘potential ability’ usually refers to how quick and likely the process of attaining the ability is. In principle, things should not be different for the ‘machine kingdom’. While machines can be characterised by a set of cognitive abilities, and measuring them is already a big challenge, known as ‘universal psychometrics’, a more informative, and yet more challenging, goal would be to also determine the potential cognitive abilities of a machine. In this paper we investigate the notion of potential cognitive ability for machines, focussing especially on universality and intelligence. We consider several machine characterisations (non-interactive and interactive) and give definitions for each case, considering permanent and temporal potentials. From these definitions, we analyse the relation between some potential abilities, we bring out the dependency on the environment distribution and we suggest some ideas about how potential abilities can be measured. Finally, we also analyse the potential of environments at different levels and briefly discuss whether machines should be designed to be intelligent or potentially intelligent.We thank the anonymous reviewers for their comments, which have helped to significantly improve this paper. This work was supported by the MEC-MINECO projects CONSOLIDER-INGENIO CSD2007-00022 and TIN 2010-21062-C02-02, GVA project PROMETEO/2008/051, the COST - European Cooperation in the field of Scientific and Technical Research IC0801 AT. Finally, we thank three pioneers ahead of their time(s). We thank Ray Solomonoff (1926-2009) and Chris Wallace (1933-2004) for all that they taught us, directly and indirectly. And, in his centenary year, we thank Alan Turing (1912-1954), with whom it perhaps all began.Hernández-Orallo, J.; Dowe, DL. (2013). On potential cognitive abilities in the machine kingdom. Minds and Machines. 23(2):179-210. https://doi.org/10.1007/s11023-012-9299-6S179210232Amari, S., Fujita, N., Shinomoto, S. (1992). Four types of learning curves. Neural Computation 4(4), 605–618.Aristotle (Translation, Introduction, and Commentary by Ross, W.D.) (1924). Aristotle’s Metaphysics. Oxford: Clarendon Press.Barmpalias, G. & Dowe, D. L. (2012). 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Forster (Eds), Handbook of the philosophy of science—Volume 7: Philosophy of statistics (pp. 901–982). Amsterdam: Elsevier.Dowe, D. L. & Hajek, A. R. (1997a). A computational extension to the turing test. Technical report #97/322, Dept Computer Science, Monash University, Melbourne, Australia, 9 pp, http://www.csse.monash.edu.au/publications/1997/tr-cs97-322-abs.html .Dowe, D. L. & Hajek, A. R. (1997b, September). A computational extension to the Turing Test. in Proceedings of the 4th conference of the Australasian Cognitive Science Society, University of Newcastle, NSW, Australia, 9 pp.Dowe, D. L. & Hajek, A. R. (1998, February). A non-behavioural, computational extension to the Turing Test. In: International conference on computational intelligence and multimedia applications (ICCIMA’98), Gippsland, Australia, pp 101–106.Dowe, D. L., Hernández-Orallo, J. (2012). IQ tests are not for machines, yet. Intelligence, 40(2), 77–81.Gallistel, C. R., Fairhurst, S., & Balsam, P. (2004). 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(Eds.), Proceedings of 3rd international conference on artificial general intelligence (pp. 25–30). New York: Atlantis Press.Hernández-Orallo, J., & Dowe, D. L. (2010). Measuring universal intelligence: Towards an anytime intelligence test. Artificial Intelligence, 174(18), 1508–1539.Hernández-Orallo, J. & Dowe, D. L. (2011, April). Mammals, machines and mind games. Who’s the smartest?. The conversation, http://theconversation.edu.au/mammals-machines-and-mind-games-whos-the-smartest-566 .Hernández-Orallo J., Dowe D. L., España-Cubillo S., Hernández-Lloreda M. V., & Insa-Cabrera J. (2011). On more realistic environment distributions for defining, evaluating and developing intelligence. In: J. Schmidhuber, K. R. Thórisson, & M. Looks (Eds.), Artificial general intelligence 2011, volume 6830, LNAI series, pp. 82–91. New York: Springer.Hernández-Orallo, J., Dowe, D. L., & Hernández-Lloreda, M. V. (2012a, March). 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On environment difficulty and discriminating power

The final publication is available at Springer via http://dx.doi.org/10.1007/s10458-014-9257-1This paper presents a way to estimate the difficulty and discriminating power of any task instance. We focus on a very general setting for tasks: interactive (possibly multiagent) environments where an agent acts upon observations and rewards. Instead of analysing the complexity of the environment, the state space or the actions that are performed by the agent, we analyse the performance of a population of agent policies against the task, leading to a distribution that is examined in terms of policy complexity. This distribution is then sliced by the algorithmic complexity of the policy and analysed through several diagrams and indicators. The notion of environment response curve is also introduced, by inverting the performance results into an ability scale. We apply all these concepts, diagrams and indicators to two illustrative problems: a class of agent-populated elementary cellular automata, showing how the difficulty and discriminating power may vary for several environments, and a multiagent system, where agents can become predators or preys, and may need to coordinate. Finally, we discuss how these tools can be applied to characterise (interactive) tasks and (multi-agent) environments. These characterisations can then be used to get more insight about agent performance and to facilitate the development of adaptive tests for the evaluation of agent abilities.I thank the reviewers for their comments, especially those aiming at a clearer connection with the field of multi-agent systems and the suggestion of better approximations for the calculation of the response curves. The implementation of the elementary cellular automata used in the environments is based on the library 'CellularAutomaton' by John Hughes for R [58]. I am grateful to Fernando Soler-Toscano for letting me know about their work [65] on the complexity of 2D objects generated by elementary cellular automata. I would also like to thank David L. Dowe for his comments on a previous version of this paper. This work was supported by the MEC/MINECO projects CONSOLIDER-INGENIO CSD2007-00022 and TIN 2010-21062-C02-02, GVA project PROMETEO/2008/051, the COST - European Cooperation in the field of Scientific and Technical Research IC0801 AT, and the REFRAME project, granted by the European Coordinated Research on Long-term Challenges in Information and Communication Sciences & Technologies ERA-Net (CHIST-ERA), and funded by the Ministerio de Economia y Competitividad in Spain (PCIN-2013-037).José Hernández-Orallo (2015). On environment difficulty and discriminating power. Autonomous Agents and Multi-Agent Systems. 29(3):402-454. https://doi.org/10.1007/s10458-014-9257-1S402454293Anderson, J., Baltes, J., & Cheng, C. T. (2011). 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(Ed.), 3rd International Conference on Artificial General Intelligence (pp. 182–183). Atlantis Press Extended report at http://users.dsic.upv.es/proy/anynt/unbiased.pdf .Hernández-Orallo, J., & Dowe, D. L. (2010). Measuring universal intelligence: Towards an anytime intelligence test. Artificial Intelligence, 174(18), 1508–1539.Hernández-Orallo, J., Dowe, D. L., España-Cubillo, S., Hernández-Lloreda, M. V., & Insa-Cabrera, J. (2011). On more realistic environment distributions for defining, evaluating and developing intelligence. In J. Schmidhuber, K. R. Thórisson, & M. Looks (Eds.), LNAI series on artificial general intelligence 2011 (Vol. 6830, pp. 82–91). Berlin: Springer.Hernández-Orallo, J., Dowe, D. L., & Hernández-Lloreda, M. V. (2014). Universal psychometrics: Measuring cognitive abilities in the machine kingdom. Cognitive Systems Research, 27, 50–74.Hernández-Orallo, J., Insa, J., Dowe, D. L. & Hibbard, B. (2012). Turing tests with turing machines. In A. 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Using Noninvasive Brain Measurement to Explore the Psychological Effects of Computer Malfunctions on Users during Human-Computer Interactions

In today’s technologically driven world, there is a need to better understand the ways that common computer malfunctions affect computer users. These malfunctions may have measurable influences on computer user’s cognitive, emotional, and behavioral responses. An experiment was conducted where participants conducted a series of web search tasks while wearing functional nearinfrared spectroscopy (fNIRS) and galvanic skin response sensors. Two computer malfunctions were introduced during the sessions which had the potential to influence correlates of user trust and suspicion. Surveys were given after each session to measure user’s perceived emotional state, cognitive load, and perceived trust. Results suggest that fNIRS can be used to measure the different cognitive and emotional responses associated with computer malfunctions. These cognitive and emotional changes were correlated with users’ self-report levels of suspicion and trust, and they in turn suggest future work that further explores the capability of fNIRS for the measurement of user experience during human-computer interactions

Robot Autonomy for Surgery

Autonomous surgery involves having surgical tasks performed by a robot operating under its own will, with partial or no human involvement. There are several important advantages of automation in surgery, which include increasing precision of care due to sub-millimeter robot control, real-time utilization of biosignals for interventional care, improvements to surgical efficiency and execution, and computer-aided guidance under various medical imaging and sensing modalities. While these methods may displace some tasks of surgical teams and individual surgeons, they also present new capabilities in interventions that are too difficult or go beyond the skills of a human. In this chapter, we provide an overview of robot autonomy in commercial use and in research, and present some of the challenges faced in developing autonomous surgical robots

Review of research in feature-based design

Research in feature-based design is reviewed. Feature-based design is regarded as a key factor towards CAD/CAPP integration from a process planning point of view. From a design point of view, feature-based design offers possibilities for supporting the design process better than current CAD systems do. The evolution of feature definitions is briefly discussed. Features and their role in the design process and as representatives of design-objects and design-object knowledge are discussed. The main research issues related to feature-based design are outlined. These are: feature representation, features and tolerances, feature validation, multiple viewpoints towards features, features and standardization, and features and languages. An overview of some academic feature-based design systems is provided. Future research issues in feature-based design are outlined. The conclusion is that feature-based design is still in its infancy, and that more research is needed for a better support of the design process and better integration with manufacturing, although major advances have already been made

IMPROVING THE DEPENDABILITY OF DESTINATION RECOMMENDATIONS USING INFORMATION ON SOCIAL ASPECTS

Prior knowledge of the social aspects of prospective destinations can be very influential in making travel destination decisions, especially in instances where social concerns do exist about specific destinations. In this paper, we describe the implementation of an ontology-enabled Hybrid Destination Recommender System (HDRS) that leverages an ontological description of five specific social attributes of major Nigerian cities, and hybrid architecture of content-based and case-based filtering techniques to generate personalised top-n destination recommendations. An empirical usability test was conducted on the system, which revealed that the dependability of recommendations from Destination Recommender Systems (DRS) could be improved if the semantic representation of social attributes information of destinations is made a factor in the destination recommendation process

A guided tour of asynchronous cellular automata

Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat