A collection of papers from Paul Hertz to Dov Gabbay - through Tarski, Gödel, Kripke - giving a general perspective about logical systems. These papers discuss questions such as the relativity and nature of logic, present tools such as consequence operators and combinations of logics, prove theorems such as translations between logics, investigate the domain of validity and application of fundamental results such as compactness and completeness. Each of these papers is presented by a specialist explaining its context, import and influence.
Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 24th Workshop on Logic, Language, Information and Communication, WoLLIC 2017, held in London, UK, in August 2017. The 28 contributed papers were carefully reviewed and selected from 61 submissions. The WoLLIC Workshop aims to foster interdisciplinary research in pure and applied logic. The idea is to have a forum which is large enough in the number of possible interactions between logic andthe sciences related to information and computation.
This second volume of a collection of papers offers new perspectives and challenges in the study of logic. It is presented in honor of the fiftieth birthday of Jean-Yves Béziau. The papers touch upon a wide range of topics including paraconsistent logic, quantum logic, geometry of oppositions, categorical logic, computational logic, fundamental logic notions (identity, rule, quantification) and history of logic (Leibniz, Peirce, Hilbert). The volume gathers personal recollections about Jean-Yves Béziau and an autobiography, followed by 25 papers written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Irving Anellis, Dov Gabbay, Ivor Grattan-Guinness, Istvan Németi, Henri Prade. These essays will be of interest to all students and researchers interested in the nature and future of logic.
The book outlines selected projects conducted under the supervision of the author. Moreover, it discusses significant relations between Interactive Granular Computing (IGrC) and numerous dynamically developing scientific domains worldwide, along with features characteristic of the author’s approach to IGrC. The results presented are a continuation and elaboration of various aspects of Wisdom Technology, initiated and developed in cooperation with Professor Andrzej Skowron. Based on the empirical findings from these projects, the author explores the following areas: (a) understanding the causes of the theory and practice gap problem (TPGP) in complex systems engineering (CSE); (b) generalizing computing models of complex adaptive systems (CAS) (in particular, natural computing models) by constructing an interactive granular computing (IGrC) model of networks of interrelated interacting complex granules (c-granules), belonging to a single agent and/or to a group of agents; (c) developing methodologies based on the IGrC model to minimize the negative consequences of the TPGP. The book introduces approaches to the above issues, using the proposed IGrC model. In particular, the IGrC model refers to the key mechanisms used to control the processes related to the implementation of CSE projects. One of the main aims was to develop a mechanism of IGrC control over computations that model a project’s implementation processes to maximize the chances of its success, while at the same time minimizing the emerging risks. In this regard, the IGrC control is usually performed by means of properly selected and enforced (among project participants) project principles. These principles constitute examples of c-granules, expressed by complex vague concepts (represented by c-granules too). The c-granules evolve with time (in particular, the meaning of the concepts is also subject of change). This methodology is illustrated using project principles applied by the author during the implementation of the POLTAX, AlgoTradix, Merix, and Excavio projects outlined in the book.
The Handbook of the History of Logic is a multi-volume research instrument that brings to the development of logic the best in modern techniques of historical and interpretative scholarship. It is the first work in English in which the history of logic is presented so extensively. The volumes are numerous and large. Authors have been given considerable latitude to produce chapters of a length, and a level of detail, that would lay fair claim on the ambitions of the project to be a definitive research work. Authors have been carefully selected with this aim in mind. They and the Editors join in the conviction that a knowledge of the history of logic is nothing but beneficial to the subject's present-day research programmes. One of the attractions of the Handbook's several volumes is the emphasis they give to the enduring relevance of developments in logic throughout the ages, including some of the earliest manifestations of the subject. Covers in depth the notion of logical consequence Discusses the central concept in logic of modality Includes the use of diagrams in logical reasoning
Author: Imre Bárány
Publisher: Springer Science & Business Media
Release Date: 2011-02-11
Szemerédi's influence on today's mathematics, especially in combinatorics, additive number theory, and theoretical computer science, is enormous. This volume is a celebration of Szemerédi's achievements and personality, on the occasion of his seventieth birthday. It exemplifies his extraordinary vision and unique way of thinking. A number of colleagues and friends, all top authorities in their fields, have contributed their latest research papers to this volume. The topics include extension and applications of the regularity lemma, the existence of k-term arithmetic progressions in various subsets of the integers, extremal problems in hypergraphs theory, and random graphs, all of them beautiful, Szemerédi type mathematics. It also contains published accounts of the first two, very original and highly successful Polymath projects, one led by Tim Gowers and the other by Terry Tao.
Author: P. Mancosu
Publisher: Springer Science & Business Media
Release Date: 2006-03-30
In the 20th century philosophy of mathematics has to a great extent been dominated by views developed during the so-called foundational crisis in the beginning of that century. These views have primarily focused on questions pertaining to the logical structure of mathematics and questions regarding the justi?cation and consistency of mathematics. Paradigmatic in this - spect is Hilbert’s program which inherits from Frege and Russell the project to formalize all areas of ordinary mathematics and then adds the requi- ment of a proof, by epistemically privileged means (?nitistic reasoning), of the consistency of such formalized theories. While interest in modi?ed v- sions of the original foundational programs is still thriving, in the second part of the twentieth century several philosophers and historians of mat- matics have questioned whether such foundational programs could exhaust the realm of important philosophical problems to be raised about the nature of mathematics. Some have done so in open confrontation (and hostility) to the logically based analysis of mathematics which characterized the cl- sical foundational programs, while others (and many of the contributors to this book belong to this tradition) have only called for an extension of the range of questions and problems that should be raised in connection with an understanding of mathematics. The focus has turned thus to a consideration of what mathematicians are actually doing when they produce mathematics. Questions concerning concept-formation, understanding, heuristics, changes instyle of reasoning, the role of analogies and diagrams etc.
Author: Jens Eder
Publisher: Walter de Gruyter
Release Date: 2011-01-01
Genre: Literary Criticism
Although fictional characters have long dominated the reception of literature, films, television programs, comics, and other media products, only recently have they begun to attract their due attention in literary and media theory. The book systematically surveys today´s diverse and at times conflicting theoretical perspectives on fictional character, spanning research on topics such as the differences between fictional characters and real persons, the ontological status of characters, the strategies of their representation and characterization, the psychology of their reception, as well as their specific forms and constellations in - and across - different media, from the book to the internet.
Author: Michele White
Publisher: MIT Press
Release Date: 2006
"White shows that despite the onscreen promise of empowerment and coherence (through depictions of materiality that structure the experience), fragmentation and confusion are constant aspects of Internet spectatorship.--BOOK JACKET.
Author: Jean-Yves Beziau
Publisher: Springer Science & Business Media
Release Date: 2007-08-08
Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic. It was revived after the flowering of thousands of new logics during the last thirty years: there was a need for a systematic theory of logics to put some order in this chaotic multiplicity. The present book contains recent works on universal logic by first-class researchers from all around the world. The book is full of new and challenging ideas that will guide the future of this exciting subject. It will be of interest for people who want to better understand what logic is. It will help those who are lost in the jungle of heterogeneous logical systems to find a way. Tools and concepts are provided here for those who want to study classes of already existing logics or want to design and build new ones.
Author: Josep Maria Font
Release Date: 2016-04-11
Abstract algebraic logic is the more general and abstract side of algebraic logic, the branch of mathematics that studies the connections between logics and their algebra-based semantics. This emerging subfield of mathematical logic consolidated since the 1980s, and is considered as the algebraic logic of the twenty-first century; as such it is increasingly becoming an indispensable tool to approach the algebraic study of any (mainly sentential) logic in a systematic way. This book is an introductory textbook on abstract algebraic logic, and takes a bottom-up approach, treating first logics with a simpler algebraic study, such as Rasiowa's implicative logics, and then guides readers, by means of successive steps of generalization and abstraction, to meet more and more complicated algebra-based semantics. An entire chapter is devoted to Blok and Pigozzi's theory of algebraizable logics, proving the main theorems and incorporating later developments by other scholars. After a chapter with the basics of the classical theory of matrices, one chapter is devoted to an in-depth exposition of the semantics of generalized matrices. There are also two more avanced chapters providing introductions to the two hierachies that organize the logical landscape according to the criteria of abstract algebraic logic, the Leibniz hierarchy and the Frege hierarchy. All throughout the book, particular care is devoted to the presentation and classification of dozens of examples of particular logics. The book is addressed to mathematicians and logicians with little or no previous exposure to algebraic logic. Some acquaintance with examples of non-classical logics is desirable in order to appreciate the extremely general theory. The book is written with students (or beginners in the field) in mind, and combines a textbook style in its main sections, including more than 400 carefully graded exercises, with a survey style in the exposition of some research directions. The book includes scattered historical notes and numerous bibliographic references.
Author: Jean-Yves Beziau
Publisher: Peter Lang Pub Incorporated
Release Date: 2012
Papers ... "selected from a larger number of contributions most of them based on talks presented at the First World Congress on the Square of Opposition organized in Montreux in June 2007"--Preface, p. 12.
This book offers an original contribution to the foundations of logic and mathematics and focuses on the internal logic of mathematical theories, from arithmetic or number theory to algebraic geometry. Arithmetical logic is the term used to refer to the internal logic of classical arithmetic, here called Fermat-Kronecker arithmetic and combines Fermat’s method of infinite descent with Kronecker’s general arithmetic of homogeneous polynomials. The book also includes a treatment of theories in physics and mathematical physics to underscore the role of arithmetic from a constructivist viewpoint. The scope of the work intertwines historical, mathematical, logical and philosophical dimensions in a unified critical perspective; as such, it will appeal to a broad readership from mathematicians to logicians, to philosophers interested in foundational questions. Researchers and graduate students in the fields of philosophy and mathematics will benefit from the author’s critical approach to the foundations of logic and mathematics.