The Role of Abductive Reasoning in Cognitive-Based Assessment
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Complexity Classifications for Propositional Abduction in Post's
Complexity Classifications for Propositional Abduction in Post’s Framework∗ Nadia Creignou1, Johannes Schmidt1, Michael Thomas2 1 LIF, UMR CNRS 6166, Aix-Marseille Universit´e 163, Avenue de Luminy, 13288 Marseille Cedex 9, France [email protected] [email protected] 2 Institut f¨ur Theoretische Informatik, Gottfried Wilhelm Leibniz Universit¨at Appelstr. 4, 30167 Hannover, Germany [email protected] Abstract. In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world’s behavior it aims at finding an explanation for some observed manifestation. In this paper we consider propositional abduction, where the knowledge base and the manifesta- tion are represented by propositional formulae. The problem of deciding p whether there exists an explanation has been shown to be Σ2 -complete in general. We focus on formulae in which the allowed connectives are taken from certain sets of Boolean functions. We consider different vari- ants of the abduction problem in restricting both the manifestations and the hypotheses. For all these variants we obtain a complexity classifica- tion for all possible sets of Boolean functions. In this way, we identify easier cases, namely NP-complete, coNP-complete and polynomial cases. Thus, we get a detailed picture of the complexity of the propositional abduction problem, hence highlighting sources of intractability. Further, we address the problem of counting the explanations and draw a com- plete picture for the counting complexity. Keywords: abduction, computational complexity, Post’s lattice, propo- sitional logic, boolean connective arXiv:1006.4923v1 [cs.CC] 25 Jun 2010 ∗ Supported by ANR Algorithms and complexity 07-BLAN-0327-04 and DFG grant VO 630/6-1. -
The Pragmatic Origins of Critical Thinking
The Pragmatic Origins of Critical Thinking Abstract Because of the ancient origins of many aspects of critical-thinking, notably logic and language skills that can be traced to traditional rhetoric, it is easy to perceive of the concept of critical thinking itself as also being ancient, or at least pre-modern. Yet the notion that there exists a form of thinking distinct from other mental qualities such as intelligence and wisdom, one unique enough to be termed “critical,” is a twentieth-century construct, one that can be traced to a specific philosophical tradition: American Pragmatism. Pragmatism Pragmatism is considered the only major Western philosophical tradition whose geographical origin was not in Europe but the United States. Just as other schools of philosophy can be traced to a single individual (such as Phenomenology, the invention of which is generally credited to Germany’s Edmund Husserl), Pragmatism has its origin in the work of the nineteenth and early twentieth century American philosopher Charles Sanders Peirce. Son of Harvard professor of astronomy and mathematics Benjamin Peirce, Charles was trained in logic, science and mathematics at a young age in the hope that he would eventually grow to become America’s answer to Immanuel Kant. In spite of this training (or possibly because of it) Peirce grew to be a prickly and irascible adult (although some of his dispositions may have also been a result of physical ailments, as well as 1 likely depression). His choice to live with the woman who would become his second wife before legally divorcing his first cost him a teaching position at Johns Hopkins University, and the enmity of powerful academics, notably Harvard President Charles Elliot who repeatedly refused Peirce a teaching position there, kept him from the academic life that might have given him formal outlets for his prodigious work in philosophy, mathematics and science. -
Abduction, Reason, and Science Abduction, Reason, and Science Processes of Discovery and Explanation
Abduction, Reason, and Science Abduction, Reason, and Science Processes of Discovery and Explanation Lorenzo Magnani University of Pavia Pavia, Italy, and Georgia Institute of Technology Atlanta, Georgia Springer Science+Business Media, LLC Library of Congress Cataloging-in-Publication Data Magnani, Lorenzo Abduction, reason, and ,cience: processes of discovcry and explanation/Lorenzo Magnani. p. cm. IncIudes bibliographical references and index. ISBN 978-1-4613-4637-1 ISBN 978-1-4419-8562-0 (eBook) DOI 10.1007/978-1-4419-8562-0 1. Science-Philosophy. 2. Abduction (Logic). 3. Discoveries in science. I. Tirle. Q175.32.A24 M34 2001 501-dc21 00-052061 Front cover: Descartes's explanation of the rainbow (from his Meteora, 1656). ISBN 978-1-4613-4637-1 © 2001 Springer Science+Business Media New York Originally published by Kluwer Academic / Plenum Publishers, New York in 2001 Softcover reprint of the hardcover 1st edition 1990 http://www.wkap.nl/ 1098765432 A c.I.P. record for this book is available from the Library of Congress. AII rights reserved No par! of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without wrilten permis sion from the Publisher To my daughter Giovanna Science does not rest upon solid bedrock. The bold structure of its theories rises, as it were, above a swamp. It is like a building erected on piles. The piles are driven down from above into the swamp, but not down to any natural or "given" base; and if we stop driving the piles deeper, it is not because we have reached firm ground. -
European Journal of Pragmatism and American Philosophy, X-1 | 2018 Eco and Peirce on Abduction 2
European Journal of Pragmatism and American Philosophy X-1 | 2018 Eco and Pragmatism Eco and Peirce on Abduction Francesco Bellucci Electronic version URL: http://journals.openedition.org/ejpap/1122 DOI: 10.4000/ejpap.1122 ISSN: 2036-4091 Publisher Associazione Pragma Electronic reference Francesco Bellucci, « Eco and Peirce on Abduction », European Journal of Pragmatism and American Philosophy [Online], X-1 | 2018, Online since 20 July 2018, connection on 19 April 2019. URL : http:// journals.openedition.org/ejpap/1122 ; DOI : 10.4000/ejpap.1122 This text was automatically generated on 19 April 2019. Licence Creative Commons Author retains copyright and grants the European Journal of Pragmatism and American Philosophy right of first publication with the work simultaneously licensed under a Creative Commons Attribution- NonCommercial-NoDerivatives 4.0 International License. Eco and Peirce on Abduction 1 Eco and Peirce on Abduction Francesco Bellucci 1 One of the key concepts that Eco took from Peirce is that of “abduction,” or reasoning to an explanatory hypothesis. This concept is central to his foundation of a semiotic or interpretative semantics, one of whose component is a theory of inference, and especially of abductive inference. Though there is probably only one “official” place where Eco expounds his theory of abductive reasoning – the article “Horns, Hooves, and Insteps” in The Sign of Three – yet Eco’s theory is spanned over tens of papers and books, including his fictional books. 2 Eco’s fictional books have often been considered as, to say the least, “profoundly connected” with his scholarly work. But Paolucci has persuasively argued that not only Eco’s philosophical work influenced his fictional work, but also, and more crucially, that his fictional works are an integral part of his philosophy: “[t]he union of the theoretical and nontheoretical works constitute Eco’s philosophical legacy, his ‘philosophy’.” (Paolucci 2017a: 254). -
LOGIC and CRITICAL THINKING: the MISSING LINK in HIGHER EDUCATION in NIGERIA Chinweuba Gregory Emeka
International Journal of History and Philosophical Research Vol.6, No.3, pp.1-13, July 2018 ___Published by European Centre for Research Training and Development UK (www.eajournals.org) LOGIC AND CRITICAL THINKING: THE MISSING LINK IN HIGHER EDUCATION IN NIGERIA Chinweuba Gregory Emeka (Ph.D) and Ezeugwu Evaristus Chukwudi (Ph.D) Philosophy Unit, General Studies Division, Enugu State University of Science and Technology, (ESUT) Enugu. ABSTRACT: Sustainable development and good living condition in the modern world are determined by people who possess more than normal reasoning abilities. The present Nigerian socio-political, economic and technological dilemma therefore results from the redundancy of mind paved by gross deficiency in logic and critical thinking competencies. This deficiency broadly stems from Nigerian poor educational system which has neglected acquisition of reflective and critical reasoning skills in theoretical and practical terms. This hampers critical competence, and results to irrational judgments, biased policies and dishonest governance. Consequently, problem solving and critical competence in various sectors of Nigerian existence have remained a mirage resulting to unsustainable development. This paper analytically investigates the meaning, cradle, essence, relevance and state of logic and critical thinking in Nigerian higher education and existence. The research finds that logic and critical thinking has been negligently relegated to one of those optional General Studies’ courses rarely needed to make up the required credit load. As such, not every department of education in Nigeria offers logic and critical thinking. This is coupled with the fact that in some Nigerian Higher Institutions, logic and critical thinking is managed by unqualified staff. The paper as well finds that knowledge of logic and critical thinking is indispensable in the daily human expressions, decisions, right choices and actions. -
Leibniz on China and Christianity: the Reformation of Religion and European Ethics Through Converting China to Christianity
Bard College Bard Digital Commons Senior Projects Spring 2016 Bard Undergraduate Senior Projects Spring 2016 Leibniz on China and Christianity: The Reformation of Religion and European Ethics through Converting China to Christianity Ela Megan Kaplan Bard College, [email protected] Follow this and additional works at: https://digitalcommons.bard.edu/senproj_s2016 Part of the European History Commons This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License. Recommended Citation Kaplan, Ela Megan, "Leibniz on China and Christianity: The Reformation of Religion and European Ethics through Converting China to Christianity" (2016). Senior Projects Spring 2016. 279. https://digitalcommons.bard.edu/senproj_s2016/279 This Open Access work is protected by copyright and/or related rights. It has been provided to you by Bard College's Stevenson Library with permission from the rights-holder(s). You are free to use this work in any way that is permitted by the copyright and related rights. For other uses you need to obtain permission from the rights- holder(s) directly, unless additional rights are indicated by a Creative Commons license in the record and/or on the work itself. For more information, please contact [email protected]. Leibniz on China and Christianity: The Reformation of Religion and European Ethics through Converting China to Christianity Senior Project submitted to The Division of Social Studies Of Bard College by Ela Megan Kaplan Annandale-on-Hudson, New York May 2016 5 Acknowledgements I would like to thank my mother, father and omniscient advisor for tolerating me for the duration of my senior project. -
Critical Thinking: Intellectual Standards Essential to Reasoning Well Within Every Domain of Human Thought, Part Two
Critical Thinking: Intellectual Standards Essential to Reasoning Well Within Every Domain of Human Thought, Part Two By Richard Paul and Linda Elder In our last critical thinking column we introduced the idea of intellectual • I hear you saying “___.” Am I hearing you correctly, or have I misun- standards and pointed out that all natural languages are repositories for such derstood you? standards, which, when appropriately applied, serve as guides for assessing Accuracy: free from errors, mistakes or distortions; true, correct. human reasoning. We argued that intellectual standards are necessary for A statement can be clear but not accurate, as in “Most dogs weigh more cultivating the intellect and living a rational life, are presupposed in many than 300 pounds.” Thinking is always more or less accurate. It is useful to concepts in modern natural languages, and are presupposed in every subject assume that a statement’s accuracy has not been fully assessed except to the and discipline. In this column, the second in the series, we introduce and extent that one has checked to determine whether it represents things as explicate some of the intellectual standards essential to reasoning well through they really are. Questions that focus on accuracy in thinking include: the problems and issues implicit in everyday human life. • How could I check that to see if it is true? Some Essential Intellectual Standards • How could I verify these alleged facts? We postulate that there are at least nine intellectual standards important • Can I trust the accuracy of these data given the source from which they come? to skilled reasoning in everyday life. -
An Outline of Critical Thinking
AN OUTLINE OF CRITICAL THINKING LEVELS OF INQUIRY 1. Information: correct understanding of basic information. 2. Understanding basic ideas: correct understanding of the basic meaning of key ideas. 3. Probing: deeper analysis into ideas, bases, support, implications, looking for complexity. 4. Critiquing: wrestling with tensions, contradictions, suspect support, problematic implications. This leads to further probing and then further critique, & it involves a recognition of the limitations of your own view. 5. Assessment: final evaluation, acknowledging the relative strengths & limitations of all sides. 6. Constructive: an articulation of your own view, recognizing its limits and areas for further inquiry. EMPHASES Issues! Reading: Know the issues an author is responding to. Writing: Animate and organize your paper around issues. Complexity! Reading: assume that there is more to an idea than is immediately obvious; assume that a key term can be used in various ways and clarify the meaning used in the article; assume that there are different possible interpretations of a text, various implications of ideals, and divergent tendencies within a single tradition, etc. Writing: Examine ideas, values, and traditions in their complexity: multiple aspects of the ideas, different possible interpretations of a text, various implications of ideals, different meanings of terms, divergent tendencies within a single tradition, etc. Support! Reading: Highlight the kind and degree of support: evidence, argument, authority Writing: Support your views with evidence, argument, and/or authority Basis! (ideas, definitions, categories, and assumptions) Reading: Highlight the key ideas, terms, categories, and assumptions on which the author is basing his views. Writing: Be aware of the ideas that give rise to your interpretation; be conscious of the definitions you are using for key terms; recognize the categories you are applying; critically examine your own assumptions. -
Presuppostions in the Slogans of Indonesian Universities
PRESUPPOSTIONS IN THE SLOGANS OF INDONESIAN UNIVERSITIES Atika Puspasari Dosen Universitas Bina Darma Jalan Ahmad Yani No.12, Palembang Sur-el: [email protected] Abstract: The objectives of the study were to identify and analyze the presuppositions implied in the slogans of Indonesian universities which are listed in the General Directorate of Higher Education website, and to discuss pragmatic transfer found in the English version of those slogans. The objects of the study were slogans of Indonesian universities. The writer used documentation technique in collecting the data. Then, qualitative method with triangulation was applied by the writer in analyzing the data. The findings showed that existential, factive, and lexical potential presuppositions were implied in the analyzed slogans. Then, actual presuppositions provide clearer and better ideas of the implied messages in the slogans. Meanwhile, the writer did not find any pragmatic transfer in the English version of the slogans. Keywords: Slogans, Presuppositions, Pragmatic Transfer Abstrak: Tujuan dari penelitian ini adalah untuk mengidentifikasi dan menganalisis praanggapan yang terkandung dalam slogan universitas-universitas di Indonesia yang terdaftar pada website dirjen Dikti. Objek penelitian ini adalah slogan dari universitas-universitas yang ada di Indonesia. Penulis menggunakan teknik dokumentasi dalam pengumpulan data dan analisis data dilakukan dengan menggunakan metode kualitatif ditambah dengan triangulasi. Temuan dari penelitian ini menunjukkan bahwa praanggapan yang terkandung dalam slogan tersebut adalah praanggapan existensial, factive , dan lexical. Kemudian, praanggapan aktual lebih memberikan ide yang lebih baik dan lebih jelas mengenai pesan yang terkandung di dalam slogan-slogan tersebut. Sedangkan temuan lainnya yaitu pragmatik transfer tidak ditemukan di dalam slogan-slogan universitas di Indonesia. -
Abductive Reasoning: Challenges Ahead
Abductive Reasoning: Challenges Ahead Atocha ALISEDA BIBLID [0495-4548 (2007) 22: 60; pp. 261-270] ABSTRACT: The motivation behind the collection of papers presented in this THEORIA forum on Abductive reasoning is my book Abductive Reasoning: Logical Investigations into the Processes of Discovery and Explanation. These contributions raise fundamental questions. One of them concerns the conjectural character of abduction. The choice of a logical framework for abduction is also discussed in detail, both its inferential aspect and search strategies. Abduction is also analyzed as inference to the best explanation, as well as a process of epistemic change, both of which chal- lenge the argument-like format of abduction. Finally, the psychological question of whether humans reason abduc- tively according to the models proposed is also addressed. I offer a brief summary of my book and then comment on and respond to several challenges that were posed to my work by the contributors to this issue. Keywords: abduction, abductive inference, discovery, heuristics. A Summary In Abductive Reasoning: Logical Investigations into Discovery and Explanation, I offer a logical analysis of a particular type of scientific reasoning, namely abduction, that is, reasoning from an observation to its possible explanations. This approach naturally leads to connec- tions with theories of explanation and empirical progress in the philosophy of science, to computationally oriented theories of belief change in artificial intelligence, and to the phi- losophical position known as Pragmatism, proposed by Charles Peirce, to whom the term abduction owes its name. More precisely, the book is divided into three parts: (I) Conceptual Framework, (II) Logical Foundations, and (III) Applications, each of which is briefly described in what follows. -
Critical Thinking in the Classroom…And Beyond
Critical Thinking in the Classroom…and Beyond Linda M. Murawski, EdD Adjunct Professor Department of Human Resources Development Graduate & Professional Studies Tusculum College Knoxville, Tennessee ABSTRACT Critical thinking in the classroom is a common term used by educators. Critical thinking has been called “the art of thinking about thinking” (Ruggiero, V.R., 2012) with the intent to improve one’s thinking. The challenge, of course, is to create learning environments that promote critical thinking both in the classroom and beyond. Teaching and practicing critical thinking provides adults with the opportunity to embrace and take charge of their learning. Adults engaged in critical thinking approach the classroom experience differently. Typically, students who implement critical thinking skills approach the courseware in a more thoughtful and effective manner, ask more challenging questions and participate in the learning process more intensely. This critical thinking process endures beyond the classroom and into the workplace. This session examines the background of critical thinking, its role in the classroom and beyond that to the workplace. INTRODUCTION of many years of research, analysis, teaching and practice, Ennis concluded that critical thinking is “focused on de- Critical thinking is a common course in college and uni- ciding what to believe or do,” (Ennis, p. 10). versity settings today. Frequently taught as a way to “im- prove” thinking, the art of critical thinking involves an Ennis separated critical thinking into two categories: dis- approach to thinking--more importantly to learning--that positions and abilities. The ideal critical thinker, in his embraces changing how one thinks about thinking. Criti- writings, is disposed to reach a “right” decision, present cal thinking incorporates how learners develop and apply that position honestly and clearly, consider others’ points thought to understand how thinking can be improved. -
Logic and Critical Thinking Course Code: Phil 1011
FEDERAL DEMOCRATIC REPUBLIC OF ETHIOPIA MINISTRY OF SCIENCE AND HIGHER EDUCATION LOGIC AND CRITICAL THINKING COURSE CODE: PHIL 1011 By: Teklay G. (AkU), Adane T. (MU), and Zelalem M. (HMU) Page 1 LOGIC AND CRITICAL THINKING MODULE COURSE CODE: PHIL101 COURSE CRDIT HOURS: 3 PREPARED BY: Mr. TEKLAY G/MESKEL (AKSUM UNIVERSITY) Mr. ADANE TEKLAY (MEKELLE UNIVERSITY) Mr. ZELALEM MAMO (HARAMAYA UNIVERSITY) AUGUST 2019 ADDIS ABABA, ETHIOPIA By: Teklay G. (AkU), Adane T. (MU), and Zelalem M. (HMU) Page 2 ORGANIZATION OF THE MODULE: 1. Module Introduction: - Teklay G. (AkU) 2. Chapter One: - Teklay G. (AkU) 3. Chapter Two: - Teklay G. (AkU) 4. Chapter Three: - Adane T. (MU) 5. Chapter Four: - Zelalem M. (HMU) 6. Chapter Five: - Zelalem M. (HMU) 7. Chapter Six: - Adane T. (MU) By: Teklay G. (AkU), Adane T. (MU), and Zelalem M. (HMU) Page 3 Table of Contents COURSE INTRODUCTION ........................................................................................................................ 8 COURSE OBJECTIVES ............................................................................................................................ 10 CHAPTER ONE ......................................................................................................................................... 11 INTRODUCING PHILOSOPHY ............................................................................................................... 11 Chapter Overview ..................................................................................................................................