Analogy in Terms of Identity, Equivalence, Similarity, and Their Cryptomorphs
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PHI 351 Nominalism
Philosophy 351 September 9, 2008 Prof. Clare Batty Universals: Nominalism 1. Recap Metaphysical realism: the world contains both universals and particulars. Certain things (particulars) are alike in attribute (property, relation, kind) because they exemplify the same universal. Metaphysical realists claim that their two-category framework not only provides us with the machinery with which to explain attribute agreement/similarity/resemblance but also a pair of important phenomena: i. The truth of subject-predicate discourse ii. Our use of abstract reference. 2. Issues we have raised about metaphysical realism a. What universals is the metaphysical realist willing to allow into his/her ontology? • Does he/she allow the universal bachelor or just unmarried, adult, male (does he/she even allow unmarried?). What about he universal green or just green (or light green)? 52 b. Are there unexemplified universals? • Certainly there might have been different properties in the world. Are there universals corresponding to these non-existent, but possible, properties? c. Is the relation of exemplification itself a universal? If so, doesn’t this commit the metaphysical realist to an infinite regress? • Suppose a and b are both F. That is, they exemplify the universal F-ness. But now they have an additional thing in common: they are both exemplifications of F-ness. That is, they both exemplify the universal exemplification of F-ness. Can you see where this is going? d. Doesn’t the metaphysical realist overestimate the degree of agreement/likeness/resemblance in the world? • Grass, peas and wasabi paste are all similar; but they are not exactly alike. 3. -
Optimization-Based Approximate Dynamic Programming
OPTIMIZATION-BASED APPROXIMATE DYNAMIC PROGRAMMING A Dissertation Presented by MAREK PETRIK Submitted to the Graduate School of the University of Massachusetts Amherst in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY September 2010 Department of Computer Science c Copyright by Marek Petrik 2010 All Rights Reserved OPTIMIZATION-BASED APPROXIMATE DYNAMIC PROGRAMMING A Dissertation Presented by MAREK PETRIK Approved as to style and content by: Shlomo Zilberstein, Chair Andrew Barto, Member Sridhar Mahadevan, Member Ana Muriel, Member Ronald Parr, Member Andrew Barto, Department Chair Department of Computer Science To my parents Fedor and Mariana ACKNOWLEDGMENTS I want to thank the people who made my stay at UMass not only productive, but also very enjoyable. I am grateful to my advisor, Shlomo Zilberstein, for guiding and supporting me throughout the completion of this work. Shlomo's thoughtful advice and probing questions greatly influenced both my thinking and research. His advice was essential not only in forming and refining many of the ideas described in this work, but also in assuring that I become a productive member of the research community. I hope that, one day, I will be able to become an advisor who is just as helpful and dedicated as he is. The members of my dissertation committee were indispensable in forming and steering the topic of this dissertation. The class I took with Andrew Barto motivated me to probe the foundations of reinforcement learning, which became one of the foundations of this thesis. Sridhar Mahadevan's exciting work on representation discovery led me to deepen my un- derstanding and appreciate better approximate dynamic programming. -
Filtering Germs: Groupoids Associated to Inverse Semigroups
FILTERING GERMS: GROUPOIDS ASSOCIATED TO INVERSE SEMIGROUPS BECKY ARMSTRONG, LISA ORLOFF CLARK, ASTRID AN HUEF, MALCOLM JONES, AND YING-FEN LIN Abstract. We investigate various groupoids associated to an arbitrary inverse semigroup with zero. We show that the groupoid of filters with respect to the natural partial order is isomorphic to the groupoid of germs arising from the standard action of the inverse semigroup on the space of idempotent filters. We also investigate the restriction of this isomorphism to the groupoid of tight filters and to the groupoid of ultrafilters. 1. Introduction An inverse semigroup is a set S endowed with an associative binary operation such that for each a 2 S, there is a unique a∗ 2 S, called the inverse of a, satisfying aa∗a = a and a∗aa∗ = a∗: The study of ´etalegroupoids associated to inverse semigroups was initiated by Renault [Ren80, Remark III.2.4]. We consider two well known groupoid constructions: the filter approach and the germ approach, and we show that the two approaches yield isomorphic groupoids. Every inverse semigroup has a natural partial order, and a filter is a nonempty down-directed up-set with respect to this order. The filter approach to groupoid construction first appeared in [Len08], and was later simplified in [LMS13]. Work in this area is ongoing; see for instance, [Bic21, BC20, Cas20]. Every inverse semigroup acts on the filters of its subsemigroup of idempotents. The groupoid of germs associated to an inverse semigroup encodes this action. Paterson pioneered the germ approach in [Pat99] with the introduction of the universal groupoid of an inverse semigroup. -
Relations on Semigroups
International Journal for Research in Engineering Application & Management (IJREAM) ISSN : 2454-9150 Vol-04, Issue-09, Dec 2018 Relations on Semigroups 1D.D.Padma Priya, 2G.Shobhalatha, 3U.Nagireddy, 4R.Bhuvana Vijaya 1 Sr.Assistant Professor, Department of Mathematics, New Horizon College Of Engineering, Bangalore, India, Research scholar, Department of Mathematics, JNTUA- Anantapuram [email protected] 2Professor, Department of Mathematics, SKU-Anantapuram, India, [email protected] 3Assistant Professor, Rayalaseema University, Kurnool, India, [email protected] 4Associate Professor, Department of Mathematics, JNTUA- Anantapuram, India, [email protected] Abstract: Equivalence relations play a vital role in the study of quotient structures of different algebraic structures. Semigroups being one of the algebraic structures are sets with associative binary operation defined on them. Semigroup theory is one of such subject to determine and analyze equivalence relations in the sense that it could be easily understood. This paper contains the quotient structures of semigroups by extending equivalence relations as congruences. We define different types of relations on the semigroups and prove they are equivalence, partial order, congruence or weakly separative congruence relations. Keywords: Semigroup, binary relation, Equivalence and congruence relations. I. INTRODUCTION [1,2,3 and 4] Algebraic structures play a prominent role in mathematics with wide range of applications in science and engineering. A semigroup -
Using Analogy to Learn About Phenomena at Scales Outside Human Perception Ilyse Resnick1*, Alexandra Davatzes2, Nora S
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Springer - Publisher Connector Resnick et al. Cognitive Research: Principles and Implications (2017) 2:21 Cognitive Research: Principles DOI 10.1186/s41235-017-0054-7 and Implications ORIGINAL ARTICLE Open Access Using analogy to learn about phenomena at scales outside human perception Ilyse Resnick1*, Alexandra Davatzes2, Nora S. Newcombe3 and Thomas F. Shipley3 Abstract Understanding and reasoning about phenomena at scales outside human perception (for example, geologic time) is critical across science, technology, engineering, and mathematics. Thus, devising strong methods to support acquisition of reasoning at such scales is an important goal in science, technology, engineering, and mathematics education. In two experiments, we examine the use of analogical principles in learning about geologic time. Across both experiments we find that using a spatial analogy (for example, a time line) to make multiple alignments, and keeping all unrelated components of the analogy held constant (for example, keep the time line the same length), leads to better understanding of the magnitude of geologic time. Effective approaches also include hierarchically and progressively aligning scale information (Experiment 1) and active prediction in making alignments paired with immediate feedback (Experiments 1 and 2). Keywords: Analogy, Magnitude, Progressive alignment, Corrective feedback, STEM education Significance statement alignment and having multiple opportunities to make Many fundamental science, technology, engineering, and alignments are critical in supporting reasoning about mathematic (STEM) phenomena occur at extreme scales scale, and that the progressive and hierarchical that cannot be directly perceived. For example, the Geo- organization of scale information may provide salient logic Time Scale, discovery of the atom, size of the landmarks for estimation. -
Analogical Processes and College Developmental Reading
Analogical Processes and College Developmental Reading By Eric J. Paulson Abstract: Although a solid body of research is analogical. An analogical process involves concerning the role of analogies in reading processes the identification of partial similarities between has emerged at a variety of age groups and reading different objects or situations to support further proficiencies, few of those studies have focused on inferences and is used to explain new concepts, analogy use by readers enrolled in college develop- solve problems, and understand new areas and mental reading courses. The current study explores ideas (Gentner, & Colhoun, 2010; Gentner & Smith, whether 232 students enrolled in mandatory (by 2012). For example, when a biology teacher relates placement test) developmental reading courses the functions of a cell to the activities in a factory in in a postsecondary educational context utilize order to introduce and explain the cell to students, analogical processes while engaged in specific this is an analogical process designed to use what reading activities. This is explored through two is already familiar to illuminate and explain a separate investigations that focus on two different new concept. A process of mapping similarities ends of the reading spectrum: the word-decoding between a source (what is known) and a target Analogy appears to be a key level and the overall text-comprehension level. (what is needed to be known) in order to better element of human thinking. The two investigations reported here build on understand the target (Holyoak & Thagard, 1997), comparable studies of analogy use with proficient analogies are commonly used to make sense of readers. -
The Idea of Mimesis: Semblance, Play, and Critique in the Works of Walter Benjamin and Theodor W
DePaul University Via Sapientiae College of Liberal Arts & Social Sciences Theses and Dissertations College of Liberal Arts and Social Sciences 8-2012 The idea of mimesis: Semblance, play, and critique in the works of Walter Benjamin and Theodor W. Adorno Joseph Weiss DePaul University, [email protected] Follow this and additional works at: https://via.library.depaul.edu/etd Recommended Citation Weiss, Joseph, "The idea of mimesis: Semblance, play, and critique in the works of Walter Benjamin and Theodor W. Adorno" (2012). College of Liberal Arts & Social Sciences Theses and Dissertations. 125. https://via.library.depaul.edu/etd/125 This Dissertation is brought to you for free and open access by the College of Liberal Arts and Social Sciences at Via Sapientiae. It has been accepted for inclusion in College of Liberal Arts & Social Sciences Theses and Dissertations by an authorized administrator of Via Sapientiae. For more information, please contact [email protected]. The Idea of Mimesis: Semblance, Play, and Critique in the Works of Walter Benjamin and Theodor W. Adorno A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy October, 2011 By Joseph Weiss Department of Philosophy College of Liberal Arts and Sciences DePaul University Chicago, Illinois 2 ABSTRACT Joseph Weiss Title: The Idea of Mimesis: Semblance, Play and Critique in the Works of Walter Benjamin and Theodor W. Adorno Critical Theory demands that its forms of critique express resistance to the socially necessary illusions of a given historical period. Yet theorists have seldom discussed just how much it is the case that, for Walter Benjamin and Theodor W. -
Data Monoids∗
Data Monoids∗ Mikolaj Bojańczyk1 1 University of Warsaw Abstract We develop an algebraic theory for languages of data words. We prove that, under certain conditions, a language of data words is definable in first-order logic if and only if its syntactic monoid is aperiodic. 1998 ACM Subject Classification F.4.3 Formal Languages Keywords and phrases Monoid, Data Words, Nominal Set, First-Order Logic Digital Object Identifier 10.4230/LIPIcs.STACS.2011.105 1 Introduction This paper is an attempt to combine two fields. The first field is the algebraic theory of regular languages. In this theory, a regular lan- guage is represented by its syntactic monoid, which is a finite monoid. It turns out that many important properties of the language are reflected in the structure of its syntactic monoid. One particularly beautiful result is the Schützenberger-McNaughton-Papert theorem, which describes the expressive power of first-order logic. Let L ⊆ A∗ be a regular language. Then L is definable in first-order logic if and only if its syntactic monoid ML is aperiodic. For instance, the language “words where there exists a position with label a” is defined by the first-order logic formula (this example does not even use the order on positions <, which is also allowed in general) ∃x. a(x). The syntactic monoid of this language is isomorphic to {0, 1} with multiplication, where 0 corresponds to the words that satisfy the formula, and 1 to the words that do not. Clearly, this monoid does not contain any non-trivial group. There are many results similar to theorem above, each one providing a connection between seemingly unrelated concepts of logic and algebra, see e.g. -