Consequence Relations
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Consequence Relations
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Author : Alex Citkin
language : en
Publisher: Oxford University Press
Release Date : 2022-06-30
Consequence Relations written by Alex Citkin and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-30 with Young Adult Nonfiction categories.
The publication of Rasiowa and Sikorski's The Mathematics of Metamathematics (1970), Rasiowa's An Algebraic Approach to Non-Classical Logics (1974), and Wójcicki's Theory of Logical Calculi (1988) created a niche in the field of mathematical and philosophical logic. This in-depth study of the concept of a consequence relation, culminating in the concept of a Lindenbaum-Tarski algebra, fills this niche. Citkin and Muravitsky consider the problem of obtaining confirmation that a statement is a consequence of a set of statements as prerequisites, on the one hand, and the problem of demonstrating that such confirmation does not exist in the structure under consideration, on the other hand. For the second part of this problem, the concept of the Lindenbaum-Tarski algebra plays a key role, which becomes even more important when the considered consequence relation is placed in the context of decidability. This role is traced in the book for various formal objective languages. The work also includes helpful exercises to aid the reader's assimilation of the book's material. Intended for advanced undergraduate and graduate students in mathematics and philosophy, this book can be used to teach special courses in logic with an emphasis on algebraic methods, for self-study, and also as a reference work.
Principles Of Knowledge Representation And Reasoning
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Author : Jon Doyle
language : en
Publisher: Morgan Kaufmann Publishers
Release Date : 1994
Principles Of Knowledge Representation And Reasoning written by Jon Doyle and has been published by Morgan Kaufmann Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with COMPUTERS categories.
The proceedings of KR '94 comprise 55 papers on topics including deduction an search, description logics, theories of knowledge and belief, nonmonotonic reasoning and belief revision, action and time, planning and decision-making and reasoning about the physical world, and the relations between KR
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.
Logical consequence is the relation that obtains between premises and conclusion(s) in a valid argument. Orthodoxy has it that valid arguments are necessarily truth-preserving, but this platitude only raises a number of further questions, such as: how does the truth of premises guarantee the truth of a conclusion, and what constraints does validity impose on rational belief? This volume presents thirteen essays by some of the most important scholars in the field of philosophical logic. The essays offer ground-breaking new insights into the nature of logical consequence; the relation between logic and inference; how the semantics and pragmatics of natural language bear on logic; the relativity of logic; and the structural properties of the consequence relation.
Explanatory Nonmonotonic Reasoning
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Author : Alexander Bochman
language : en
Publisher: World Scientific
Release Date : 2005
Explanatory Nonmonotonic Reasoning written by Alexander Bochman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Computers categories.
Many approaches in the field of nonmonotonic and ?commonsense? reasoning are actually different representations of the same basic ideas and constructions. This book gives a logical formalization of the original, explanatory approach to nonmonotonic reasoning. It uses the basic formalism of biconsequence relations, as well as derived systems of default, autoepistemic and causal inference, to cover in a single framework such diverse systems as default logic, autoepistemic and modal nonmonotonic logics, input/output and causal logics, argumentation theory, and semantics of general logic programs with negation as failure. This approach provides a clear separation between logical (monotonic) and nonmonotonic aspects of nonmonotonic reasoning. The separation allows, in particular, to single out the logics underlying modern logic programming and restore thereby the connection between logic programming and logic.
A Logical Theory Of Nonmonotonic Inference And Belief Change
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Author : Alexander Bochman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
A Logical Theory Of Nonmonotonic Inference And Belief Change written by Alexander Bochman 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 2013-03-14 with Computers categories.
The main subject and objective of this book are logical foundations of non monotonic reasoning. This bears a presumption that there is such a thing as a general theory of non monotonic reasoning, as opposed to a bunch of systems for such a reasoning existing in the literature. It also presumes that this kind of reasoning can be analyzed by logical tools (broadly understood), just as any other kind of reasoning. In order to achieve our goal, we will provide a common logical basis and semantic representation in which different kinds of non monotonic reasoning can be interpreted and studied. The suggested framework will subsume ba sic forms of nonmonotonic inference, including not only the usual skeptical one, but also various forms of credulous (brave) and defeasible reasoning, as well as some new kinds such as contraction inference relations that express relative independence of pieces of data. In addition, the same framework will serve as a basis for a general theory of belief change which, among other things, will allow us to unify the main approaches to belief change existing in the literature, as well as to provide a constructive view of the semantic representation used. This book is a monograph rather than a textbook, with all its advantages (mainly for the author) and shortcomings (for the reader).
Logica Universalis
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Author : Jean-Yves Beziau
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-06
Logica Universalis written by Jean-Yves Beziau 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 2005-12-06 with Mathematics categories.
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.
Logic A History Of Its Central Concepts
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Author : Dov M. Gabbay
language : en
Publisher: Newnes
Release Date : 2012-12-31
Logic A History Of Its Central Concepts written by Dov M. Gabbay and has been published by Newnes this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-31 with Mathematics categories.
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
One True Logic
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Author : Owen Griffiths
language : en
Publisher: Oxford University Press
Release Date : 2022-05-12
One True Logic written by Owen Griffiths and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-12 with Philosophy categories.
Logical monism is the claim that there is a single correct logic, the 'one true logic' of our title. The view has evident appeal, as it reflects assumptions made in ordinary reasoning as well as in mathematics, the sciences, and the law. In all these spheres, we tend to believe that there are determinate facts about the validity of arguments. Despite its evident appeal, however, logical monism must meet two challenges. The first is the challenge from logical pluralism, according to which there is more than one correct logic. The second challenge is to determine which form of logical monism is the correct one. One True Logic is the first monograph to explicitly articulate a version of logical monism and defend it against the first challenge. It provides a critical overview of the monism vs pluralism debate and argues for the former. It also responds to the second challenge by defending a particular monism, based on a highly infinitary logic. It breaks new ground on a number of fronts and unifies disparate discussions in the philosophical and logical literature. In particular, it generalises the Tarski-Sher criterion of logicality, provides a novel defence of this generalisation, offers a clear new argument for the logicality of infinitary logic and replies to recent pluralist arguments.
The Many Valued And Nonmonotonic Turn In Logic
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Author : Dov M. Gabbay
language : en
Publisher: Elsevier
Release Date : 2007-08-13
The Many Valued And Nonmonotonic Turn In Logic written by Dov M. Gabbay and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-13 with Mathematics categories.
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 in point. Dialetheic logics allow certain selected sentences to have, as a third truth value, the classical values of truth and falsity together. So such logics also admit classically inconsistent inputs. A central task is to construct a right non-monotonic consequence relation that allows for these many-valued, and inconsistent, inputs.The Many Valued and Non-Monotonic Turn in 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, AI, linguistics, cognitive science, argumentation theory, and the history of ideas. - Detailed and comprehensive chapters covering the entire range of modal logic. - Contains the latest scholarly discoveries and interprative insights that answers many questions in the field of logic.
Handbook Of Philosophical Logic
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Author : Dov M. Gabbay
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Handbook Of Philosophical Logic written by Dov M. Gabbay 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 2013-03-14 with Philosophy categories.
It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as well as to consumers of logic in many applied areas. The main logic article in the Encyclopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good! The first edition was the second handbook published for the logic com- nity. It followed the North Holland one volume Handbook of Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook of Philosophical Logic, published 1983-1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence circles. These areas were under increasing commercial pressure to provide devices which help and/or replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organi- tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.