DOCSLIB.ORG

March 29 – April 07, 2013 Rio De Janeiro, Brazil

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
March 29 – April 07, 2013 Rio De Janeiro, Brazil Handbook of the 4th World Congress and School on Universal Logic March 29 { April 07, 2013 Rio de Janeiro, Brazil UNILOG'2013 www.uni-log.org ECEME { Escola de Comando e Estado-Maior do Ex´ercito Rio de Janeiro { Brasil Edited by Jean-Yves B´eziau,Arthur Buchsbaum and Alexandre Costa-Leite Revised by Alvaro Altair Contents 1 Organizers of UNILOG'13 5 1.1 Scientific Committee . 5 1.2 Organizing Committee . 5 1.3 Supporting Organizers . 6 2 Aim of the event 6 3 4th World School on Universal Logic 8 3.1 Aim of the School . 8 3.2 Tutorials . 9 3.2.1 Why Study Logic? . 9 3.2.2 How to get your Logic Article or Book published in English 9 3.2.3 Non-Deterministic Semantics . 10 3.2.4 Logic for the Blind as a Stimulus for the Design of Inno- vative Teaching Materials . 13 3.2.5 Hybrid Logics . 16 3.2.6 Psychology of Reasoning . 17 3.2.7 Truth-Values . 19 3.2.8 The Origin of Indian Logic and Indian Syllogism . 23 3.2.9 Logical Forms . 25 3.2.10 An Introduction to Arabic Logic . 26 3.2.11 Quantum Cognition . 28 3.2.12 Towards a General Theory of Classifications . 29 3.2.13 Connecting Logics . 31 3.2.14 Relativity of Mathematical Concepts . 32 3.2.15 Undecidability and Incompleteness are Everywhere . 33 3.2.16 Logic, Algebra and Implication . 34 3.2.17 Hypersequents and Applications . 36 3.2.18 Introduction to Modern Metamathematics . 37 3.2.19 Erotetic Logics . 37 3.2.20 History of Paraconsistent Logic . 38 3.2.21 Institutions . 41 3.2.22 Description Logics . 42 3.2.23 Ideospheres . 43 3.2.24 Mathematical Fuzzy Logic . 43 3.2.25 Logics of Plurality . 45 3.2.26 Graded Consequence . 47 3.2.27 The Notions of Empathy and Transcendence in Quine's Philosophical System . 51 3.2.28 Logic, Inquiry, and Discovery: Peirce's vision of Logic . 53 3.2.29 Graph calculi for relational reasoning . 55 3.2.30 Continuous-valued Logic Algebra . 56 2 4 4th World Congress on Universal Logic 57 4.1 Invited Keynote Speakers . 57 4.1.1 Irving H. Anellis . 57 4.1.2 Arnon Avron . 57 4.1.3 Gianluigi Bellin . 58 4.1.4 Ot´avioBueno . 59 4.1.5 Hans Burkhardt . 60 4.1.6 Manuela Busaniche . 61 4.1.7 Carlos Caleiro . 62 4.1.8 Roberto Casati . 64 4.1.9 Roberto Marcondes Cesar Jr. 64 4.1.10 Agata Ciabattoni . 65 4.1.11 Bob Coecke . 65 4.1.12 Simon Colton . 66 4.1.13 Newton C. A. da Costa . 67 4.1.14 Dennis Dieks . 68 4.1.15 Itala Maria Loffredo D'Ottaviano . 68 4.1.16 J. Michael Dunn . 69 4.1.17 Hector Freytes . 70 4.1.18 Andr´eFuhrmann . 71 4.1.19 Anthony Galton . 71 4.1.20 Jonathan Ginzburg . 72 4.1.21 Edward Hermann Haeusler . 73 4.1.22 Yuri Gurevich . 74 4.1.23 Zhitao He . 75 4.1.24 Beata Konikowska . 75 4.1.25 Arnold Koslow . 77 4.1.26 Tamar Lando . 77 4.1.27 Vincenzo Marra . 78 4.1.28 Daniele Mundici . 78 4.1.29 Sara Negri . 79 4.1.30 Hiroakira Ono . 80 4.1.31 Stephen Read . 80 4.1.32 Giovanni Sambin . 81 4.1.33 Jonathan Seldin . 81 4.1.34 Gila Sher . 82 4.1.35 Sun-Joo Shin . 82 4.1.36 Barbara Tversky . 83 4.1.37 Safak Ural . 84 4.1.38 Luca Vigan`o . 84 4.1.39 Heinrich Wansing . 85 4.1.40 Andrzej Wi´sniewski . 86 4.1.41 Edward N. Zalta . 88 4.1.42 Secret Speaker . 88 4.2 Workshops . 89 3 4.2.1 Scope of Logic through History What is/was logic? Historical Perspectives . 89 4.2.2 Logic and Metaphysics . 93 4.2.3 Many-Valued Logics . 100 4.2.4 Between First and Second-Order Logic . 116 4.2.5 Generalizing Truth-Functionality { GeTFun 1.0 . 122 4.2.6 Non-Classical Mathematics . 142 4.2.7 Intuitionistic Modal Logic and Applications (IMLA 2013) 151 4.2.8 SHAPES 2.0 { The Shape of Things . 155 4.2.9 Abstract Proof Theory . 165 4.2.10 Relevant Logics . 174 4.2.11 Thinking and Rationality . 179 4.2.12 Medieval Logic . 189 4.2.13 Logical Quantum Structures . 195 4.2.14 Logic and Linguistics . 204 4.2.15 Universal Logic and Artificial Intelligence . 217 4.3 Contest { Scope of Logic Theorems . 220 4.4 Call for Papers for Contributing Speakers . 229 4.5 Sessions . 232 4.5.1 Universal . 232 4.5.2 Combination . 238 4.5.3 Modal . 245 4.5.4 Empirical . 258 4.5.5 Paradox . 262 4.5.6 Tools . 272 4.5.7 Philosophy . 306 4.5.8 Quantifiers . 317 4.5.9 Class . 323 4.5.10 History . 337 4.5.11 Algebra and Category Theory . 353 5 Book Exhibition 370 6 Sponsors and Partners 371 7 Index of Authors 372 4 1 Organizers of UNILOG'13 1.1 Scientific Committee • Arnon Avron { University of Tel-Aviv, Israel • Joham van Benthem { University of Amsterdam, Stanford University, The Netherlands and USA • Ross Brady { La Trobe University, Melbourne, Australia • Carlos Caleiro { Instituto Superior T´ecnico,Lisbon, Portugal • Walter Carnielli { State University of Campinas, Campinas, Brazil • J. Michael Dunn { School of Informatics and Computing, Indiana Univer- sity, Bloomington, USA • Dov Gabbay { King's College, London, UK • Huacan He { Northwestern Polytechnical University, Xi'an, China • Gerhard Jaeger { University of Bern, Switzerland • Arnold Koslow { City University of New York, United States • Istvan Nemeti { Hungarian Academy of Sciences, Hungary • Vladimir Vasyukov { Academy of Sciences, Moscow, Russia • Heinrich Wansing { Ruhr-University Bochum, Germany 1.2 Organizing Committee • Jean-Yves B´eziau (Chair) { Federal University of Rio de Janeiro, CNPq, Rio de Janeiro, Brazil • Oswaldo Chateaubriand { Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil • Alexandre Costa-Leite { University of Bras´ılia,Brazil • Francisco Ant^onioD´oria{ Federal University of Rio de Janeiro, Brazil • Itala Maria Loffredo D'Ottaviano { President of the Brazilian Logic Soci- ety • Katarzyna Gan-Krzywoszy´nska { Jagiellonian University, Krak´ow,Poland • Edward Hermann Haeusler { Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil • Jo~aoRicardo Moderno { President of the Brazilian Academy of Philosophy 5 • Mario Benevides { Federal University of Rio de Janeiro, Rio de Janeiro, Brazil • Raja Natarajan { Tata Institute of Fundamental Research, Mumbai, India • Claudia Passos { Federal University of Rio de Janeiro, Rio de Janeiro, Brazil • Alexandre Rademaker { Getulio Vargas Foundation, Rio de Janeiro, Brazil • Marcos Silva { Federal University of Cear´a,Fortaleza, Brazil • Miray Yazgan { Istanbul University, Turkey 1.3 Supporting Organizers • Alexandre Garcia { IME, Rio de Janeiro, Brazil. • Alvaro Altair { Federal University of Santa Catarina, Brazil • Arthur Buchsbaum { Federal University of Santa Catarina, Brazil • Catherine Chantilly { Brazilian Academy of Philosophy, Brazil • Edson Bezerra { Federal University of Rio de Janeiro, Brazil • F´abioSalgado de Carvalho { University of Brasilia, Brazil • Manuel Doria { Universidade Federal do Rio de Janeiro, Brazil • Yaakoov Israel { BeitMarketing, Rio de Janeiro, Brazil • Przemyslaw Krzywoszy´nski{ Adam Mickiewicz University, Pozna´n,Poland • Manuel Mouteira { Federal University of Rio de Janeiro, Brazil • Valeria de Paiva { University of Birmingham, United Kingdom • Luiz Carlos Pereira { Pontifical Catholic University, Rio de Janeiro, Brazil 2 Aim of the event In the same way that universal algebra is a general theory of algebraic structures, universal logic is a general theory of logical structures. During the 20th century, numerous logics have been created: intuitionistic logic, deontic logic, many- valued logic, relevant logic, linear logic, non monotonic logic, etc. Universal logic is not a new logic, it is a way of unifying this multiplicity of logics by developing general tools and concepts that can be applied to all logics. One aim of universal logic is to determine the domain of validity of such and such metatheorem (e.g. the completeness theorem) and to give general formulations of metatheorems. This is very useful for applications and helps 6 to make the distinction between what is really essential to a particular logic and what is not, and thus gives a better understanding of this particular logic. Universal logic can also be seen as a toolkit for producing a specific logic required for a given situation, e.g. a paraconsistent deontic temporal logic. This is the fourth edition of a world event dedicated to universal logic, af- ter very successful editions in Switzerland (2005), China (2007) and Portugal (2010). This event is a combination of a school and a congress. The school of- fers tutorials on a wide range of subjects. The congress will follow with invited talks and contributed talks organized in many workshops. There will also be a contest. This event is intended to be a major event in logic, providing a platform for future research guidelines. Such an event is of interest for all people dealing with logic in one way or another: pure logicians, mathematicians, computer scientists, AI researchers, linguists, psychologists, philosophers, etc. The whole event will happen at the feet of the Sugar Loaf in Rio de Janeiro, Brazil, known as The Wonder City. UNILOG'2013:.
Load more

Recommended publications
  • Naturalism and the a Priori Penelope Maddy
    5 Naturalism and the A Priori PenelopeMaddy The naturalism I aim to practise is a descendantof Quine's. I My goal here is to place this naturalism in what I hope to be an illuminating historical context, to trace the status of the a priori through its various twists and turns, and eventu- ally to draw some tentative conclusions about the naturalistic status of the a priori. To do this, I first return to Kant. While it's surely no surprise that an examination of the a priori should start from Kant, perhapshis relevanceto natu- ralism is less obvious. Let me begin, then, with an introductory word on that connection. Though my naturalism differs from Quine's in a couple of significant ways, these disagreements won't matter until the very end. so we can begin with Quine's leading idea: the 'abandonmentof the goal of a first philosophy' (Quine 1975: 72). The interconnectionsbetween Quine and Carnap will take centre stage later, but for now we needonly note that the bare rejection of first philosophy can be seen as evolving out of Carnap's classification of many traditional metaphys- ical claims as 'pseudo-statement[s] without cognitive content' (Carnap 1950: 250). Carnap's idea is that legitimate scientific questions, 'theoretical questions', are asked within the linguistic framework of scientific language,with its associ- ated principles of evidence; in contrast, metaphysical pseudo-questionsare posed outside of all linguistic frameworks; perhaps as preamble to the adoption of a linguistic framework, as such, they are asked without the backing of associated evidential rules that would make them answerable,and indeed, that would give them sense.
    [Show full text]
  • Journal of Applied Logic
    JOURNAL OF APPLIED LOGIC AUTHOR INFORMATION PACK TABLE OF CONTENTS XXX . • Description p.1 • Impact Factor p.1 • Abstracting and Indexing p.1 • Editorial Board p.1 • Guide for Authors p.5 ISSN: 1570-8683 DESCRIPTION . This journal welcomes papers in the areas of logic which can be applied in other disciplines as well as application papers in those disciplines, the unifying theme being logics arising from modelling the human agent. For a list of areas covered see the Editorial Board. The editors keep close contact with the various application areas, with The International Federation of Compuational Logic and with the book series Studies in Logic and Practical Reasoning. Benefits to authors We also provide many author benefits, such as free PDFs, a liberal copyright policy, special discounts on Elsevier publications and much more. Please click here for more information on our author services. Please see our Guide for Authors for information on article submission. This journal has an Open Archive. All published items, including research articles, have unrestricted access and will remain permanently free to read and download 48 months after publication. All papers in the Archive are subject to Elsevier's user license. If you require any further information or help, please visit our Support Center IMPACT FACTOR . 2016: 0.838 © Clarivate Analytics Journal Citation Reports 2017 ABSTRACTING AND INDEXING . Zentralblatt MATH Scopus EDITORIAL BOARD . Executive Editors Dov M. Gabbay, King's College London, London, UK Sarit Kraus, Bar-llan University,
    [Show full text]
  • Logical Foundations: Personal Perspective
    LOGICAL FOUNDATIONS: PERSONAL PERSPECTIVE YURI GUREVICH Abstract. This is an attempt to illustrate the glorious history of logical foundations and to discuss the uncertain future. Apologia1. I dread this scenario. The deadline is close. A reminder from the Chief Editor arrives. I forward it to the guest author and find out that they had a difficult real-world problem, and the scheduled article is not ready. I am full of sympathy. But the result is all the same: the article is not there. That happened once before in the long history of this column, in 2016. Then the jubilee of the 1966 Congress of Mathematicians gave me an excuse for a micro-memoir on the subject. This time around I decided to repurpose a recent talk of mine [2]. But a talk, especially one with ample time for a subsequent discussion, is much different from a paper. It would normally take me months to turn the talk into a paper. Quick repurposing is necessarily imperfect, to say the least. Hence this apologia. 1. Prelude What should logic study? Of course logic should study deductive rea- soning where the conclusions are true whenever the premises are true. But what other kinds of reasoning and argumentation should logic study? Ex- perts disagree about that. Typically it is required that reasoning be correct arXiv:2103.03930v1 [cs.LO] 5 Mar 2021 in some objective sense, so that, for example, demagoguery is not a subject of logic. My view of logic is more expansive. Logic should study argumentation of any kind, whether it is directed to a narrow circle of mathematicians, the twelve members of a jury, your family, your government, the voters of your country, the whole humanity.
    [Show full text]
  • Making Logical Form Type-Logical Glue Semantics for Minimalist Syntax
    Making Logical Form type-logical Glue Semantics for Minimalist syntax Matthew Gotham University of Oslo UiO Forum for Theoretical Linguistics 12 October 2016 Slides available at <http://folk.uio.no/matthegg/research#talks> Matthew Gotham (Oslo) Making LF type-logical FTL, 12.10.2016 1 / 63 What this talk is about Slides available at <http://folk.uio.no/matthegg/research#talks> An implementation of Glue Semantics —an approach that treats the syntax-semantics interface as deduction in a type logic— for Minimalist syntax, i.e. syntactic theories in the ST!EST!REST!GB!...‘Chomskyan’ tradition. Q How Minimalist, as opposed to (say) GB-ish? A Not particularly, but the factoring together of subcategorization and structure building (in the mechanism of feature-checking) is, if not crucial to this analysis, then certainly useful. and a comparison of this approach with more mainstream approaches to the syntax-semantics interface. Matthew Gotham (Oslo) Making LF type-logical FTL, 12.10.2016 2 / 63 Outline 1 The mainstream approach 2 A fast introduction to Glue Semantics 3 Implementation in Minimalism The form of syntactic theory assumed The connection to Glue 4 Comparison with the mainstream approach Interpreting (overt) movement Problems with the mainstream approach Glue analysis Nested DPs Scope islands Matthew Gotham (Oslo) Making LF type-logical FTL, 12.10.2016 3 / 63 The mainstream approach How semantics tends to be done for broadly GB/P&P/Minimalist syntax Aer Heim & Kratzer (1998) Syntax produces structures that are interpreted recursively
    [Show full text]
  • Proceedings of the LFG 00 Conference University of California, Berkeley Editors: Miriam Butt and Tracy Holloway King 2000 CSLI P
    Proceedings of the LFG 00 Conference University of California, Berkeley Editors: Miriam Butt and Tracy Holloway King 2000 CSLI Publications ISSN 1098-6782 Editors' Note This year's conference was held as part of a larger Berkeley Formal Grammar Conference, which included a day of workshops and the annual HPSG conference. The program committee for LFG'00 were Rachel Nordlinger and Chris Manning. We would like to thank them for putting together the program that gave rise to this collection of papers. We would also like to thank all those who contributed to this conference, especially the local organizing committee, namely Andreas Kathol, and our reviewers, without whom the conference would not have been possible. Miriam Butt and Tracy Holloway King Functional Identity and Resource-Sensitivity in Control Ash Asudeh Stanford University and Xerox PARC Proceedings of the LFG00 Conference University of California, Berkeley Miriam Butt and Tracy Holloway King (Editors) 2000 CSLI Publications http://csli-publications.stanford.edu/ 2 1 Introduction1 Glue semantics provides a semantics for Lexical Functional Grammar (LFG) that is expressed using linear logic (Girard, 1987; Dalrymple, 1999) and provides an interpretation for the f(unctional)-structure level of syntactic representation, connecting it to the level of s(emantic)-structure in LFG’s parallel projection archi- tecture (Kaplan, 1987, 1995). Due to its use of linear logic for meaning assembly, Glue is resource-sensitive: semantic resources contributed by lexical entries and resulting f-structures must each be used in a successful proof exactly once. In this paper, I will examine the tension between a resource-sensitive semantics which interprets f-structures and structure-sharing in f-structures as expressed by functional control resulting from lexical functional identity equations.
    [Show full text]
  • RELATIONAL NOUNS, PRONOUNS, and Resumptionw Relational Nouns, Such As Neighbour, Mother, and Rumour, Present a Challenge to Synt
    Linguistics and Philosophy (2005) 28:375–446 Ó Springer 2005 DOI 10.1007/s10988-005-2656-7 ASH ASUDEH RELATIONAL NOUNS, PRONOUNS, AND RESUMPTIONw ABSTRACT. This paper presents a variable-free analysis of relational nouns in Glue Semantics, within a Lexical Functional Grammar (LFG) architecture. Rela- tional nouns and resumptive pronouns are bound using the usual binding mecha- nisms of LFG. Special attention is paid to the bound readings of relational nouns, how these interact with genitives and obliques, and their behaviour with respect to scope, crossover and reconstruction. I consider a puzzle that arises regarding rela- tional nouns and resumptive pronouns, given that relational nouns can have bound readings and resumptive pronouns are just a specific instance of bound pronouns. The puzzle is: why is it impossible for bound implicit arguments of relational nouns to be resumptive? The puzzle is highlighted by a well-known variety of variable-free semantics, where pronouns and relational noun phrases are identical both in category and (base) type. I show that the puzzle also arises for an established variable-based theory. I present an analysis of resumptive pronouns that crucially treats resumptives in terms of the resource logic linear logic that underlies Glue Semantics: a resumptive pronoun is a perfectly ordinary pronoun that constitutes a surplus resource; this surplus resource requires the presence of a resumptive-licensing resource consumer, a manager resource. Manager resources properly distinguish between resumptive pronouns and bound relational nouns based on differences between them at the level of semantic structure. The resumptive puzzle is thus solved. The paper closes by considering the solution in light of the hypothesis of direct compositionality.
    [Show full text]
  • 29 Alethic Modal Logics and Semantics
    29 Alethic Modal Logics and Semantics GERHARD SCHURZ 1 Introduction The first axiomatic development of modal logic was untertaken by C. I. Lewis in 1912. Being anticipated by H. McCall in 1880, Lewis tried to cure logic from the ‘paradoxes’ of extensional (i.e. truthfunctional) implication … (cf. Hughes and Cresswell 1968: 215). He introduced the stronger notion of strict implication <, which can be defined with help of a necessity operator ᮀ (for ‘it is neessary that:’) as follows: A < B iff ᮀ(A … B); in words, A strictly implies B iff A necessarily implies B (A, B, . for arbitrary sen- tences). The new primitive sentential operator ᮀ is intensional (non-truthfunctional): the truth value of A does not determine the truth-value of ᮀA. To demonstrate this it suf- fices to find two particular sentences p, q which agree in their truth value without that ᮀp and ᮀq agree in their truth-value. For example, it p = ‘the sun is identical with itself,’ and q = ‘the sun has nine planets,’ then p and q are both true, ᮀp is true, but ᮀq is false. The dual of the necessity-operator is the possibility operator ‡ (for ‘it is possible that:’) defined as follows: ‡A iff ÿᮀÿA; in words, A is possible iff A’s negation is not necessary. Alternatively, one might introduce ‡ as new primitive operator (this was Lewis’ choice in 1918) and define ᮀA as ÿ‡ÿA and A < B as ÿ‡(A ŸÿB). Lewis’ work cumulated in Lewis and Langford (1932), where the five axiomatic systems S1–S5 were introduced.
    [Show full text]
  • Principles of Knowledge, Belief and Conditional Belief Guillaume Aucher
    Principles of Knowledge, Belief and Conditional Belief Guillaume Aucher To cite this version: Guillaume Aucher. Principles of Knowledge, Belief and Conditional Belief. Interdisciplinary Works in Logic, Epistemology, Psychology and Linguistics, pp.97 - 134, 2014, 10.1007/978-3-319-03044-9_5. hal-01098789 HAL Id: hal-01098789 https://hal.inria.fr/hal-01098789 Submitted on 29 Dec 2014 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. Principles of knowledge, belief and conditional belief Guillaume Aucher 1 Introduction Elucidating the nature of the relationship between knowledge and belief is an old issue in epistemology dating back at least to Plato. Two approaches to addressing this problem stand out from the rest. The first consists in providing a definition of knowledge, in terms of belief, that would somehow pin down the essential ingredient binding knowledge to belief. The second consists in providing a complete characterization of this relationship in terms of logical principles relating these two notions. The accomplishement of either of these two objectives would certainly contribute to solving this problem. The success of the first approach is hindered by the so-called ‘Gettier problem’. Until recently, the view that knowledge could be defined in terms of belief as ‘justified true belief’ was endorsed by most philosophers.
    [Show full text]
  • Believing the Axioms. I Penelope Maddy the Journal of Symbolic
    Believing the Axioms. I Penelope Maddy The Journal of Symbolic Logic, Vol. 53, No. 2. (Jun., 1988), pp. 481-511. Stable URL: http://links.jstor.org/sici?sici=0022-4812%28198806%2953%3A2%3C481%3ABTAI%3E2.0.CO%3B2-3 The Journal of Symbolic Logic is currently published by Association for Symbolic Logic. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/journals/asl.html. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is an independent not-for-profit organization dedicated to and preserving a digital archive of scholarly journals. For more information regarding JSTOR, please contact [email protected]. http://www.jstor.org Tue Apr 3 15:14:09 2007 THEJOURNALOF SYMBOLICLOGIC Volume 53, Number 2, June 1988 BELIEVING THE AXIOMS. I PENELOPE MADDY Nothing venture, nothing win, Blood is thick, but water's thin. -Gilbert & Sullivan $0. Introduction. Ask a beginning philosophy of mathematics student why we believe the theorems of mathematics and you are likely to hear, "because we have proofs!" The more sophisticated might add that those proofs are based on true axioms, and that our rules of inference preserve truth.
    [Show full text]
  • Logic Colloquium 2007 Edited by Francoise¸ Delon, Ulrich Kohlenbach, Penelope Maddy and Frank Stephan Frontmatter More Information
    Cambridge University Press 978-0-521-76065-2 - Logic Colloquium 2007 Edited by Francoise¸ Delon, Ulrich Kohlenbach, Penelope Maddy and Frank Stephan Frontmatter More information Logic Colloquium 2007 The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings in the field. The current volume, Logic Colloquium 2007, with contributions from ple- nary speakers and selected special session speakers, contains both expository and research papers by some of the best logicians in the world. This volume covers many areas of contemporary logic: model theory, proof theory, set theory, and computer science, as well as philosophical logic, including tutorials on cardinal arithmetic, on Pillay’s conjecture, and on automatic structures. This volume will be invaluable for experts as well as those interested in an overview of central contemporary themes in mathematical logic. Fran¸coiseDelon was Directrice d’´etudesat the Centre de Formation des PEGC of Reims and Humboldt Stipendiatin at Freiburg and is presently a Directrice de Recherche at Centre National de la Recherche Scientifique. Ulrich Kohlenbach is a Professor of Mathematics at TU Darmstadt (Germany). He is the coordinating editor of Annals of Pure and Applied Logic and the president of the Deutsche Vereinigung f¨urMathematische Logik und f¨urGrundlagen der Exakten Wissenschaften. Penelope Maddy is a Distinguished Professor of Logic and Philosophy of Science at the University of California, Irvine. She is a Fellow of the American Academy of Arts and Sciences and is currently the president of the Association for Symbolic Logic. Frank Stephan is an Associate Professor in the departments of mathematics and computer science at the National University of Singapore.
    [Show full text]
  • Existence and Reference in Medieval Logic
    GYULA KLIMA EXISTENCE AND REFERENCE IN MEDIEVAL LOGIC 1. Introduction: Existential Assumptions in Modern vs. Medieval Logic “The expression ‘free logic’ is an abbreviation for the phrase ‘free of existence assumptions with respect to its terms, general and singular’.”1 Classical quantification theory is not a free logic in this sense, as its standard formulations commonly assume that every singular term in every model is assigned a referent, an element of the universe of discourse. Indeed, since singular terms include not only singular constants, but also variables2, standard quantification theory may be regarded as involving even the assumption of the existence of the values of its variables, in accordance with Quine’s famous dictum: “to be is to be the value of a variable”.3 But according to some modern interpretations of Aristotelian syllogistic, Aristotle’s theory would involve an even stronger existential assumption, not shared by quantification theory, namely, the assumption of the non-emptiness of common terms.4 Indeed, the need for such an assumption seems to be supported not only by a number of syllogistic forms, which without this assumption appear to be invalid, but also by the doctrine of Aristotle’s De Interpretatione concerning the logical relationships among categorical propositions, commonly summarized in the Square of Opposition. For example, Aristotle’s theory states that universal affirmative propositions imply particular affirmative propositions. But if we formalize such propositions in quantification theory, we get formulae between which the corresponding implication does not hold. So, evidently, there is some discrepancy between the ways Aristotle and quantification theory interpret these categoricals.
    [Show full text]
  • Probabilistic Semantics for Modal Logic
    Probabilistic Semantics for Modal Logic By Tamar Ariela Lando A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Philosophy in the Graduate Division of the University of California, Berkeley Committee in Charge: Paolo Mancosu (Co-Chair) Barry Stroud (Co-Chair) Christos Papadimitriou Spring, 2012 Abstract Probabilistic Semantics for Modal Logic by Tamar Ariela Lando Doctor of Philosophy in Philosophy University of California, Berkeley Professor Paolo Mancosu & Professor Barry Stroud, Co-Chairs We develop a probabilistic semantics for modal logic, which was introduced in recent years by Dana Scott. This semantics is intimately related to an older, topological semantics for modal logic developed by Tarski in the 1940’s. Instead of interpreting modal languages in topological spaces, as Tarski did, we interpret them in the Lebesgue measure algebra, or algebra of measurable subsets of the real interval, [0, 1], modulo sets of measure zero. In the probabilistic semantics, each formula is assigned to some element of the algebra, and acquires a corresponding probability (or measure) value. A formula is satisfed in a model over the algebra if it is assigned to the top element in the algebra—or, equivalently, has probability 1. The dissertation focuses on questions of completeness. We show that the propo- sitional modal logic, S4, is sound and complete for the probabilistic semantics (formally, S4 is sound and complete for the Lebesgue measure algebra). We then show that we can extend this semantics to more complex, multi-modal languages. In particular, we prove that the dynamic topological logic, S4C, is sound and com- plete for the probabilistic semantics (formally, S4C is sound and complete for the Lebesgue measure algebra with O-operators).
    [Show full text]