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Tableau Methods For Propositional Logic And Term Logic
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Author :Tomasz Jarmuzek Publisher :Peter Lang Gmbh, Internationaler Verlag Der Wissenschaften ISBN 13 :9783631833728 Total Pages :228 pages Book Rating :4.8/5 (337 download)
Book Synopsis Tableau Methods for Propositional Logic and Term Logic by : Tomasz Jarmuzek
Download or read book Tableau Methods for Propositional Logic and Term Logic written by Tomasz Jarmuzek and published by Peter Lang Gmbh, Internationaler Verlag Der Wissenschaften. This book was released on 2021-01-27 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book aims to formalise tableau methods for the logics of propositions and names. The methods described are based on Set Theory. The tableau rule was reduced to an ordered n-tuple of sets of expressions where the first element is a set of premises, and the following elements are its supersets.
Book Synopsis Handbook of Tableau Methods by : M. D'Agostino
Download or read book Handbook of Tableau Methods written by M. D'Agostino and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent years have been blessed with an abundance of logical systems, arising from a multitude of applications. A logic can be characterised in many different ways. Traditionally, a logic is presented via the following three components: 1. an intuitive non-formal motivation, perhaps tie it in to some application area 2. a semantical interpretation 3. a proof theoretical formulation. There are several types of proof theoretical methodologies, Hilbert style, Gentzen style, goal directed style, labelled deductive system style, and so on. The tableau methodology, invented in the 1950s by Beth and Hintikka and later per fected by Smullyan and Fitting, is today one of the most popular, since it appears to bring together the proof-theoretical and the semantical approaches to the pre of a logical system and is also very intuitive. In many universities it is sentation the style first taught to students. Recently interest in tableaux has become more widespread and a community crystallised around the subject. An annual tableaux conference is being held and proceedings are published. The present volume is a Handbook a/Tableaux pre senting to the community a wide coverage of tableaux systems for a variety of logics. It is written by active members of the community and brings the reader up to frontline research. It will be of interest to any formal logician from any area.
Book Synopsis Mathematical Logic for Computer Science by : Mordechai Ben-Ari
Download or read book Mathematical Logic for Computer Science written by Mordechai Ben-Ari and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a mathematics textbook with theorems and proofs. The choice of topics has been guided by the needs of computer science students. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and yet sufficiently elementary for undergraduates. In order to provide a balanced treatment of logic, tableaux are related to deductive proof systems. The book presents various logical systems and contains exercises. Still further, Prolog source code is available on an accompanying Web site. The author is an Associate Professor at the Department of Science Teaching, Weizmann Institute of Science.
Book Synopsis First-Order Logic by : Raymond R. Smullyan
Download or read book First-Order Logic written by Raymond R. Smullyan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Except for this preface, this study is completely self-contained. It is intended to serve both as an introduction to Quantification Theory and as an exposition of new results and techniques in "analytic" or "cut-free" methods. We use the term "analytic" to apply to any proof procedure which obeys the subformula principle (we think of such a procedure as "analysing" the formula into its successive components). Gentzen cut-free systems are perhaps the best known example of ana lytic proof procedures. Natural deduction systems, though not usually analytic, can be made so (as we demonstrated in [3]). In this study, we emphasize the tableau point of view, since we are struck by its simplicity and mathematical elegance. Chapter I is completely introductory. We begin with preliminary material on trees (necessary for the tableau method), and then treat the basic syntactic and semantic fundamentals of propositional logic. We use the term "Boolean valuation" to mean any assignment of truth values to all formulas which satisfies the usual truth-table conditions for the logical connectives. Given an assignment of truth-values to all propositional variables, the truth-values of all other formulas under this assignment is usually defined by an inductive procedure. We indicate in Chapter I how this inductive definition can be made explicit-to this end we find useful the notion of a formation tree (which we discuss earlier).
Book Synopsis A Beginner's Guide to Mathematical Logic by : Raymond M. Smullyan
Download or read book A Beginner's Guide to Mathematical Logic written by Raymond M. Smullyan and published by Courier Corporation. This book was released on 2014-03-19 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combining stories of great writers and philosophers with quotations and riddles, this original text for first courses in mathematical logic examines problems related to proofs, propositional logic and first-order logic, undecidability, and other topics. 2014 edition.
Book Synopsis Proof Methods for Modal and Intuitionistic Logics by : M. Fitting
Download or read book Proof Methods for Modal and Intuitionistic Logics written by M. Fitting and published by Springer Science & Business Media. This book was released on 1983-04-30 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Necessity is the mother of invention. " Part I: What is in this book - details. There are several different types of formal proof procedures that logicians have invented. The ones we consider are: 1) tableau systems, 2) Gentzen sequent calculi, 3) natural deduction systems, and 4) axiom systems. We present proof procedures of each of these types for the most common normal modal logics: S5, S4, B, T, D, K, K4, D4, KB, DB, and also G, the logic that has become important in applications of modal logic to the proof theory of Peano arithmetic. Further, we present a similar variety of proof procedures for an even larger number of regular, non-normal modal logics (many introduced by Lemmon). We also consider some quasi-regular logics, including S2 and S3. Virtually all of these proof procedures are studied in both propositional and first-order versions (generally with and without the Barcan formula). Finally, we present the full variety of proof methods for Intuitionistic logic (and of course Classical logic too). We actually give two quite different kinds of tableau systems for the logics we consider, two kinds of Gentzen sequent calculi, and two kinds of natural deduction systems. Each of the two tableau systems has its own uses; each provides us with different information about the logics involved. They complement each other more than they overlap. Of the two Gentzen systems, one is of the conventional sort, common in the literature.
Book Synopsis Automated Reasoning with Analytic Tableaux and Related Methods by : Didier Galmiche
Download or read book Automated Reasoning with Analytic Tableaux and Related Methods written by Didier Galmiche and published by Springer Science & Business Media. This book was released on 1997-04-29 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 1998 International Conference on Analytic Tableaux and Related Methods, TABLEAUX'98, held in Oisterwijk near Tilburg, The Netherlands, in May 1998. The volume presents 17 revised full papers and three system descriptions selected from 34 submissions; also included are several abstracts of invited lectures, tutorials, and system comparison papers. The book presents new research results for automated deduction in various non-standard logics as well as in classical logic. Areas of application include software verification, systems verification, deductive databases, knowledge representation and its required inference engines, and system diagnosis.
Book Synopsis Diagrammatic Representation and Inference by : Amrita Basu
Download or read book Diagrammatic Representation and Inference written by Amrita Basu and published by Springer Nature. This book was released on 2021-09-21 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 12th International Conference on the Theory and Application of Diagrams, Diagrams 2021, held virtually in September 2021. The 16 full papers and 25 short papers presented together with 16 posters were carefully reviewed and selected from 94 submissions. The papers are organized in the following topical sections: design of concrete diagrams; theory of diagrams; diagrams and mathematics; diagrams and logic; new representation systems; analysis of diagrams; diagrams and computation; cognitive analysis; diagrams as structural tools; formal diagrams; and understanding thought processes. 10 chapters are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Book Synopsis Numerical Term Logic by : Lorne Szabolcsi
Download or read book Numerical Term Logic written by Lorne Szabolcsi and published by . This book was released on 2008 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an edited volume of the unpublished work of numerical logic pioneer, Lome Szabolcsi, who died suddenly at age 28.
Book Synopsis Logic for Philosophy by : Theodore Sider
Download or read book Logic for Philosophy written by Theodore Sider and published by Oxford University Press. This book was released on 2010-01-07 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logic for Philosophy is an introduction to logic for students of contemporary philosophy. It is suitable both for advanced undergraduates and for beginning graduate students in philosophy. It covers (i) basic approaches to logic, including proof theory and especially model theory, (ii) extensions of standard logic that are important in philosophy, and (iii) some elementary philosophy of logic. It emphasizes breadth rather than depth. For example, it discusses modal logic and counterfactuals, but does not prove the central metalogical results for predicate logic (completeness, undecidability, etc.) Its goal is to introduce students to the logic they need to know in order to read contemporary philosophical work. It is very user-friendly for students without an extensive background in mathematics. In short, this book gives you the understanding of logic that you need to do philosophy.
Download or read book Logical Options written by John L. Bell and published by Broadview Press. This book was released on 2001-03-30 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic. Each logic is introduced with a brief description of some aspect of its philosophical significance, and wherever possible semantic and proof methods are employed to facilitate comparison of the various systems. The book is designed to be useful for philosophy students and professional philosophers who have learned some classical first-order logic and would like to learn about other logics important to their philosophical work.
Download or read book Logic with Trees written by Colin Howson and published by Routledge. This book was released on 2005-10-11 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logic With Trees is a new and original introduction to modern formal logic. Unlike most texts, it also contains discussions on more philosophical issues such as truth, conditionals and modal logic. It presents the formal material with clarity, preferring informal explanations and arguments to intimidatingly rigorous development. Worked examples and excercises enable the readers to check their progress. Logic With Trees equips students with * a complete and clear account of the truth-tree system for first order logic * the importance of logic and its relevance to many different disciplines * the skills to grasp sophisticated formal reasoning techniques necessary to explore complex metalogic * the ability to contest claims that `ordinary' reasoning is well represented by formal first order logic The issues covered include a thorough discussion of truth-functional and full first order logic, using the truth-tree or semantic tableau approach. Completeness and Soundness proofs are given for both truth-functional and first order trees. Much use is made of induction, which is presented in a clear and consistent manner. There is also discussion of alternative deductive systems, an introduction to transfinite numbers and categoricity, the Lowenhein-Skolem theories and the celebrated findings of Godel and Church. The book concludes with an account of Kripke's attempted solution of the liar paradox and a discussion of the weakness of truth-functional account of conditionals. Particularly useful to those who favour critical accounts of formal reasoning, it will be of interest to students of philosophy at first level and beyond and also students of mathematics and computer science.
Book Synopsis Automated Reasoning with Analytic Tableaux and Related Methods by : Bernhard Beckert
Download or read book Automated Reasoning with Analytic Tableaux and Related Methods written by Bernhard Beckert and published by Springer. This book was released on 2005-09-14 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the research papers presented at the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2005) held September 14 –17, 2005 in Koblenz, Germany.
Book Synopsis Logic and Structure by : Dirk van Dalen
Download or read book Logic and Structure written by Dirk van Dalen and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: New corrected printing of a well-established text on logic at the introductory level.
Book Synopsis Automated Deduction - CADE 28 by : André Platzer
Download or read book Automated Deduction - CADE 28 written by André Platzer and published by Springer Nature. This book was released on 2021 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions.
Book Synopsis Logic for Applications by : Anil Nerode
Download or read book Logic for Applications written by Anil Nerode and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: In writing this book, our goal was to produce a text suitable for a first course in mathematical logic more attuned than the traditional textbooks to the recent dramatic growth in the applications of logic to computer science. Thus our choice of topics has been heavily influenced by such applications. Of course, we cover the basic traditional topics - syntax, semantics, soundness, completeness and compactness - as well as a few more advanced results such as the theorems of Skolem-Lowenheim and Herbrand. Much of our book, however, deals with other less traditional topics. Resolution theorem proving plays a major role in our treatment of logic, especially in its application to Logic Programming and PROLOG. We deal extensively with the mathematical foundations of all three of these subjects. In addition, we include two chapters on nonclassical logic- modal and intuitionistic - that are becoming increasingly important in computer science. We develop the basic material on the syntax and se mantics (via Kripke frames) for each of these logics. In both cases, our approach to formal proofs, soundness and completeness uses modifications of the same tableau method introduced for classical logic. We indicate how it can easily be adapted to various other special types of modal log ics. A number of more advanced topics (including nonmonotonic logic) are also briefly introduced both in the nonclassical logic chapters and in the material on Logic Programming and PROLOG.
Book Synopsis Automated Reasoning with Analytic Tableaux and Related Methods by : Uwe Egly
Download or read book Automated Reasoning with Analytic Tableaux and Related Methods written by Uwe Egly and published by Springer. This book was released on 2003-08-02 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2002, held in Copenhagen, Denmark, in July/August 2002. The 20 revised full papers and two system descriptions presented together with two invited contributions were carefully reviewed and selected for inclusion in the book. All current issues surrounding the mechanization of logical reasoning with tableaux and similar methods are addressed. Among the logic calculi investigated are linear logic, temporal logic, modal logics, hybrid logic, multi-modal logics, fuzzy logics, Goedel logic, Lukasiewicz logic, intermediate logics, quantified boolean logic, and, of course, classical first-order logic.
