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Logic and Language in Wittgenstein's Tractatus

This historical study investigates Ludwig Wittgenstein's early philosophy of logic and language, as it is presented in his Tractatus Logico-Philosophicus. The study makes a case for the Tractatus as an insightful critique of the philosophies of Bertrand Russell and Gottlob Frege-the Founding Fathers of analytic philosophy.

Logic and Lexicon: The Semantics of the Indefinite (Studies in Linguistics and Philosophy #56)

Semantic underspecification is an essential and pervasive property of natural language. This monograph provides a comprehensive survey of the various phenomena in the field of ambiguity and vagueness. The book discusses the major theories of semantic indefiniteness, which have been proposed in linguistics, philosophy and computer science. It argues for a view of indefiniteness as the potential for further contextual specification, and proposes a unified logical treatment of indefiniteness on this basis. The inherent inconsistency of natural language induced by irreducible imprecision is investigated, and treated in terms of a dynamic extension of the proposed logic. The book is an extended edition of a German monograph and is addressed to advanced students and researchers in theoretical and computational linguistics, logic, philosophy of language, and NL- oriented AI. Although it makes extensive use of logical formalisms, it requires only some basic familiarity with standard predicate logic concepts since all technical terms are carefully explained.

Logic and Philosophy in the Lvov—Warsaw School (Synthese Library #198)

Logic and Philosophy / Logique et Philosophie (Institut International de Philosophie #5)

The Entretiens of the Institut International de Philosophie for 1978 were held in connection with the World Congress of Philosophy in Dusseldorf, from August 27 to September 1. The theme of the Entretiens was Logic and Philosophy (Logique et philosophie). The undersigned, then President of LI.P., was responsible for the planning of the programme. The programme was designed to consist of four sections with the headings Classical and Intuitionist Logic, Modal Logic and its Applications, Inductive Logic and its Applications, and Logic and Epistemology. The aim was also to convey to philosophers who are not experts in logic an informative and representative impression of some of the main sectors of the vast and rapidly expanding field of philosophical logic. At the same time it was thought that this impression should not be conveyed in the form of a series of survey papers but through presentations and discussions of specific topics falling under the main headings men­ tioned above. For each section a rapporteur was nominated to read a paper and an interlocuteur to comment on it. The programme chairman is grateful that he was able to engage a representative selection of front rank philosophi­ cal logicians to perform the various tasks. The papers and the comments are printed in this volume in the order in which they appeared in the Programme of the Entretiens.

Logic and Philosophy of Mathematics in the Early Husserl (Synthese Library #345)

Logic and Philosophy of Mathematics in the Early Husserl focuses on the first ten years of Edmund Husserl’s work, from the publication of his Philosophy of Arithmetic (1891) to that of his Logical Investigations (1900/01), and aims to precisely locate his early work in the fields of logic, philosophy of logic and philosophy of mathematics. Unlike most phenomenologists, the author refrains from reading Husserl’s early work as a more or less immature sketch of claims consolidated only in his later phenomenology, and unlike the majority of historians of logic she emphasizes the systematic strength and the originality of Husserl’s logico-mathematical work. The book attempts to reconstruct the discussion between Husserl and those philosophers and mathematicians who contributed to new developments in logic, such as Leibniz, Bolzano, the logical algebraists (especially Boole and Schröder), Frege, and Hilbert and his school. It presents both a comprehensive critical examination of some of the major works produced by Husserl and his antagonists in the last decade of the 19th century and a formal reconstruction of many texts from Husserl’s Nachlaß that have not yet been the object of systematical scrutiny. This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to analytical philosophers and phenomenologists with a background in standard logic.

Logic and Philosophy of Science in Uppsala (Synthese Library #236)

The International Congresses of Logic, Methodology and Philosophy of Science, which are held every fourth year, give a cross-section of ongoing research in logic and philosophy of science. Both the invited lectures and the many contributed papers are conductive to this end. At the 9th Congress held in Uppsala in 1991 there were 54 invited lectures and around 650 contributed papers divided into 15 different sections. Some of the speakers who presented contributed papers that attracted special interest were invited to submit their papers for publication, and the result is the present volume. A few papers appear here more or less as they were presented at the Congress whereas others are expansions or elaborations of the talks given at the Congress. A selection of this kind, containing 38 papers drawn from the 650 contributed papers presented at the Uppsala Congress, cannot do justice to all facets of the field as it appeared at the Congress. But it should allow the reader to get a representative survey of contemporary research in large areas of philosophical logic and philosophy of science. About half of the papers of the volume appear in sections listed at the Congress under the heading Philosophical and Foundational Problems about the Sciences. The section Foundations of Logic, Mathematics and Computer Science is represented by three papers, Foundations of Physical Sciences by six papers, Foundations of Biological Sciences by three papers, Foundations of Cognitive Science and AI by one paper, and Foundations of Linguistics by three papers.

Logic and Probability in Quantum Mechanics (Synthese Library #78)

During the academic years 1972-1973 and 1973-1974, an intensive sem­ inar on the foundations of quantum mechanics met at Stanford on a regular basis. The extensive exploration of ideas in the seminar led to the org~ization of a double issue of Synthese concerned with the foundations of quantum mechanics, especially with the role of logic and probability in quantum meChanics. About half of the articles in the volume grew out of this seminar. The remaining articles have been so­ licited explicitly from individuals who are actively working in the foun­ dations of quantum mechanics. Seventeen of the twenty-one articles appeared in Volume 29 of Syn­ these. Four additional articles and a bibliography on -the history and philosophy of quantum mechanics have been added to the present volume. In particular, the articles by Bub, Demopoulos, and Lande, as well as the second article by Zanotti and myself, appear for the first time in the present volume. In preparing the articles for publication I am much indebted to Mrs. Lillian O'Toole, Mrs. Dianne Kanerva, and Mrs. Marguerite Shaw, for their extensive assistance.

Logic and Program Semantics: Essays Dedicated to Dexter Kozen on the Occasion of His 60th Birthday (Lecture Notes in Computer Science #7230)

This Festschrift volume is published in honor of Dexter Kozen on the occasion of his 60th birthday. Dexter Kozen has been a leader in the development of Kleene Algebras (KAs). The contributions in this volume reflect the breadth of his work and influence. The volume includes 19 full papers related to Dexter Kozen's research. They deal with coalgebraic methods, congruence closure; the completeness of various programming logics; decision procedure for logics; alternation; algorithms and complexity; and programming languages and program analysis. The second part of this volume includes laudatios from several collaborators, students and friends, including the members of his current band.

Logic and Reality in the Philosophy of John Stuart Mill (Synthese Historical Library #34)

'Nobody reads Mill today,' wrote a reviewer in Time magazine a few years ago. ! One could scarcely praise Mr Melvin Maddocks, who penned that remark, for his awareness of the present state of Mill studies, for of all nineteenth century philosophers who wrote in English, it is 1. S. Mill who remains the most read today. Yet it would not be so far from the truth to say that very few people pay much serious attention nowadays to Mill's writings about logic and metaphysics (as distinct from those on ethical and social issues), despite the fact that Mill put enormous effort into their composition and through them exerted a considerable influen­ ce on the course of European philosophy for the rest of his century. But the only sections of A System of Logic (1843) and An Examination of Sir William Hamilton's Philosophy (1865) to which much reference is now made comprise only a small proportion of those very large books, and the prevailing assumption is that Mill's theories about logical and meta­ physical questions are, with few exceptions, of merely antiquarian in­ terest. Bertrand Russell once said that Mill's misfortune was to be born at the wrong time (Russell (1951), p. 2). It can certainly appear that Mill chose an inauspicious time to attempt a major work on logic.

Logic and Scientific Methods: Volume One of the Tenth International Congress of Logic, Methodology and Philosophy of Science, Florence, August 1995 (Synthese Library #259)

This is the first of two volumes comprising the papers submitted for publication by the invited participants to the Tenth International Congress of Logic, Methodology and Philosophy of Science, held in Florence, August 1995. The Congress was held under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science. The invited lectures published in the two volumes demonstrate much of what goes on in the fields of the Congress and give the state of the art of current research. The two volumes cover the traditional subdisciplines of mathematical logic and philosophical logic, as well as their interfaces with computer science, linguistics and philosophy. Philosophy of science is broadly represented, too, including general issues of natural sciences, social sciences and humanities. The papers in Volume One are concerned with logic, mathematical logic, the philosophy of logic and mathematics, and computer science.

Logic and Structure (Universitext)

New corrected printing of a well-established text on logic at the introductory level.

Logic and Structure (Universitext)

New corrected printing of a well-established text on logic at the introductory level.

Logic and Structure (Universitext)

New corrected printing of a well-established text on logic at the introductory level.

Logic and Structure (Universitext)

Dirk van Dalen’s popular textbook Logic and Structure, now in its fifth edition, provides a comprehensive introduction to the basics of classical and intuitionistic logic, model theory and Gödel’s famous incompleteness theorem. Propositional and predicate logic are presented in an easy-to-read style using Gentzen’s natural deduction. The book proceeds with some basic concepts and facts of model theory: a discussion on compactness, Skolem-Löwenheim, non-standard models and quantifier elimination. The discussion of classical logic is concluded with a concise exposition of second-order logic. In view of the growing recognition of constructive methods and principles, intuitionistic logic and Kripke semantics is carefully explored. A number of specific constructive features, such as apartness and equality, the Gödel translation, the disjunction and existence property are also included. The last chapter on Gödel's first incompleteness theorem is self-contained and provides a systematic exposition of the necessary recursion theory. This new edition has been properly revised and contains a new section on ultra-products.

Logic and Structure (Universitext)

New corrected printing of a well-established text on logic at the introductory level.

Logic and the Foundations of Game and Decision Theory - LOFT 8: 8th International Conference, Amsterdam, The Netherlands, July 3-5, 2008, Revised Selected Papers (Lecture Notes in Computer Science #6006)

Logic and the Limits of Philosophy in Kant and Hegel

This text examines the boundary between logic and philosophy in Kant and Hegel. Through a detailed analysis of 'quantity', it highlights the different ways Kant and Hegel handle this boundary. Kant is consistent in maintaining this boundary, but Hegel erases it and in the process transforms both logic and philosophy.

Logic and the Nature of God (Library of Philosophy and Religion)

The book '... should be assured of the attention of the many on both sides of the Atlantic who are fascinated by this subject.' John Hick

Logic and the Nature of Reality

This book is not merely about metaphysics; it is an essay in metaphysics. Furthermore, it is written in the firm conviction that metaphysics is possible and meaningful metaphysical statements can and should be made. However, I felt it necessary to approach the perennial problems of metaphysics through the avenues of linguistic analysis. I have tried not only to infiltrate the position of the linguists but to show that a fifth column already existed there. Yet the objections to metaphysics needed to be met or at least some indication of how they could be met had to be shown. It is never enough to demonstrate that objections are un­ founded - some positive indications of a possible metaphysics had to be offered. This book, as a consequence, tries also to draw at least in broad outline, a metaphysical position that seems to me to be well-founded. In the present state of philoso­ phy in the United States especially, this is sufficient reason for publishing another book in philosophy. I want to express my appreciation to a number of people. To my colleagues at North Carolina I am grateful for stimulating criticisms that often helped me see my way through to solutions. To Professors B. Blanshard (Yale University), and Ledger Wood (Princeton University), I am grateful for reading the manuscript.

Logic as a Tool: A Guide to Formal Logical Reasoning (Wiley Desktop Editions Ser.)

Written in a clear, precise and user-friendly style, Logic as a Tool: A Guide to Formal Logical Reasoning is intended for undergraduates in both mathematics and computer science, and will guide them to learn, understand and master the use of classical logic as a tool for doing correct reasoning. It offers a systematic and precise exposition of classical logic with many examples and exercises, and only the necessary minimum of theory. The book explains the grammar, semantics and use of classical logical languages and teaches the reader how grasp the meaning and translate them to and from natural language. It illustrates with extensive examples the use of the most popular deductive systems -- axiomatic systems, semantic tableaux, natural deduction, and resolution -- for formalising and automating logical reasoning both on propositional and on first-order level, and provides the reader with technical skills needed for practical derivations in them. Systematic guidelines are offered on how to perform logically correct and well-structured reasoning using these deductive systems and the reasoning techniques that they employ. •Concise and systematic exposition, with semi-formal but rigorous treatment of the minimum necessary theory, amply illustrated with examples •Emphasis both on conceptual understanding and on developing practical skills •Solid and balanced coverage of syntactic, semantic, and deductive aspects of logic •Includes extensive sets of exercises, many of them provided with solutions or answers•Supplemented by a website including detailed slides, additional exercises and solutionsFor more information browse the book's website at: https://logicasatool.wordpress.com

Logic as a Tool: A Guide to Formal Logical Reasoning

Written in a clear, precise and user-friendly style, Logic as a Tool: A Guide to Formal Logical Reasoning is intended for undergraduates in both mathematics and computer science, and will guide them to learn, understand and master the use of classical logic as a tool for doing correct reasoning. It offers a systematic and precise exposition of classical logic with many examples and exercises, and only the necessary minimum of theory. The book explains the grammar, semantics and use of classical logical languages and teaches the reader how grasp the meaning and translate them to and from natural language. It illustrates with extensive examples the use of the most popular deductive systems -- axiomatic systems, semantic tableaux, natural deduction, and resolution -- for formalising and automating logical reasoning both on propositional and on first-order level, and provides the reader with technical skills needed for practical derivations in them. Systematic guidelines are offered on how to perform logically correct and well-structured reasoning using these deductive systems and the reasoning techniques that they employ. •Concise and systematic exposition, with semi-formal but rigorous treatment of the minimum necessary theory, amply illustrated with examples •Emphasis both on conceptual understanding and on developing practical skills •Solid and balanced coverage of syntactic, semantic, and deductive aspects of logic •Includes extensive sets of exercises, many of them provided with solutions or answers•Supplemented by a website including detailed slides, additional exercises and solutionsFor more information browse the book's website at: https://logicasatool.wordpress.com

Logic as Universal Science: Russell's Early Logicism and its Philosophical Context (History of Analytic Philosophy)

Logic as Universal Science offers a detailed reconstruction of the underlying philosophy in The Principles of Mathematics showing how Russell sought to deliver a death blow to the dominant Kantian view that formal logic is a concise and dry science and unable to enlarge our understanding.

Logic-Based Artificial Intelligence (The Springer International Series in Engineering and Computer Science #597)

The use of mathematical logic as a formalism for artificial intelligence was recognized by John McCarthy in 1959 in his paper on Programs with Common Sense. In a series of papers in the 1960's he expanded upon these ideas and continues to do so to this date. It is now 41 years since the idea of using a formal mechanism for AI arose. It is therefore appropriate to consider some of the research, applications and implementations that have resulted from this idea. In early 1995 John McCarthy suggested to me that we have a workshop on Logic-Based Artificial Intelligence (LBAI). In June 1999, the Workshop on Logic-Based Artificial Intelligence was held as a consequence of McCarthy's suggestion. The workshop came about with the support of Ephraim Glinert of the National Science Foundation (IIS-9S2013S), the American Association for Artificial Intelligence who provided support for graduate students to attend, and Joseph JaJa, Director of the University of Maryland Institute for Advanced Computer Studies who provided both manpower and financial support, and the Department of Computer Science. We are grateful for their support. This book consists of refereed papers based on presentations made at the Workshop. Not all of the Workshop participants were able to contribute papers for the book. The common theme of papers at the workshop and in this book is the use of logic as a formalism to solve problems in AI.

Logic-Based Program Synthesis and Transformation: 22nd International Symposium, LOPSTR 2012, Leuven, Belgium, September 18-20, 2012, Revised Selected Papers (Lecture Notes in Computer Science #7844)

This book constitutes the thoroughly refereed post-conference proceedings of the 22nd International Symposium on Logic-Based Program Synthesis and Transformation, LOPSTR 2012, held in Leuven, Belgium in September 2012. The 13 revised full papers presented together with 2 invited talks were carefully reviewed and selected from 27 submissions. Among the topics covered are specification, synthesis, verification, analysis, optimization, specialization, security, certification, applications and tools, program/model manipulation, and transformation techniques for any programming language paradigm.

Logic-Based Program Synthesis and Transformation: 31st International Symposium, LOPSTR 2021, Tallinn, Estonia, September 7–8, 2021, Proceedings (Lecture Notes in Computer Science #13290)

This book constitutes the refereed proceedings of the 31st International Conference on Logic-Based Program Synthesis and Transformation, LOPSTR 2021, which was held during September 7-8, 2021.* The 8 papers presented in this volume were carefully reviewed and selected from a total of 15 reviewed submissions. Additionally, the book also contains 1 full-length invited talk. *Conference was held as a hybrid event due to the COVID-19 pandemic.