The Many Valued and Nonmonotonic Turn in Logic Book
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The Many Valued and Nonmonotonic Turn in Logic


  • Author : Dov M. Gabbay
  • Publisher : Elsevier
  • Release Date : 2007-08-13
  • Genre: Mathematics
  • Pages : 690
  • ISBN 10 : 008054939X

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The Many Valued and Nonmonotonic Turn in Logic Excerpt :

The present volume of the Handbook of the History of Logic brings together two of the most important developments in 20th century non-classical logic. These are many-valuedness and non-monotonicity. On the one approach, in deference to vagueness, temporal or quantum indeterminacy or reference-failure, sentences that are classically non-bivalent are allowed as inputs and outputs to consequence relations. Many-valued, dialetheic, fuzzy and quantum logics are, among other things, principled attempts to regulate the flow-through of sentences that are neither true nor false. On the second, or non-monotonic, approach, constraints are placed on inputs (and sometimes on outputs) of a classical consequence relation, with a view to producing a notion of consequence that serves in a more realistic way the requirements of real-life inference. Many-valued logics produce an interesting problem. Non-bivalent inputs produce classically valid consequence statements, for any choice of outputs. A major task of many-valued logics of all stripes is to fashion an appropriately non-classical relation of consequence. The chief preoccupation of non-monotonic (and default) logicians is how to constrain inputs and outputs of the consequence relation. In what is called “left non-monotonicity , it is forbidden to add new sentences to the inputs of true consequence-statements. The restriction takes notice of the fact that new information will sometimes override an antecedently (and reasonably) derived consequence. In what is called “right non-monotonicity , limitations are imposed on outputs of the consequence relation. Most notably, perhaps, is the requirement that the rule of or-introduction not be given free sway on outputs. Also prominent is the effort of paraconsistent logicians, both preservationist and dialetheic, to limit the outputs of inconsistent inputs, which in classical contexts are wholly unconstrained. In some instances, our two themes coincide. Dialetheic logics are a case i

The Rise of Modern Logic  from Leibniz to Frege Book

The Rise of Modern Logic from Leibniz to Frege


  • Author : Dov M. Gabbay
  • Publisher : Elsevier
  • Release Date : 2004-03-08
  • Genre: Mathematics
  • Pages : 780
  • ISBN 10 : 9780080532875

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The Rise of Modern Logic from Leibniz to Frege Excerpt :

With the publication of the present volume, the Handbook of the History of Logic turns its attention to the rise of modern logic. The period covered is 1685-1900, with this volume carving out the territory from Leibniz to Frege. What is striking about this period is the earliness and persistence of what could be called 'the mathematical turn in logic'. Virtually every working logician is aware that, after a centuries-long run, the logic that originated in antiquity came to be displaced by a new approach with a dominantly mathematical character. It is, however, a substantial error to suppose that the mathematization of logic was, in all essentials, Frege's accomplishment or, if not his alone, a development ensuing from the second half of the nineteenth century. The mathematical turn in logic, although given considerable torque by events of the nineteenth century, can with assurance be dated from the final quarter of the seventeenth century in the impressively prescient work of Leibniz. It is true that, in the three hundred year run-up to the Begriffsschrift, one does not see a smoothly continuous evolution of the mathematical turn, but the idea that logic is mathematics, albeit perhaps only the most general part of mathematics, is one that attracted some degree of support throughout the entire period in question. Still, as Alfred North Whitehead once noted, the relationship between mathematics and symbolic logic has been an "uneasy" one, as is the present-day association of mathematics with computing. Some of this unease has a philosophical texture. For example, those who equate mathematics and logic sometimes disagree about the directionality of the purported identity. Frege and Russell made themselves famous by insisting (though for different reasons) that logic was the senior partner. Indeed logicism is the view that mathematics can be re-expressed without relevant loss in a suitably framed symbolic logic. But for a number of thinkers who took an algebraic approac

Handbook of the History of Logic  Inductive logic Book

Handbook of the History of Logic Inductive logic


  • Author : Dov M. Gabbay
  • Publisher : Elsevier
  • Release Date : 2004
  • Genre: Induction (Logic)
  • Pages : 802
  • ISBN 10 : 9780444529367

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Handbook of the History of Logic Inductive logic Excerpt :

In designing the Handbook of the History of Logic, the Editors have taken the view that the history of logic holds more than an antiquarian interest, and that a knowledge of logic's rich and sophisticated development is, in various respects, relevant to the research programmes of the present day. Ancient logic is no exception. The present volume attests to the distant origins of some of modern logic's most important features, such as can be found in the claim by the authors of the chapter on Aristotle's early logic that, from its infancy, the theory of the syllogism is an example of an intuitionistic, non-monotonic, relevantly paraconsistent logic. Similarly, in addition to its comparative earliness, what is striking about the best of the Megarian and Stoic traditions is their sophistication and originality.

Mediaeval and Renaissance Logic Book

Mediaeval and Renaissance Logic


  • Author : Dov M. Gabbay
  • Publisher : Elsevier
  • Release Date : 2008-03-14
  • Genre: Mathematics
  • Pages : 728
  • ISBN 10 : 0080560857

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Mediaeval and Renaissance Logic Excerpt :

Starting at the very beginning with Aristotle's founding contributions, logic has been graced by several periods in which the subject has flourished, attaining standards of rigour and conceptual sophistication underpinning a large and deserved reputation as a leading expression of human intellectual effort. It is widely recognized that the period from the mid-19th century until the three-quarter mark of the century just past marked one of these golden ages, a period of explosive creativity and transforming insights. It has been said that ignorance of our history is a kind of amnesia, concerning which it is wise to note that amnesia is an illness. It would be a matter for regret, if we lost contact with another of logic's golden ages, one that greatly exceeds in reach that enjoyed by mathematical symbolic logic. This is the period between the 11th and 16th centuries, loosely conceived of as the Middle Ages. The logic of this period does not have the expressive virtues afforded by the symbolic resources of uninterpreted calculi, but mediaeval logic rivals in range, originality and intellectual robustness a good deal of the modern record. The range of logic in this period is striking, extending from investigation of quantifiers and logic consequence to inquiries into logical truth; from theories of reference to accounts of identity; from work on the modalities to the stirrings of the logic of relations, from theories of meaning to analyses of the paradoxes, and more. While the scope of mediaeval logic is impressive, of greater importance is that nearly all of it can be read by the modern logician with at least some prospect of profit. The last thing that mediaeval logic is, is a museum piece. Mediaeval and Renaissance Logic is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science and AI, linguist

Logic and the Modalities in the Twentieth Century Book

Logic and the Modalities in the Twentieth Century


  • Author : Dov M. Gabbay
  • Publisher : North Holland
  • Release Date : 2004
  • Genre: Mathematics
  • Pages : 740
  • ISBN 10 : STANFORD:36105126921407

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Logic and the Modalities in the Twentieth Century Excerpt :

With the publication of the present volume, the Handbook of the History of Logic turns its attention to the remarkable renaissance of modal logic in the 20th century. Beginning with the early systems of C.I. Lewis in 1912, modal logic was a fixture in the century's research programme in logic, but for many years it ran on a parallel track to the rich developments in the more dominant classical logic. One of the great achievements of classical logic was the comparatively early production of a deep semantics for it. Modal logic would have to wait until the seminal work of Hintikka, Kanger and Kripke in the late 1950s and early 1960s. With modal semantics now in hand, it is not too much to say that modal logic leapt its tracks and challenged classical logic head-on for dominance. Part of what makes this an interesting challenge is the sheer proliferation of well-studied systems that burst out of the modal research programme. Further expansion came by way of adaptation of model operators to epistemic and deontic interpretations, and an ensuing exuberance of further systems. Another important development was relevant logic, and with it a change to a more general conception of modal logic, in which the modalities of a system are now represented by a broader range of qualifications on its sentences. Under press of developments in computer science and argumentation theory (chiefly dialogue logic), recognition started to be given to sentence-qualifications other than necessity, obligatoriness and relevance. These include agents, times,tense, change, situations, roles, and with them the modalization of logic came to encompass, temporal and tense logic, dynamic logic, situation logic, dialogue logic, game theoretic logic, and much more. Logic and the Modalities in the Twentieth Century is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, hi

Computational Logic Book
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Computational Logic


  • Author : Dov M. Gabbay
  • Publisher : North Holland
  • Release Date : 2014-12-12
  • Genre: Mathematics
  • Pages : 736
  • ISBN 10 : 0444516247

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Computational Logic Excerpt :

Handbook of the History of Logic brings to the development of logic the best in modern techniques of historical and interpretative scholarship. Computational logic was born in the twentieth century and evolved in close symbiosis with the advent of the first electronic computers and the growing importance of computer science, informatics and artificial intelligence. With more than ten thousand people working in research and development of logic and logic-related methods, with several dozen international conferences and several times as many workshops addressing the growing richness and diversity of the field, and with the foundational role and importance these methods now assume in mathematics, computer science, artificial intelligence, cognitive science, linguistics, law and many engineering fields where logic-related techniques are used inter alia to state and settle correctness issues, the field has diversified in ways that even the pure logicians working in the early decades of the twentieth century could have hardly anticipated. Logical calculi, which capture an important aspect of human thought, are now amenable to investigation with mathematical rigour and computational support and fertilized the early dreams of mechanised reasoning: "Calculemus”. The Dartmouth Conference in 1956 - generally considered as the birthplace of artificial intelligence - raised explicitly the hopes for the new possibilities that the advent of electronic computing machinery offered: logical statements could now be executed on a machine with all the far-reaching consequences that ultimately led to logic programming, deduction systems for mathematics and engineering, logical design and verification of computer software and hardware, deductive databases and software synthesis as well as logical techniques for analysis in the field of mechanical engineering. This volume covers some of the main subareas of computational logic and its applications. Chapters by leading authorities in the

Handbook of Logic and Language Book

Handbook of Logic and Language


  • Author : Johan F.A.K. van Benthem
  • Publisher : Elsevier
  • Release Date : 2010-12-17
  • Genre: Mathematics
  • Pages : 1168
  • ISBN 10 : 0444537279

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Handbook of Logic and Language Excerpt :

The logical study of language is becoming more interdisciplinary, playing a role in fields such as computer science, artificial intelligence, cognitive science and game theory. This new edition, written by the leading experts in the field, presents an overview of the latest developments at the interface of logic and linguistics as well as a historical perspective. It is divided into three parts covering Frameworks, General Topics and Descriptive Themes. Completely revised and updated - includes over 25% new material Discusses the interface between logic and language Many of the authors are creators or active developers of the theories

Logic from Russell to Church Book

Logic from Russell to Church


  • Author : Dov M. Gabbay
  • Publisher : Elsevier
  • Release Date : 2009-06-16
  • Genre: Mathematics
  • Pages : 1068
  • ISBN 10 : 9780080885476

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Logic from Russell to Church Excerpt :

This volume is number five in the 11-volume Handbook of the History of Logic. It covers the first 50 years of the development of mathematical logic in the 20th century, and concentrates on the achievements of the great names of the period--Russell, Post, Gödel, Tarski, Church, and the like. This was the period in which mathematical logic gave mature expression to its four main parts: set theory, model theory, proof theory and recursion theory. Collectively, this work ranks as one of the greatest achievements of our intellectual history. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, and artificial intelligence, for whom the historical background of his or her work is a salient consideration. • The entire range of modal logic is covered • Serves as a singular contribution to the intellectual history of the 20th century • Contains the latest scholarly discoveries and interpretative insights

The Oxford Handbook of Philosophy of Mathematics and Logic Book

The Oxford Handbook of Philosophy of Mathematics and Logic


  • Author : Stewart Shapiro
  • Publisher : Oxford University Press
  • Release Date : 2005-02-10
  • Genre: Mathematics
  • Pages : 856
  • ISBN 10 : 9780190287535

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The Oxford Handbook of Philosophy of Mathematics and Logic Excerpt :

Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.

Inductive Logic Book

Inductive Logic


  • Author : Dov M. Gabbay
  • Publisher : Elsevier
  • Release Date : 2011-05-27
  • Genre: Mathematics
  • Pages : 800
  • ISBN 10 : 9780080931692

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Inductive Logic Excerpt :

This volume is number ten in the 11-volume Handbook of the History of Logic. While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic — as this handbook attests — is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of scientific turning points in Inductive Logic, including probability theory and decision theory. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration. • Chapter on the Port Royal contributions to probability theory and decision theory • Serves as a singular contribution to the intellectual history of the 20th century • Contains the latest scholarly discoveries and interpretative insights

British Logic in the Nineteenth Century Book

British Logic in the Nineteenth Century


  • Author : Dov M. Gabbay
  • Publisher : Elsevier
  • Release Date : 2008-03-10
  • Genre: Mathematics
  • Pages : 750
  • ISBN 10 : 0080557015

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British Logic in the Nineteenth Century Excerpt :

The present volume of the Handbook of the History of Logic is designed to establish 19th century Britain as a substantial force in logic, developing new ideas, some of which would be overtaken by, and other that would anticipate, the century's later capitulation to the mathematization of logic. British Logic in the Nineteenth Century is indispensable reading and a definitive research resource for anyone with an interest in the history of logic. - Detailed and comprehensive chapters covering the entire range of modal logic - Contains the latest scholarly discoveries and interpretative insights that answer many questions in the field of logic

Words of Power Book

Words of Power


  • Author : Andrea Nye
  • Publisher : Routledge
  • Release Date : 2019-11-04
  • Genre: Philosophy
  • Pages : 202
  • ISBN 10 : 9781000737172

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Words of Power Excerpt :

Originally published in 1990. A common complaint of philosophers, and men in general, has been that women are illogical. On the other hand, rationality, defined as the ability to follow logical argument, is often claimed to be a defining characteristic of man. Andrea Nye undermines assumptions such as: logic is unitary, logic is independent of concrete human relations, logic transcends historical circumstances as well as gender. In a series of studies of the logics of historical figures Parmenides, Plato, Aristotle, Zeno, Abelard, Ockham, and Frege she traces the changing interrelationships between logical innovation and oppressive speech strategies, showing that logic is not transcendent truth but abstract forms of language spoken by men, whether Greek ruling citizens, imperial administrators, church officials, or scientists. She relates logical techniques, such as logical division, syllogisms, and truth functions, to ways in which those with power speak to and about those subject to them. She shows, in the specific historical settings of Ancient and Hellenistic Greece, medieval Europe, and Germany between the World Wars, how logicians reworked language so that dialogue and reciprocity are impossible and one speaker is forced to accept the words of another. In the personal, as well as confrontative style of her readings, Nye points the way to another power in the words of women that might break into and challenge rational discourses that have structured Western thought and practice.

Handbook of Practical Logic and Automated Reasoning Book
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Handbook of Practical Logic and Automated Reasoning


  • Author : John Harrison
  • Publisher : Cambridge University Press
  • Release Date : 2009-03-12
  • Genre: Computers
  • Pages : 703
  • ISBN 10 : 9780521899574

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Handbook of Practical Logic and Automated Reasoning Excerpt :

A one-stop reference, self-contained, with theoretical topics presented in conjunction with implementations for which code is supplied.

The SAGE Handbook of the History  Philosophy and Sociology of International Relations Book

The SAGE Handbook of the History Philosophy and Sociology of International Relations


  • Author : Andreas Gofas
  • Publisher : SAGE
  • Release Date : 2018-07-19
  • Genre: Political Science
  • Pages : 616
  • ISBN 10 : 9781526415608

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The SAGE Handbook of the History Philosophy and Sociology of International Relations Excerpt :

The SAGE Handbook of the History, Philosophy and Sociology of International Relations offers a panoramic overview of the broad field of International Relations by integrating three distinct but interrelated foci. It retraces the historical development of International Relations (IR) as a professional field of study, explores the philosophical foundations of IR, and interrogates the sociological mechanisms through which scholarship is produced and the field is structured. Comprising 38 chapters from both established scholars and an emerging generation of innovative meta-theorists and theoretically driven empiricists, the handbook fosters discussion of the field from the inside out, forcing us to come to grips with the widely held perception that IR is experiencing an existential crisis quite unlike anything else in its hundred-year history. This timely and innovative reference volume reflects on situated scholarly practices in a way that projects our collective thinking into the future. PART ONE: THE INWARD GAZE: INTRODUCTORY REFLECTIONS PART TWO: IMAGINING THE INTERNATIONAL, ACKNOWLEDGING THE GLOBAL PART THREE: THE SEARCH FOR (AN) IDENTITY PART FOUR: INTERNATIONAL RELATIONS AS A PROFESSION PART FIVE: LOOKING AHEAD: THE FUTURE OF META-ANALYSIS

British Logic in the Nineteenth Century Book

British Logic in the Nineteenth Century


  • Author : Dov M. Gabbay
  • Publisher : North Holland
  • Release Date : 2008-03-10
  • Genre: Mathematics
  • Pages : 760
  • ISBN 10 : 0444516107

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British Logic in the Nineteenth Century Excerpt :

The present volume of the Handbook of the History of Logic is designed to establish 19th century Britain as a substantial force in logic, developing new ideas, some of which would be overtaken by, and other that would anticipate, the century's later capitulation to the mathematization of logic. British Logic in the Nineteenth Century is indispensable reading and a definitive research resource for anyone with an interest in the history of logic.