Logic And Implication
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Logic And Implication
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Author : Petr Cintula
language : en
Publisher: Springer Nature
Release Date : 2022-01-01
Logic And Implication written by Petr Cintula and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Philosophy categories.
This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to (abstract) algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions. Based on their recent work, the authors develop a powerful uniform framework for the study of non-classical logics. In a self-contained and didactic style, starting from very elementary notions, they build a general theory with a substantial number of abstract results. The theory is then applied to obtain numerous results for prominent families of logics and their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and relevant logics. The book may be of interest to a wide audience, especially students and scholars in the fields of mathematics, philosophy, computer science, or related areas, looking for an introduction to a general theory of non-classical logics and their algebraic semantics.
Foundations Of Logico Linguistics
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Author : W.S. Cooper
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Foundations Of Logico Linguistics written by W.S. Cooper and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Language Arts & Disciplines categories.
In 1962 a mimeographed sheet of paper fell into my possession. It had been prepared by Ernest Adams of the Philosophy Department at Berkeley as a handout for a colloquim. Headed 'SOME FALLACIES OF FORMAL LOGIC' it simply listed eleven little pieces of reasoning, all in ordinary English, and all absurd. I still have the sheet, and quote a couple of the arguments here to give the idea. • If you throw switch S and switch T, the motor will start. There fore, either if you throw switch S the motor will start, or, if you throw switch T the motor will start . • It is not the case that if John passes history he will graduate. Therefore, John will pass history. The disconcerting thing about these inferences is, of course, that under the customary truth-functional interpretation of and, or, not, and if-then, they are supposed to be valid. What, if anything, is wrong? At first I was not disturbed by the examples. Having at that time consider able personal commitment to rationality in general and formal logic in par ticular, I felt it my duty and found myself easily able (or so I thought) to explain away most of them. But on reflection I had to admit that my expla nations had an ad hoc character, varying suspiciously from example to example.
The Formalization Of Implication In Propositional Logic
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Author : Patrick Foster Schindler
language : en
Publisher:
Release Date : 1963
The Formalization Of Implication In Propositional Logic written by Patrick Foster Schindler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with categories.
"This thesis presents the results or an attempt to isolate and give an axiomatic basis for the pure-implication fragment or each or several logical systems. C. I. Lewis points out that exact logic may be taken as a canon or deductive inference, and that the chief business of a canon or deduction is to delineate correctly the properties of the relation of 'implication'. It seems clear, then, that criticism or any logical calculus must include consideration of just what properties are imputed to the relation of 'implication' by that calculus." --
Introduction To Logic Third Edition
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Author : Genesereth Michael
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Introduction To Logic Third Edition written by Genesereth Michael and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Mathematics categories.
This book is a gentle but rigorous introduction to Formal Logic. It is intended primarily for use at the college level. However, it can also be used for advanced secondary school students, and it can be used at the start of graduate school for those who have not yet seen the material. The approach to teaching logic used here emerged from more than 20 years of teaching logic to students at Stanford University and from teaching logic to tens of thousands of others via online courses on the World Wide Web. The approach differs from that taken by other books in logic in two essential ways, one having to do with content, the other with form. Like many other books on logic, this one covers logical syntax and semantics and proof theory plus induction. However, unlike other books, this book begins with Herbrand semantics rather than the more traditional Tarskian semantics. This approach makes the material considerably easier for students to understand and leaves them with a deeper understanding of what logic is all about. In addition to this text, there are online exercises (with automated grading), online logic tools and applications, online videos of lectures, and an online forum for discussion. They are available at http://intrologic.stanford.edu/
The Semantics And Proof Theory Of The Logic Of Bunched Implications
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Author : David J. Pym
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
The Semantics And Proof Theory Of The Logic Of Bunched Implications written by David J. Pym and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
This is a monograph about logic. Specifically, it presents the mathe matical theory of the logic of bunched implications, BI: I consider Bl's proof theory, model theory and computation theory. However, the mono graph is also about informatics in a sense which I explain. Specifically, it is about mathematical models of resources and logics for reasoning about resources. I begin with an introduction which presents my (background) view of logic from the point of view of informatics, paying particular attention to three logical topics which have arisen from the development of logic within informatics: • Resources as a basis for semantics; • Proof-search as a basis for reasoning; and • The theory of representation of object-logics in a meta-logic. The ensuing development represents a logical theory which draws upon the mathematical, philosophical and computational aspects of logic. Part I presents the logical theory of propositional BI, together with a computational interpretation. Part II presents a corresponding devel opment for predicate BI. In both parts, I develop proof-, model- and type-theoretic analyses. I also provide semantically-motivated compu tational perspectives, so beginning a mathematical theory of resources. I have not included any analysis, beyond conjecture, of properties such as decidability, finite models, games or complexity. I prefer to leave these matters to other occasions, perhaps in broader contexts.
A Friendly Introduction To Mathematical Logic
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Author : Christopher C. Leary
language : en
Publisher: Lulu.com
Release Date : 2015
A Friendly Introduction To Mathematical Logic written by Christopher C. Leary and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Education categories.
At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.
Problems Of The Logic Of Scientific Knowledge
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Author : P.V. Tavanec
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Problems Of The Logic Of Scientific Knowledge written by P.V. Tavanec and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Implication And Linear Inference
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Author : Bernard Bosanquet
language : en
Publisher: Forgotten Books
Release Date : 2015-06-26
Implication And Linear Inference written by Bernard Bosanquet and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-26 with Philosophy categories.
Excerpt from Implication and Linear Inference My object in the present work is to develop and elucidate the non-syllogistic principle on which my Logic was founded. In order to make the central idea clear, I have permitted myself some detailed criticism of other writers, while I have abstained from complicated systematic construction. Still following Mr. Bradley, and influenced further by Mr. Joseph, especially in the distinction between Syllogism and Deduction, I have laid even more stress than before on the principle of coherence, and have insisted on "implication" as a term free from reference to reasoning in its traditional shapes. I have thus been able, as I hope, to do much more justice to Mr. Bradley's positive account of inference than was done in my former work. The contrast expressed in the title of the book has forced itself on me continually, not only in the logical studies of which specimens appear in my criticism, but in all common-sense argument and observation, and in actual acquaintance with reasoning as conducted by great writers and capable publicists. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Implication And Linear Inference
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Author : Bernard Bosanquet
language : en
Publisher:
Release Date : 1968
Implication And Linear Inference written by Bernard Bosanquet and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Logic categories.
A Spiral Workbook For Discrete Mathematics
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Author : Harris Kwong
language : en
Publisher: Open SUNY Textbooks
Release Date : 2015-11-06
A Spiral Workbook For Discrete Mathematics written by Harris Kwong and has been published by Open SUNY Textbooks this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-06 with Mathematics categories.
A Spiral Workbook for Discrete Mathematics covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions,relations, and elementary combinatorics, with an emphasis on motivation. The text explains and claries the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a nal polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a dierent perspective or at a higher level of complexity, in order to slowly develop the student's problem-solving and writing skills.