How Peircean Was the “'Fregean' Revolution” in Logic?
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Stanislaw Piatkiewicz and the Beginnings of Mathematical Logic in Poland
HISTORIA MATHEMATICA 23 (1996), 68±73 ARTICLE NO. 0005 Stanisøaw PiaËtkiewicz and the Beginnings of Mathematical Logic in Poland TADEUSZ BATO G AND ROMAN MURAWSKI View metadata, citation and similar papers at core.ac.uk brought to you by CORE Department of Mathematics and Computer Science, Adam Mickiewicz University, ul. Matejki 48/49, 60-769 PoznanÂ, Poland provided by Elsevier - Publisher Connector This paper presents information on the life and work of Stanisøaw PiaËtkiewicz (1849±?). His Algebra w logice (Algebra in Logic) of 1888 contains an exposition of the algebra of logic and its use in representing syllogisms. This was the ®rst original Polish publication on symbolic logic. It appeared 20 years before analogous works by èukasiewicz and Stamm. 1996 Academic Press, Inc. In dem Aufsatz werden Informationen zu Leben und Werk von Stanisøaw PiaËtkiewicz (1849±?) gegeben. Sein Algebra w logice (Algebra in der Logik) von 1888 enthaÈlt eine Darstel- lung der Algebra der Logik und ihre Anwendung auf die Syllogistik. PiaËtkiewicz' Schrift war die erste polnische Publikation uÈ ber symbolische Logik. Sie erschien 20 Jahre vor aÈhnlichen Arbeiten von èukasiewicz und Stamm. 1996 Academic Press, Inc. W pracy przedstawiono osobeË i dzieøo Stanisøawa PiaËtkiewicza (1849±?). W szczego lnosÂci analizuje sieË jego rozpraweË Algebra w logice z roku 1888, w kto rej zajmowaø sieË on nowymi no wczas ideami algebry logiki oraz ich zastosowaniami do sylogistyki. Praca ta jest pierwszaË oryginalnaË polskaË publikacjaË z zakresu logiki symbolicznej. Ukazaøa sieË 20 lat przed analog- icznymi pracami èukasiewicza i Stamma. 1996 Academic Press, Inc. MSC 1991 subject classi®cations: 03-03, 01A55. -
A Survey of Abstract Algebraic Logic 15 Bras
J. M. Font A Survey of Abstract Algebraic R. Jansana D. Pigozzi Logic Contents Introduction 14 1. The First Steps 16 1.1. Consequence operations and logics . 17 1.2. Logical matrices . 20 1.3. Lindenbaum-Tarski algebras . 22 2. The Lindenbaum-Tarski Process Fully Generalized 24 2.1. Frege's principles . 24 2.2. Algebras and matrices canonically associated with a logic . 26 3. The Core Theory of Abstract Algebraic Logic 29 3.1. Elements of the general theory of matrices . 29 3.2. Protoalgebraic logics . 33 3.3. Algebraizable logics . 38 3.4. The Leibniz hierarchy . 43 4. Extensions of the Core Theory 50 4.1. k-deductive systems and universal algebra . 50 4.2. Gentzen systems and their generalizations . 55 4.3. Equality-free universal Horn logic . 61 4.4. Algebras of Logic . 64 5. Generalized Matrix Semantics and Full Models 71 6. Extensions to More Complex Notions of Logic 79 6.1. The semantics-based approach . 80 6.2. The categorial approach . 85 References 88 Special Issue on Abstract Algebraic Logic { Part II Edited by Josep Maria Font, Ramon Jansana, and Don Pigozzi Studia Logica 74: 13{97, 2003. c 2003 Kluwer Academic Publishers. Printed in the Netherlands. 14 J. M. Font, R. Jansana, and D. Pigozzi Introduction Algebraic logic was born in the XIXth century with the work of Boole, De Morgan, Peirce, Schr¨oder, etc. on classical logic, see [12, 16]. They took logical equivalence rather than truth as the primitive logical predicate, and, exploiting the similarity between logical equivalence and equality, they devel- oped logical systems in which metalogical investigations take on a distinctly algebraic character. -
What Is Abstract Algebraic Logic?
What is Abstract Algebraic Logic? Umberto Rivieccio University of Genoa Department of Philosophy Via Balbi 4 - Genoa, Italy email [email protected] Abstract Our aim is to answer the question of the title, explaining which kind of problems form the nucleus of the branch of algebraic logic that has come to be known as Abstract Algebraic Logic. We give a concise account of the birth and evolution of the field, that led from the discovery of the connections between certain logical systems and certain algebraic structures to a general theory of algebraization of logics. We consider first the so-called algebraizable logics, which may be regarded as a paradigmatic case in Abstract Algebraic Logic; then we shift our attention to some wider classes of logics and to the more general framework in which they are studied. Finally, we review some other topics in Abstract Algebraic Logic that, though equally interesting and promising for future research, could not be treated here in detail. 1 Introduction Algebraic logic can be described in very general terms as the study of the relations between algebra and logic. One of the main reasons that motivate such a study is the possibility to treat logical problems with algebraic methods. This means that, in order to solve a logical problem, we may try to translate it into algebraic terms, find the solution using algebraic techniques, and then translate back the result into logic. This strategy proved to be fruitful, since algebra is an old and well{established field of mathematics, that offers powerful tools to treat problems that would possibly be much harder to solve using the logical machinery alone. -
Uluslararası Ders Kitapları Ve Eğitim Materyalleri Dergisi
Uluslararası Ders Kitapları ve Eğitim Materyalleri Dergisi The Effect of Artifiticial Intelligence on Society and Artificial Intelligence the View of Artificial Intelligence in the Context of Film (I.A.) İpek Sucu İstanbul Gelişim Üniversitesi, Reklam Tasarımı ve İletişim Bölümü ABSTRACT ARTICLE INFO Consumption of produced, quick adoption of discovery, parallel to popularity, our interest in new and different is at the top; We live in the age of technology. A sense of wonder and satisfaction that mankind has existed in all ages throughout human history; it was the key to discoveries and discoveries. “Just as the discovery of fire was the most important invention in the early ages, artificial intelligence is also the most important project of our time.” (Aydın and Değirmenci, 2018: 25). It is the nature of man and the nearby brain. It is Z Artificial Intelligence ”technology. The concept of artificial intelligence has been frequently mentioned recently. In fact, I believe in artificial intelligence, the emergence of artificial intelligence goes back to ancient times. Various artificial intelligence programs have been created and robots have started to be built depending on the technological developments. The concepts such as deep learning and natural language processing are also on the agenda and films about artificial intelligence. These features were introduced to robots and the current concept of “artificial intelligence was reached. In this study, the definition, development and applications of artificial intelligence, the current state of artificial intelligence, the relationship between artificial intelligence and new media, the AI Artificial Intelligence (2001) film will be analyzed and evaluated within the scope of the subject and whether the robots will have certain emotions like people. -
Mathematical Induction - a Miscellany of Theory, History and Technique
Mathematical Induction - a miscellany of theory, history and technique Theory and applications for advanced secondary students Part 4 Peter Haggstrom This work is subject to Copyright. It is a chapter in a larger work. You can however copy this chapter for educational purposes under the Statutory License of the Copyright Act 1968 - Part VB For more information [email protected] Copyright 2009 [email protected] The building blocks of Gödelʼs Theorem The foundations of Gödel’s Theorem (ie his undecidability theorem) are to be found in about 50 papers contained in a book by Jean van Heijenoort:, “From Frege to Gödel: A Source Book in Mathematical Logic, 1879 - 1931”. Every serious logic student has read this book. Van Heijenoort is worth mentioning even if only for his colourful past which is described by Benjamin H Yandell in his book “The Honors Class: Hilbert’s Problems and Their Solvers”, A K Peters, 2002, page 66. I quote in full: “ I assumed van Heijenoort was merely a logician as I gratefully pored over his book and was astounded when I learned that as a young man, in the 1930s, he had followed Leon Trotsky from Turkey to France to Norway to Mexico, as his body guard and secretary. Anita Feferman’s ”From Trotsky to Gödel”: The Life of Jean van Heijenoort” tells van Heijenoort’s remarkable story. Trotsky and his camp were pursued by Stalinist agents; van Heijenoort always packed a gun. Van Heijenoort had an affair with an artist Frida Kahlo. He epitomized cool and was attractive to women, and this continued even after he became a logician, He had grown tired of the rigors of life with Trotsky and traveled to New York in 1939 on a somewhat vague mission. -
Machine Learning
Graham Capital Management Research Note, September 2017 Machine Learning Erik Forseth1, Ed Tricker2 Abstract Machine learning is more fashionable than ever for problems in data science, predictive modeling, and quantitative asset management. Developments in the field have revolutionized many aspects of modern life. Nevertheless, it is sometimes difficult to understand where real value ends and speculative hype begins. Here we attempt to demystify the topic. We provide a historical perspective on artificial intelligence and give a light, semi-technical overview of prevailing tools and techniques. We conclude with a brief discussion of the implications for investment management. Keywords Machine learning, AI 1Quantitative Researcher 2Head of Research and Development 1. Introduction by the data they are fed—which attempt to find a solution to some mathematical optimization problem. There remains a Machine Learning is the study of computer algorithms that vast gulf between the space of tasks which can be formulated improve automatically through experience. in this way, and the space of tasks that require, for example, – Tom Mitchell (1997) reasoning or abstract planning. There is a fundamental divide Machine Learning (ML) has emerged as one of the most between the capability of a computer model to map inputs to exciting areas of research across nearly every dimension of outputs, versus our own human intelligence [Chollet (2017)]. contemporary digital life. From medical diagnostics to recom- In grouping these methods under the moniker “artificial in- mendation systems—such as those employed by Amazon or telligence,” we risk imbuing them with faculties they do not Netflix—adaptive computer algorithms have radically altered have. -
What Is a Logic Translation? in Memoriam Joseph Goguen
, 1{29 c 2009 Birkh¨auserVerlag Basel/Switzerland What is a Logic Translation? In memoriam Joseph Goguen Till Mossakowski, R˘azvan Diaconescu and Andrzej Tarlecki Abstract. We study logic translations from an abstract perspective, with- out any commitment to the structure of sentences and the nature of logical entailment, which also means that we cover both proof-theoretic and model- theoretic entailment. We show how logic translations induce notions of logical expressiveness, consistency strength and sublogic, leading to an explanation of paradoxes that have been described in the literature. Connectives and quanti- fiers, although not present in the definition of logic and logic translation, can be recovered by their abstract properties and are preserved and reflected by translations under suitable conditions. 1. Introduction The development of a notion of logic translation presupposes the development of a notion of logic. Logic has been characterised as the study of sound reasoning, of what follows from what. Hence, the notion of logical consequence is central. It can be obtained in two complementary ways: via the model-theoretic notion of satisfaction in a model and via the proof-theoretic notion of derivation according to proof rules. These notions can be captured in a completely abstract manner, avoiding any particular commitment to the nature of models, sentences, or rules. The paper [40], which is the predecessor of our current work, explains the notion of logic along these lines. Similarly, an abstract notion of logic translation can be developed, both at the model-theoretic and at the proof-theoretic level. A central question concern- ing such translations is their interaction with logical structure, such as given by logical connectives, and logical properties. -
Tractatus Logico-Philosophicus</Em>
University of South Florida Scholar Commons Graduate Theses and Dissertations Graduate School 8-6-2008 Three Wittgensteins: Interpreting the Tractatus Logico-Philosophicus Thomas J. Brommage Jr. University of South Florida Follow this and additional works at: https://scholarcommons.usf.edu/etd Part of the American Studies Commons Scholar Commons Citation Brommage, Thomas J. Jr., "Three Wittgensteins: Interpreting the Tractatus Logico-Philosophicus" (2008). Graduate Theses and Dissertations. https://scholarcommons.usf.edu/etd/149 This Dissertation is brought to you for free and open access by the Graduate School at Scholar Commons. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Scholar Commons. For more information, please contact [email protected]. Three Wittgensteins: Interpreting the Tractatus Logico-Philosophicus by Thomas J. Brommage, Jr. A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Philosophy College of Arts and Sciences University of South Florida Co-Major Professor: Kwasi Wiredu, B.Phil. Co-Major Professor: Stephen P. Turner, Ph.D. Charles B. Guignon, Ph.D. Richard N. Manning, J. D., Ph.D. Joanne B. Waugh, Ph.D. Date of Approval: August 6, 2008 Keywords: Wittgenstein, Tractatus Logico-Philosophicus, logical empiricism, resolute reading, metaphysics © Copyright 2008 , Thomas J. Brommage, Jr. Acknowledgments There are many people whom have helped me along the way. My most prominent debts include Ray Langely, Billy Joe Lucas, and Mary T. Clark, who trained me in philosophy at Manhattanville College; and also to Joanne Waugh, Stephen Turner, Kwasi Wiredu and Cahrles Guignon, all of whom have nurtured my love for the philosophy of language. -
Everybody Is Talking About Virtual Assistants, but How Are Users Really Using Them?
Everybody is talking about Virtual Assistants, but how are users really using them? 32nd Human Computer Interaction Conference, July 2018 Dr Marta Pérez García Sarita Saffon López Héctor Donis https://doi.org/10.14236/ewic/HCI2018.96 Everybody is talking about Virtual Assistants, but how are users really using them? The 2010s arrived focusing on algorithms of machine learning by enabling computers to have access to large Abstract amounts of data, which comes back to what was expected in the 1950s (Samuel, 1959; Koza, 1996). This Voice activated virtual assistants are growing rapidly in kind of application through a simplified interaction in number, variety and visibility, driven by media coverage, games and hobbies is what enabled the adoption of AI corporate communications, and inclusion in a growing at a user level. What is happening with AI variety of devices. This trend can also be observed by implementation today on our daily basis then? One of how difficult it is becoming to find, among internet many examples of our closest and most frequent users, people who have not used or even heard of this interactions with it is the virtual personal assistants new technology. Having said this, there is a visible (Arafa and Mamdani, 2000). shortage of academic research on this topic. Therefore, in the interest of creating a knowledge base around Regardless of the wave of technology adoption with voice activated virtual assistants based on artificial virtual assistants, little has been written in academia intelligence, this multi-country exploratory research about it so that theory can be built upon. Most study was carried out. -
First Order Logic
Artificial Intelligence CS 165A Mar 10, 2020 Instructor: Prof. Yu-Xiang Wang ® First Order Logic 1 Recap: KB Agents True sentences TELL Knowledge Base Domain specific content; facts ASK Inference engine Domain independent algorithms; can deduce new facts from the KB • Need a formal logic system to work • Need a data structure to represent known facts • Need an algorithm to answer ASK questions 2 Recap: syntax and semantics • Two components of a logic system • Syntax --- How to construct sentences – The symbols – The operators that connect symbols together – A precedence ordering • Semantics --- Rules the assignment of sentences to truth – For every possible worlds (or “models” in logic jargon) – The truth table is a semantics 3 Recap: Entailment Sentences Sentence ENTAILS Representation Semantics Semantics World Facts Fact FOLLOWS A is entailed by B, if A is true in all possiBle worlds consistent with B under the semantics. 4 Recap: Inference procedure • Inference procedure – Rules (algorithms) that we apply (often recursively) to derive truth from other truth. – Could be specific to a particular set of semantics, a particular realization of the world. • Soundness and completeness of an inference procedure – Soundness: All truth discovered are valid. – Completeness: All truth that are entailed can be discovered. 5 Recap: Propositional Logic • Syntax:Syntax – True, false, propositional symbols – ( ) , ¬ (not), Ù (and), Ú (or), Þ (implies), Û (equivalent) • Semantics: – Assigning values to the variables. Each row is a “model”. • Inference rules: – Modus Pronens etc. Most important: Resolution 6 Recap: Propositional logic agent • Representation: Conjunctive Normal Forms – Represent them in a data structure: a list, a heap, a tree? – Efficient TELL operation • Inference: Solve ASK question – Use “Resolution” only on CNFs is Sound and Complete. -
Explanations
© Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. CHAPTER 1 Explanations 1.1 SALLIES Language is an instrument of Logic, but not an indispensable instrument. Boole 1847a, 118 We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of exact science are mathematics and logic; the mathematical sect puts out the logical eye, the logical sect puts out the mathematical eye; each believing that it sees better with one eye than with two. De Morgan 1868a,71 That which is provable, ought not to be believed in science without proof. Dedekind 1888a, preface If I compare arithmetic with a tree that unfolds upwards in a multitude of techniques and theorems whilst the root drives into the depthswx . Frege 1893a, xiii Arithmetic must be discovered in just the same sense in which Columbus discovered the West Indies, and we no more create numbers than he created the Indians. Russell 1903a, 451 1.2 SCOPE AND LIMITS OF THE BOOK 1.2.1 An outline history. The story told here from §3 onwards is re- garded as well known. It begins with the emergence of set theory in the 1870s under the inspiration of Georg Cantor, and the contemporary development of mathematical logic by Gottlob Frege andŽ. especially Giuseppe Peano. A cumulation of these and some related movements was achieved in the 1900s with the philosophy of mathematics proposed by Alfred North Whitehead and Bertrand Russell. -
24° Congresso UECI TOSSIGNANO (BO-Imola) Villa Santa Maria
Unione Esperantista Cattolica Italiana U.E.C.I IDO Fare24° clicCongresso per modificare UECI lo stile del sottotitolo dello schema TOSSIGNANO (BO-Imola) Villa Santa Maria - 4-8 giugno 2010 www.ueci.it 4 I protagonisti • Louis Couturat era un matematico, logico e glottoteta francese, noto per i suoi contributi allo sviluppo delle logica formale. • Fu fondatore della Delegazione per l'adozione di una lingua ausiliaria internazionale. (Ris-Orangis , 17 gennaio 1868 – 3 agosto 1914) 2424° Congresso UECI 4-8 GIUGNO 2010 Il marchese Louis de Beaufront • Il marchese Louis de Beaufront (1855 – 1935) è stato un linguista, glottoteta ed esperantista francese. • La sua vita rimane piena di misteri: si seppe dopo la sua morte che non era marchese, che era di padre sconosciuto e che il suo vero nome era in realtà Louis Chevreux. Precettore privato al servizio di ricche famiglie, celibe. • Consacrò tutto il suo tempo libero alla diffusione della lingua, creò le basi del movimento esperantista. 24° Congresso UECI 4-8 GIUGNO 2010 • Alcune divergenze lo opposero all'iniziatore della lingua, Ludwik Lejzer Zamenhof e alla maggioranza degli esperantisti francesi. • Non partecipò al primo congresso esperantista di Boulogne-sur- Mer dove fu adottato il Fundamento de Esperanto, cioè le norme intangibili che garantiscono la stabilità della lingua. • Louis de Beaufront creò l’IDO come tentativo di creare una versione più semplice dell'esperanto. • Ido in esperanto significa discendente ma è anche l'abbreviazione di esperantido 24° Congresso UECI 4-8 GIUGNO 2010 LA STORIA • Nell'ottobre 1907, a Parigi, un comitato internazionale di 12 membri si riunì per scegliere la lingua artificiale più adatta alla comunicazione internazionale.