Foundations Of Logical Consequence
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Foundations Of Logical Consequence
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Author : Colin R. Caret
language : en
Publisher: Mind Association Occasional
Release Date : 2015
Foundations Of Logical Consequence written by Colin R. Caret and has been published by Mind Association Occasional this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
This volume presents new work on a central issue in the philosophy of logic. Leading figures in the field offer ground-breaking insights into topics including the nature of logical consequence; the relation between logic and inference; the relativity of logic; and the structural properties of the consequence relation.
Foundations Of Logic Programming
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Author : J. W. Lloyd
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Foundations Of Logic Programming written by J. W. Lloyd 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 Computers categories.
This book gives an account oC the mathematical Coundations oC logic programming. I have attempted to make the book selC-contained by including prooCs of almost all the results needed. The only prerequisites are some Camiliarity with a logic programming language, such as PROLOG, and a certain mathematical maturity. For example, the reader should be Camiliar with induction arguments and be comCortable manipulating logical expressions. Also the last chapter assumes some acquaintance with the elementary aspects of metric spaces, especially properties oC continuous mappings and compact spaces. Chapter 1 presents the declarative aspects of logic programming. This chapter contains the basic material Crom first order logic and fixpoint theory which will be required. The main concepts discussed here are those oC a logic program, model, correct answer substitution and fixpoint. Also the unification algorithm is discussed in some detail. Chapter 2 is concerned with the procedural semantics oC logic programs. The declarative concepts are implemented by means oC a specialized Corm oC resolution, called SLD-resolution. The main results of this chapter concern the soundness and completeness oC SLD-resolution and the independence oC the computation rule. We also discuss the implications of omitting the occur check from PROLOG implementations. Chapter 3 discusses negation. Current PROLOG systems implement a form of negation by means of the negation as failure rule. The main results of this chapter are the soundness and completeness oC the negation as failure rule.
The Foundations Of Mathematics
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Author : Kenneth Kunen
language : en
Publisher:
Release Date : 2009
The Foundations Of Mathematics written by Kenneth Kunen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.
Philosophical Approaches To The Foundations Of Logic And Mathematics
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Author : Marcin Trepczyński
language : en
Publisher: BRILL
Release Date : 2021-01-25
Philosophical Approaches To The Foundations Of Logic And Mathematics written by Marcin Trepczyński and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-25 with Philosophy categories.
Philosophical Approaches to the Foundations of Logic and Mathematics consists of eleven articles addressing various aspects of the "roots" of logic and mathematics, their basic concepts and the mechanisms that work in the practice of their use.
Propositional Logics
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Author : Richard L. Epstein
language : en
Publisher:
Release Date : 2012-06-01
Propositional Logics written by Richard L. Epstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-01 with Mathematics categories.
Propositional Logics presents the history, philosophy, and mathematics of the major systems of propositional logic. Classical logic, modal logics, many-valued logics, intuitionism, paraconsistent logics, and dependent implication are examined in separate chapters. Each begins with a motivation in the originators' own terms, followed by the standard formal semantics, syntax, and completeness theorem. The chapters on the various logics are largely self-contained so that the book can be used as a reference. An appendix summarizes the formal semantics and axiomatizations of the logics. The view that unifies the exposition is that propositional logics comprise a spectrum. As the aspect of propositions under consideration varies, the logic varies. Each logic is shown to fall naturally within a general framework for semantics. A theory of translations between logics is presented that allows for further comparisons, and necessary conditions are given for a translation to preserve meaning. For this third edition the material has been re-organized to make the text easier to study, and a new section on paraconsistent logics with simple semantics has been added which challenges standard views on the nature of consequence relations. The text includes worked examples and hundreds of exercises, from routine to open problems, making the book with its clear and careful exposition ideal for courses or individual study.
Logical Pluralism And Logical Consequence
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Author : Erik Stei
language : en
Publisher: Cambridge University Press
Release Date : 2023-03-30
Logical Pluralism And Logical Consequence written by Erik Stei and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-30 with Philosophy categories.
Logical pluralism is the view that there is more than one correct logic. This is not necessarily a controversial claim but in its most exciting formulations, pluralism extends to logics that have typically been considered rival accounts of logical consequence – to logics, that is, which adopt seemingly contradictory views about basic logical laws or arguments. The logical pluralist challenges the philosophical orthodoxy that an argument is either deductively valid or invalid by claiming that there is more than one way for an argument to be valid. In this book, Erik Stei defends logical monism, provides a detailed analysis of different possible formulations of logical pluralism, and offers an original account of the plurality of correct logics that incorporates the benefits of both pluralist and monist approaches to logical consequence. His book will be valuable for a range of readers in the philosophy of logic.
Foundations Of Logic And Linguistics
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Author : Georg Dorn
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
Foundations Of Logic And Linguistics written by Georg Dorn 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 2013-11-21 with Philosophy categories.
This volume comprises a selection of papers that were contributed to the 7th International Congress of Logic, Methodology and Philosophy of Science, which was held in Salzburg from the 11th - 16th July, 1983. There were 14 sections in this congress: 1. proof theory and foundations of mathematics 2. model theory and its applica ti on 3. recursion theory and theory of computation 4. axiomatic set theory 5. philosophical logic 6. general methodology of science 7. foundations of probability and induction 8. foundations and philosophy of the physical sciences 9. foundati ons and phi 1 osophy of biology 10. foundations and philosophy of psychology foundations and philosophy 11. of the social sciences 12. foundati ons and philosophy of linguistics 13. history of logic, methodology and philosophy of science 14. fundamental principles of the ethics of science In each section, three or four invited addresses were given, which will be published in the Congress Proceedings (Ruth Barcan Marcus, Georg J. W. Dorn and Paul Weingartner, eds. : Logic, Metho dology and Philosophy of Science VII. Proceedings of the Seventh International Congress of Logic, Methodology and Philosophy of v PREFACE Science, Salzburg, 1983. - Amsterdam, New York, Oxford: North-Holland Publishing 'Company, 1985. ) Every section with the exception of section 14 also contained contributed papers.
Sets Logic And Mathematical Foundations
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Author : Stephen Cole Kleene
language : en
Publisher:
Release Date : 1968
Sets Logic And Mathematical Foundations written by Stephen Cole Kleene 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, Symbolic and mathematical categories.
Grounded Consequence For Defeasible Logic
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Author : Aldo Antonelli
language : en
Publisher: Cambridge University Press
Release Date : 2005-06-27
Grounded Consequence For Defeasible Logic written by Aldo Antonelli and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-27 with Science categories.
This is a title on the foundations of defeasible logic, which explores the formal properties of everyday reasoning patterns whereby people jump to conclusions, reserving the right to retract them in the light of further information. Although technical in nature the book contains sections that outline basic issues by means of intuitive and simple examples. This book is primarily targeted at philosophers interested in the foundations of defeasible logic, logicians, and specialists in artificial intelligence and theoretical computer science.
Foundations Of Fuzzy Logic And Semantic Web Languages Open Access
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Author : Umberto Straccia
language : en
Publisher: CRC Press
Release Date : 2016-04-19
Foundations Of Fuzzy Logic And Semantic Web Languages Open Access written by Umberto Straccia and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Computers categories.
Managing vagueness/fuzziness is starting to play an important role in Semantic Web research, with a large number of research efforts underway. Foundations of Fuzzy Logic and Semantic Web Languages provides a rigorous and succinct account of the mathematical methods and tools used for representing and reasoning with fuzzy information within Semantic