Ologs: a Categorical Framework for Knowledge Representation
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Artificial Intelligence in Health Care: the Hope, the Hype, the Promise, the Peril
Artificial Intelligence in Health Care: The Hope, the Hype, the Promise, the Peril Michael Matheny, Sonoo Thadaney Israni, Mahnoor Ahmed, and Danielle Whicher, Editors WASHINGTON, DC NAM.EDU PREPUBLICATION COPY - Uncorrected Proofs NATIONAL ACADEMY OF MEDICINE • 500 Fifth Street, NW • WASHINGTON, DC 20001 NOTICE: This publication has undergone peer review according to procedures established by the National Academy of Medicine (NAM). Publication by the NAM worthy of public attention, but does not constitute endorsement of conclusions and recommendationssignifies that it is the by productthe NAM. of The a carefully views presented considered in processthis publication and is a contributionare those of individual contributors and do not represent formal consensus positions of the authors’ organizations; the NAM; or the National Academies of Sciences, Engineering, and Medicine. Library of Congress Cataloging-in-Publication Data to Come Copyright 2019 by the National Academy of Sciences. All rights reserved. Printed in the United States of America. Suggested citation: Matheny, M., S. Thadaney Israni, M. Ahmed, and D. Whicher, Editors. 2019. Artificial Intelligence in Health Care: The Hope, the Hype, the Promise, the Peril. NAM Special Publication. Washington, DC: National Academy of Medicine. PREPUBLICATION COPY - Uncorrected Proofs “Knowing is not enough; we must apply. Willing is not enough; we must do.” --GOETHE PREPUBLICATION COPY - Uncorrected Proofs ABOUT THE NATIONAL ACADEMY OF MEDICINE The National Academy of Medicine is one of three Academies constituting the Nation- al Academies of Sciences, Engineering, and Medicine (the National Academies). The Na- tional Academies provide independent, objective analysis and advice to the nation and conduct other activities to solve complex problems and inform public policy decisions. -
Graph-Based Reasoning in Collaborative Knowledge Management for Industrial Maintenance Bernard Kamsu-Foguem, Daniel Noyes
Graph-based reasoning in collaborative knowledge management for industrial maintenance Bernard Kamsu-Foguem, Daniel Noyes To cite this version: Bernard Kamsu-Foguem, Daniel Noyes. Graph-based reasoning in collaborative knowledge manage- ment for industrial maintenance. Computers in Industry, Elsevier, 2013, Vol. 64, pp. 998-1013. 10.1016/j.compind.2013.06.013. hal-00881052 HAL Id: hal-00881052 https://hal.archives-ouvertes.fr/hal-00881052 Submitted on 7 Nov 2013 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Open Archive Toulouse Archive Ouverte (OATAO) OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in: http://oatao.univ-toulouse.fr/ Eprints ID: 9587 To link to this article: doi.org/10.1016/j.compind.2013.06.013 http://www.sciencedirect.com/science/article/pii/S0166361513001279 To cite this version: Kamsu Foguem, Bernard and Noyes, Daniel Graph-based reasoning in collaborative knowledge management for industrial -
Double Categories of Open Dynamical Systems (Extended Abstract)
Double Categories of Open Dynamical Systems (Extended Abstract) David Jaz Myers Johns Hopkins University A (closed) dynamical system is a notion of how things can be, together with a notion of how they may change given how they are. The idea and mathematics of closed dynamical systems has proven incredibly useful in those sciences that can isolate their object of study from its environment. But many changing situations in the world cannot be meaningfully isolated from their environment – a cell will die if it is removed from everything beyond its walls. To study systems that interact with their environment, and to design such systems in a modular way, we need a robust theory of open dynamical systems. In this extended abstract, we put forward a general definition of open dynamical system. We define two general sorts of morphisms between these systems: covariant morphisms which include trajectories, steady states, and periodic orbits; and contravariant morphisms which allow for plugging variables of some systems into parameters of other systems. We define an indexed double category of open dynamical systems indexed by their interface and use a double Grothendieck construction to construct a double category of open dynamical systems. In our main theorem, we construct covariantly representable indexed double functors from the indexed double category of dynamical systems to an indexed double category of spans. This shows that all covariantly representable structures of dynamical systems — including trajectories, steady states, and periodic orbits — compose according to the laws of matrix arithmetic. 1 Open Dynamical Systems The notion of a dynamical system pervades mathematical modeling in the sciences. -
Applied Category Theory for Genomics – an Initiative
Applied Category Theory for Genomics { An Initiative Yanying Wu1,2 1Centre for Neural Circuits and Behaviour, University of Oxford, UK 2Department of Physiology, Anatomy and Genetics, University of Oxford, UK 06 Sept, 2020 Abstract The ultimate secret of all lives on earth is hidden in their genomes { a totality of DNA sequences. We currently know the whole genome sequence of many organisms, while our understanding of the genome architecture on a systematic level remains rudimentary. Applied category theory opens a promising way to integrate the humongous amount of heterogeneous informations in genomics, to advance our knowledge regarding genome organization, and to provide us with a deep and holistic view of our own genomes. In this work we explain why applied category theory carries such a hope, and we move on to show how it could actually do so, albeit in baby steps. The manuscript intends to be readable to both mathematicians and biologists, therefore no prior knowledge is required from either side. arXiv:2009.02822v1 [q-bio.GN] 6 Sep 2020 1 Introduction DNA, the genetic material of all living beings on this planet, holds the secret of life. The complete set of DNA sequences in an organism constitutes its genome { the blueprint and instruction manual of that organism, be it a human or fly [1]. Therefore, genomics, which studies the contents and meaning of genomes, has been standing in the central stage of scientific research since its birth. The twentieth century witnessed three milestones of genomics research [1]. It began with the discovery of Mendel's laws of inheritance [2], sparked a climax in the middle with the reveal of DNA double helix structure [3], and ended with the accomplishment of a first draft of complete human genome sequences [4]. -
Artificial Consciousness and the Consciousness-Attention Dissociation
Consciousness and Cognition 45 (2016) 210–225 Contents lists available at ScienceDirect Consciousness and Cognition journal homepage: www.elsevier.com/locate/concog Review article Artificial consciousness and the consciousness-attention dissociation ⇑ Harry Haroutioun Haladjian a, , Carlos Montemayor b a Laboratoire Psychologie de la Perception, CNRS (UMR 8242), Université Paris Descartes, Centre Biomédical des Saints-Pères, 45 rue des Saints-Pères, 75006 Paris, France b San Francisco State University, Philosophy Department, 1600 Holloway Avenue, San Francisco, CA 94132 USA article info abstract Article history: Artificial Intelligence is at a turning point, with a substantial increase in projects aiming to Received 6 July 2016 implement sophisticated forms of human intelligence in machines. This research attempts Accepted 12 August 2016 to model specific forms of intelligence through brute-force search heuristics and also reproduce features of human perception and cognition, including emotions. Such goals have implications for artificial consciousness, with some arguing that it will be achievable Keywords: once we overcome short-term engineering challenges. We believe, however, that phenom- Artificial intelligence enal consciousness cannot be implemented in machines. This becomes clear when consid- Artificial consciousness ering emotions and examining the dissociation between consciousness and attention in Consciousness Visual attention humans. While we may be able to program ethical behavior based on rules and machine Phenomenology learning, we will never be able to reproduce emotions or empathy by programming such Emotions control systems—these will be merely simulations. Arguments in favor of this claim include Empathy considerations about evolution, the neuropsychological aspects of emotions, and the disso- ciation between attention and consciousness found in humans. -
Knowledge Representation in Bicategories of Relations
Knowledge Representation in Bicategories of Relations Evan Patterson Department of Statistics, Stanford University Abstract We introduce the relational ontology log, or relational olog, a knowledge representation system based on the category of sets and relations. It is inspired by Spivak and Kent’s olog, a recent categorical framework for knowledge representation. Relational ologs interpolate between ologs and description logic, the dominant formalism for knowledge representation today. In this paper, we investigate relational ologs both for their own sake and to gain insight into the relationship between the algebraic and logical approaches to knowledge representation. On a practical level, we show by example that relational ologs have a friendly and intuitive—yet fully precise—graphical syntax, derived from the string diagrams of monoidal categories. We explain several other useful features of relational ologs not possessed by most description logics, such as a type system and a rich, flexible notion of instance data. In a more theoretical vein, we draw on categorical logic to show how relational ologs can be translated to and from logical theories in a fragment of first-order logic. Although we make extensive use of categorical language, this paper is designed to be self-contained and has considerable expository content. The only prerequisites are knowledge of first-order logic and the rudiments of category theory. 1. Introduction arXiv:1706.00526v2 [cs.AI] 1 Nov 2017 The representation of human knowledge in computable form is among the oldest and most fundamental problems of artificial intelligence. Several recent trends are stimulating continued research in the field of knowledge representation (KR). -
Automatic Knowledge Retrieval from the Web
Automatic Knowledge Retrieval from the Web Marcin Skowron and Kenji Araki Graduate School of Information Science and Technology, Hokkaido University, Kita-ku Kita 14-jo Nishi 8-chome, 060–0814 Sapporo, Japan Abstract. This paper presents the method of automatic knowledge retrieval from the web. The aim of the system that implements it, is to automatically create entries to a knowledge database, similar to the ones that are being provided by the volunteer contributors. As only a small fraction of the statements accessible on the web can be treated as valid knowledge concepts we considered the method for their filtering and verification, based on the similarity measurements with the concepts found in the manually created knowledge database. The results demonstrate that the system can retrieve valid knowledge concepts both for topics that are described in the manually created database, as well as the ones that are not covered there. 1 Introduction Despite the years of research in the field of Artificial Intelligence, the creation of a machine with the ability to think is still far from realization. Although computer systems are capable of performing several complicated tasks that require human beings to extensively use their thinking capabilities, machines still cannot engage into really meaningful conversation or understand what people talk about. One of the main unresolved problems is the lack of machine usable knowledge. Without it, machines cannot reason about the everyday world in a similar way to human beings. In the last decade we have witnessed a few attempts to create knowledge databases using various approaches: man- ual, machine learning and mass collaboration of volunteer contributors. -
Computability and Complexity
Computability and Complexity Lecture Notes Herbert Jaeger, Jacobs University Bremen Version history Jan 30, 2018: created as copy of CC lecture notes of Spring 2017 Feb 16, 2018: cleaned up font conversion hickups up to Section 5 Feb 23, 2018: cleaned up font conversion hickups up to Section 6 Mar 15, 2018: cleaned up font conversion hickups up to Section 7 Apr 5, 2018: cleaned up font conversion hickups up to the end of these lecture notes 1 1 Introduction 1.1 Motivation This lecture will introduce you to the theory of computation and the theory of computational complexity. The theory of computation offers full answers to the questions, • what problems can in principle be solved by computer programs? • what functions can in principle be computed by computer programs? • what formal languages can in principle be decided by computer programs? Full answers to these questions have been found in the last 70 years or so, and we will learn about them. (And it turns out that these questions are all the same question). The theory of computation is well-established, transparent, and basically simple (you might disagree at first). The theory of complexity offers many insights to questions like • for a given problem / function / language that has to be solved / computed / decided by a computer program, how long does the fastest program actually run? • how much memory space has to be used at least? • can you speed up computations by using different computer architectures or different programming approaches? The theory of complexity is historically younger than the theory of computation – the first surge of results came in the 60ties of last century. -
Category Theory and Cyber Physical Systems
Category theory and Cyber physical systems Eswaran Subrahmanian (CMU/NIST) Spencer Breiner (NIST) July 22, 2017 CPS workshop Robert Bosch Center for Cyber Physical Systems IISC Bangalore, India Talk outline • Basic elements of CPS • CPS as composition of different systems • Category theory • A formalism for representing different formalisms • A formalism for composing system from from formalisms. • Ologs • A CT based knowledge representation scheme • Examples of database intergration • Cyber and Physical system and composition. • String diagram for Process composition • Basic elements • Antilock brakes - Top level • Antilock brakes – Expanding The modulator • Redesign for traction control + stability control • Incorporating semantics • Conclusion Cyber physical system: A definition Cyber Physical Systems Interconnected Systems & Control Internet of Things Sensing and Acting Physical Environment Things Person Network Physical World 3 Basic elements and composition of CPS Basic elements • Perceptual devices: Identification and Measurements • Actuating devices: activation results in action • Physical devices: transmission, amplification of power, • Logical devices: computational/logical • Humans devices: mental model Multiple Modeling formalisms: logic, state machines, differential equations, stochastic models, etc. Requires composition and compositionality to ensure desired behavior Category theory • Category Theory (CT) is a potential solution. • CT is the mathematical theory of abstract processes and composition • CT could be thought of as the conceptual operating system. Categories & Composition • A category is a universe of resources (objects) �, �, �, … and processes (arrows) �, �, ℎ, … • Every process has input and output resources, indicated �:�→�. • The main property of categorical processes is that they compose: Category theory: relationship to domains Category Theory as a universal Modeling Language (Spivak, 2015*) The Category Theory (CT) view of modeling – two postulates: 1. -
Diagrammatics in Categorification and Compositionality
Diagrammatics in Categorification and Compositionality by Dmitry Vagner Department of Mathematics Duke University Date: Approved: Ezra Miller, Supervisor Lenhard Ng Sayan Mukherjee Paul Bendich Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics in the Graduate School of Duke University 2019 ABSTRACT Diagrammatics in Categorification and Compositionality by Dmitry Vagner Department of Mathematics Duke University Date: Approved: Ezra Miller, Supervisor Lenhard Ng Sayan Mukherjee Paul Bendich An abstract of a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics in the Graduate School of Duke University 2019 Copyright c 2019 by Dmitry Vagner All rights reserved Abstract In the present work, I explore the theme of diagrammatics and their capacity to shed insight on two trends|categorification and compositionality|in and around contemporary category theory. The work begins with an introduction of these meta- phenomena in the context of elementary sets and maps. Towards generalizing their study to more complicated domains, we provide a self-contained treatment|from a pedagogically novel perspective that introduces almost all concepts via diagrammatic language|of the categorical machinery with which we may express the broader no- tions found in the sequel. The work then branches into two seemingly unrelated disciplines: dynamical systems and knot theory. In particular, the former research defines what it means to compose dynamical systems in a manner analogous to how one composes simple maps. The latter work concerns the categorification of the slN link invariant. In particular, we use a virtual filtration to give a more diagrammatic reconstruction of Khovanov-Rozansky homology via a smooth TQFT. -
Inventing Computational Rhetoric
INVENTING COMPUTATIONAL RHETORIC By Michael W. Wojcik A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Digital Rhetoric and Professional Writing — Master of Arts 2013 ABSTRACT INVENTING COMPUTATIONAL RHETORIC by Michael W. Wojcik Many disciplines in the humanities are developing “computational” branches which make use of information technology to process large amounts of data algorithmically. The field of computational rhetoric is in its infancy, but we are already seeing interesting results from applying the ideas and goals of rhetoric to text processing and related areas. After considering what computational rhetoric might be, three approaches to inventing computational rhetorics are presented: a structural schema, a review of extant work, and a theoretical exploration. Copyright by MICHAEL W. WOJCIK 2013 For Malea iv ACKNOWLEDGEMENTS Above all else I must thank my beloved wife, Malea Powell, without whose prompting this thesis would have remained forever incomplete. I am also grateful for the presence in my life of my terrific stepdaughter, Audrey Swartz, and wonderful granddaughter Lucille. My thesis committee, Dean Rehberger, Bill Hart-Davidson, and John Monberg, pro- vided me with generous guidance and inspiration. Other faculty members at Michigan State who helped me explore relevant ideas include Rochelle Harris, Mike McLeod, Joyce Chai, Danielle Devoss, and Bump Halbritter. My previous academic program at Miami University did not result in a degree, but faculty there also contributed greatly to my the- oretical understanding, particularly Susan Morgan, Mary-Jean Corbett, Brit Harwood, J. Edgar Tidwell, Lori Merish, Vicki Smith, Alice Adams, Fran Dolan, and Keith Tuma. -
Information Extraction Using Natural Language Processing
INFORMATION EXTRACTION USING NATURAL LANGUAGE PROCESSING Cvetana Krstev University of Belgrade, Faculty of Philology Information Retrieval and/vs. Natural Language Processing So close yet so far Outline of the talk ◦ Views on Information Retrieval (IR) and Natural Language Processing (NLP) ◦ IR and NLP in Serbia ◦ Language Resources (LT) in the core of NLP ◦ at University of Belgrade (4 representative resources) ◦ LR and NLP for Information Retrieval and Information Extraction (IE) ◦ at University of Belgrade (4 representative applications) Wikipedia ◦ Information retrieval ◦ Information retrieval (IR) is the activity of obtaining information resources relevant to an information need from a collection of information resources. Searches can be based on full-text or other content-based indexing. ◦ Natural Language Processing ◦ Natural language processing is a field of computer science, artificial intelligence, and computational linguistics concerned with the interactions between computers and human (natural) languages. As such, NLP is related to the area of human–computer interaction. Many challenges in NLP involve: natural language understanding, enabling computers to derive meaning from human or natural language input; and others involve natural language generation. Experts ◦ Information Retrieval ◦ As an academic field of study, Information Retrieval (IR) is finding material (usually documents) of an unstructured nature (usually text) that satisfies an information need from within large collection (usually stored on computers). ◦ C. D. Manning, P. Raghavan, H. Schutze, “Introduction to Information Retrieval”, Cambridge University Press, 2008 ◦ Natural Language Processing ◦ The term ‘Natural Language Processing’ (NLP) is normally used to describe the function of software or hardware components in computer system which analyze or synthesize spoken or written language.