Propositional Logics

Author : Richard L Epstein
Publisher : Advanced Reasoning Forum
Page : 509 pages
File Size : 49,7 Mb
Release : 2018-11-05
Category : Philosophy
ISBN : 9780983452171

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Propositional Logics 3rd edition by Richard L Epstein Pdf

This book 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.

Author : Witold A. Pogorzelski,Piotr Wojtylak
Publisher : Springer Science & Business Media
Page : 178 pages
File Size : 48,9 Mb
Release : 2008-05-25
Category : Mathematics
ISBN : 9783764385187

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Completeness Theory for Propositional Logics by Witold A. Pogorzelski,Piotr Wojtylak Pdf

This book develops the theory of one of the most important notions in the methodology of formal systems. Particularly, completeness plays an important role in propositional logic where many variants of the notion have been defined. This approach allows also for a more profound view upon some essential properties of propositional systems. For these purposes, the theory of logical matrices, and the theory of consequence operations is exploited.

Author : R.L. Epstein
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 52,9 Mb
Release : 2013-11-11
Category : Philosophy
ISBN : 9789400905252

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The Semantic Foundations of Logic Volume 1: Propositional Logics by R.L. Epstein Pdf

This book grew out of my confusion. If logic is objective how can there be so many logics? Is there one right logic, or many right ones? Is there some underlying unity that connects them? What is the significance of the mathematical theorems about logic which I've learned if they have no connection to our everyday reasoning? The answers I propose revolve around the perception that what one pays attention to in reasoning determines which logic is appropriate. The act of abstracting from our reasoning in our usual language is the stepping stone from reasoned argument to logic. We cannot take this step alone, for we reason together: logic is reasoning which has some objective value. For you to understand my answers, or perhaps better, conjectures, I have retraced my steps: from the concrete to the abstract, from examples, to general theory, to further confirming examples, to reflections on the significance of the work.

Author : Fouad Sabry
Publisher : One Billion Knowledgeable
Page : 154 pages
File Size : 51,7 Mb
Release : 2023-06-24
Category : Computers
ISBN : PKEY:6610000470242

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Propositional Logic by Fouad Sabry Pdf

What Is Propositional Logic The field of logic that is known as propositional calculus. There are a few other names for it, including propositional logic, statement logic, sentential calculus, sentential logic, and occasionally zeroth-order logic. It examines propositions as well as the relations that exist between propositions, as well as the formulation of arguments that are founded on propositions. By combining individual statements with various logical connectives, one can create compound propositions. Atomic propositions are those that don't have any logical connectives in them, as the name suggests. How You Will Benefit (I) Insights, and validations about the following topics: Chapter 1: Propositional calculus Chapter 2: Axiom Chapter 3: First-order logic Chapter 4: Modus tollens Chapter 5: Consistency Chapter 6: Contradiction Chapter 7: Rule of inference Chapter 8: List of rules of inference Chapter 9: Deduction theorem Chapter 10: Theory (mathematical logic) (II) Answering the public top questions about propositional logic. (III) Real world examples for the usage of propositional logic in many fields. (IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of propositional logic' technologies. Who This Book Is For Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of propositional logic.

Author : Craig DeLancey
Publisher : Open SUNY Textbooks
Page : 128 pages
File Size : 46,5 Mb
Release : 2017-02-06
Category : Electronic
ISBN : 1942341431

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A Concise Introduction to Logic by Craig DeLancey Pdf

Author : Avicenna
Publisher : Springer Science & Business Media
Page : 301 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Philosophy
ISBN : 9789401026246

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The Propositional Logic of Avicenna by Avicenna Pdf

The main purpose of this work is to provide an English translation of and commentary on a recently published Arabic text dealing with con ditional propositions and syllogisms. The text is that of A vicenna (Abu represents his views on the subject as they were held throughout his life.

Author : Jan Krajicek
Publisher : Cambridge University Press
Page : 361 pages
File Size : 48,7 Mb
Release : 1995-11-24
Category : Computers
ISBN : 9780521452052

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Bounded Arithmetic, Propositional Logic and Complexity Theory by Jan Krajicek Pdf

Discusses the deep connections between logic and complexity theory, and lists a number of intriguing open problems.

Author : Peter Fritz
Publisher : Cambridge University Press
Page : 137 pages
File Size : 55,8 Mb
Release : 2024-05-16
Category : Philosophy
ISBN : 9781009188630

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Propositional Quantifiers by Peter Fritz Pdf

Propositional quantifiers are quantifiers binding proposition letters, understood as variables. This Element introduces propositional quantifiers and explains why they are especially interesting in the context of propositional modal logics. It surveys the main results on propositionally quantified modal logics which have been obtained in the literature, presents a number of open questions, and provides examples of applications of such logics to philosophical problems.

Author : Oscar Levin
Publisher : Createspace Independent Publishing Platform
Page : 238 pages
File Size : 50,8 Mb
Release : 2018-07-30
Category : Electronic
ISBN : 1724572636

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Discrete Mathematics by Oscar Levin Pdf

Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.

Author : Richard L. Epstein
Publisher : Unknown
Page : 510 pages
File Size : 52,8 Mb
Release : 2012-06-01
Category : Mathematics
ISBN : 0983452164

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Propositional Logics by Richard L. Epstein Pdf

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.

Author : Samson Abramsky,Juha Kontinen,Jouko Väänänen,Heribert Vollmer
Publisher : Birkhäuser
Page : 286 pages
File Size : 54,6 Mb
Release : 2016-06-29
Category : Mathematics
ISBN : 9783319318035

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Dependence Logic by Samson Abramsky,Juha Kontinen,Jouko Väänänen,Heribert Vollmer Pdf

In this volume, different aspects of logics for dependence and independence are discussed, including both the logical and computational aspects of dependence logic, and also applications in a number of areas, such as statistics, social choice theory, databases, and computer security. The contributing authors represent leading experts in this relatively new field, each of whom was invited to write a chapter based on talks given at seminars held at the Schloss Dagstuhl Leibniz Center for Informatics in Wadern, Germany (in February 2013 and June 2015) and an Academy Colloquium at the Royal Netherlands Academy of Arts and Sciences (March 2014). Altogether, these chapters provide the most up-to-date look at this developing and highly interdisciplinary field and will be of interest to a broad group of logicians, mathematicians, statisticians, philosophers, and scientists. Topics covered include a comprehensive survey of many propositional, modal, and first-order variants of dependence logic; new results concerning expressive power of several variants of dependence logic with different sets of logical connectives and generalized dependence atoms; connections between inclusion logic and the least-fixed point logic; an overview of dependencies in databases by addressing the relationships between implication problems for fragments of statistical conditional independencies, embedded multivalued dependencies, and propositional logic; various Markovian models used to characterize dependencies and causality among variables in multivariate systems; applications of dependence logic in social choice theory; and an introduction to the theory of secret sharing, pointing out connections to dependence and independence logic.

Author : Eduardo Fermé,Joao Leite
Publisher : Springer
Page : 719 pages
File Size : 41,6 Mb
Release : 2014-09-16
Category : Computers
ISBN : 9783319115580

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Logics in Artificial Intelligence by Eduardo Fermé,Joao Leite Pdf

This book constitutes the proceedings of the 14th European Conference on Logics in Artificial Intelligence, JELIA 2014, held in Funchal, Madeira, Portugal, in September 2014. The 35 full papers and 14 short papers included in this volume were carefully reviewed and selected from 121 submissions. They are organized in topical sections named: description logics; automated reasoning; logics for uncertain reasoning; non-classical logics; answer-set programming; belief revision; dealing with inconsistency in ASP and DL; reason about actions and causality; system descriptions; short system descriptions; and short papers. The book also contains 4 full paper invited talks.

Author : Torben Braüner
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 47,5 Mb
Release : 2010-11-17
Category : Philosophy
ISBN : 9789400700024

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Hybrid Logic and its Proof-Theory by Torben Braüner Pdf

This is the first book-length treatment of hybrid logic and its proof-theory. Hybrid logic is an extension of ordinary modal logic which allows explicit reference to individual points in a model (where the points represent times, possible worlds, states in a computer, or something else). This is useful for many applications, for example when reasoning about time one often wants to formulate a series of statements about what happens at specific times. There is little consensus about proof-theory for ordinary modal logic. Many modal-logical proof systems lack important properties and the relationships between proof systems for different modal logics are often unclear. In the present book we demonstrate that hybrid-logical proof-theory remedies these deficiencies by giving a spectrum of well-behaved proof systems (natural deduction, Gentzen, tableau, and axiom systems) for a spectrum of different hybrid logics (propositional, first-order, intensional first-order, and intuitionistic).

Author : Richard L. Epstein
Publisher : Princeton University Press
Page : 545 pages
File Size : 45,6 Mb
Release : 2006-07-23
Category : Mathematics
ISBN : 9780691123004

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Classical Mathematical Logic by Richard L. Epstein Pdf

In Classical Mathematical Logic, Richard L. Epstein relates the systems of mathematical logic to their original motivations to formalize reasoning in mathematics. The book also shows how mathematical logic can be used to formalize particular systems of mathematics. It sets out the formalization not only of arithmetic, but also of group theory, field theory, and linear orderings. These lead to the formalization of the real numbers and Euclidean plane geometry. The scope and limitations of modern logic are made clear in these formalizations. The book provides detailed explanations of all proofs and the insights behind the proofs, as well as detailed and nontrivial examples and problems. The book has more than 550 exercises. It can be used in advanced undergraduate or graduate courses and for self-study and reference. Classical Mathematical Logic presents a unified treatment of material that until now has been available only by consulting many different books and research articles, written with various notation systems and axiomatizations.

Author : Harrie C.M. de Swart
Publisher : Springer
Page : 318 pages
File Size : 52,6 Mb
Release : 2003-07-01
Category : Computers
ISBN : 9783540362807

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Relational Methods in Computer Science by Harrie C.M. de Swart Pdf

This book constitutes the thoroughly refereed joint post-proceedings of the 6th International Conference on Relational Methods in Computer Science, RelMICS 2001 and the 1st Workshop of COST Action 274 TARSKI, Theory and Application of Relational Structures as Knowledge Instruments held in Oisterwijk, The Netherlands, in October 2001. The 20 revised full papers presented together with an invited paper were carefully reviewed and selected. The papers are organized in topical sections on algebraic and logical foundations of real world relations, mechanization of relational reasoning, and relational scaling and preferences.