Proof Methods For Modal And Intuitionistic Logics
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Proof Methods For Modal And Intuitionistic Logics
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Author : M. Fitting
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
Proof Methods For Modal And Intuitionistic Logics written by M. Fitting 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 2013-04-18 with Philosophy categories.
"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.
Interpolation And Definability
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Author : Dov M. Gabbay
language : en
Publisher: Oxford University Press
Release Date : 2005-05-12
Interpolation And Definability written by Dov M. Gabbay 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 2005-05-12 with Computers categories.
This book is a specialized monograph on interpolation and definability, a notion central in pure logic and with significant meaning and applicability in all areas where logic is applied, especially computer science, artificial intelligence, logic programming, philosophy of science and natural language.Suitable for researchers and graduate students in mathematics, computer science and philosophy, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (second edition), J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and NonmonotonicReasoning, P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2, and David J. Pym and Eike Ritter's Reductive Logic and Proof Search: Proof theory, semantics and control.
Theorem Proving With Analytic Tableaux And Related Methods
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Author : P. Miglioli
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-04-24
Theorem Proving With Analytic Tableaux And Related Methods written by P. Miglioli 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 1996-04-24 with Computers categories.
This books presents the refereed proceedings of the Fifth International Workshop on Analytic Tableaux and Related Methods, TABLEAUX '96, held in Terrasini near Palermo, Italy, in May 1996. The 18 full revised papers included together with two invited papers present state-of-the-art results in this dynamic area of research. Besides more traditional aspects of tableaux reasoning, the collection also contains several papers dealing with other approaches to automated reasoning. The spectrum of logics dealt with covers several nonclassical logics, including modal, intuitionistic, many-valued, temporal and linear logic.
Theorem Proving With Analytic Tableaux And Related Methods
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Author : Peter Baumgartner
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-04-26
Theorem Proving With Analytic Tableaux And Related Methods written by Peter Baumgartner 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 1995-04-26 with Computers categories.
This volume constitutes the proceedings of the 4th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods, TABLEAU '95, held at Schloß Rheinfels, St. Goar, Germany in May 1995. Originally tableau calculi and their relatives were favored primarily as a pedagogical device because of their advantages at the presentation level. The 23 full revised papers in this book bear witness that these methods have now gained fundamental importance in theorem proving, particularly as competitors for resolution methods. The book is organized in sections on extensions, modal logic, intuitionistic logic, the connection method and model elimination, non-clausal proof procedures, linear logic, higher-order logic, and applications
The Method Of Socratic Proofs
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Author : Dorota Leszczyńska-Jasion
language : en
Publisher: Springer Nature
Release Date : 2025-06-13
The Method Of Socratic Proofs written by Dorota Leszczyńska-Jasion and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-13 with Philosophy categories.
This book contains a systematic and formal attempt to model solutions to problems such as: Is it possible to prove a question? Is it possible to prove something by the use of questions? Do the existing paradigms in the logic of questions allow one to combine questions and proofs? What are the results in this field? In developing answers, the book focuses on the applications of the method of Socratic proofs, and goes beyond that. It starts out with an overview of the leading paradigms, issues, problems and ready solutions in the logic of questions, and places Inferential Erotetic Logic and the method of Socratic proofs against a wider background. It then introduces these two methods in more detail and explains how they can be used for classical logic, intuitionistic propositional logic and for basic modal logics. Next, the book deals with issues specific to the field of the logic of questions, introducing the tools of Minimal Erotetic Semantics (MiES). The final chapters describe the translations between proof systems: from a Socratic transformation, derived in an erotetic calculus, into a sequent system.
Handbook Of Tableau Methods
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Author : Marcello D'Agostino
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-03-31
Handbook Of Tableau Methods written by Marcello D'Agostino 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 1999-03-31 with Philosophy categories.
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.
Proof Analysis
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Author : Sara Negri
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-29
Proof Analysis written by Sara Negri and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-29 with Mathematics categories.
This book continues from where the authors' previous book, Structural Proof Theory, ended. It presents an extension of the methods of analysis of proofs in pure logic to elementary axiomatic systems and to what is known as philosophical logic. A self-contained brief introduction to the proof theory of pure logic is included that serves both the mathematically and philosophically oriented reader. The method is built up gradually, with examples drawn from theories of order, lattice theory and elementary geometry. The aim is, in each of the examples, to help the reader grasp the combinatorial behaviour of an axiom system, which typically leads to decidability results. The last part presents, as an application and extension of all that precedes it, a proof-theoretical approach to the Kripke semantics of modal and related logics, with a great number of new results, providing essential reading for mathematical and philosophical logicians.
A Companion To Philosophical Logic
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Author : Dale Jacquette
language : en
Publisher: John Wiley & Sons
Release Date : 2008-04-15
A Companion To Philosophical Logic written by Dale Jacquette and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-15 with Philosophy categories.
This collection of newly comissioned essays by international contributors offers a representative overview of the most important developments in contemporary philosophical logic. Presents controversies in philosophical implications and applications of formal symbolic logic. Surveys major trends and offers original insights.
Fibring Logics
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Author : Dov M. Gabbay
language : en
Publisher: Clarendon Press
Release Date : 1998-11-05
Fibring Logics written by Dov M. Gabbay and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-05 with Mathematics categories.
Modern applications of logic, in mathematics, theoretical computer science, and linguistics, require combined systems involving many different logics working together. In this book the author offers a basic methodology for combining-or fibring-systems. This means that many existing complex systems can be broken down into simpler components, hence making them much easier to manipulate. Using this methodology the book discusses ways of obtaining a wide variety of multimodal, modal intuitionistic, modal substructural and fuzzy systems in a uniform way. It also covers self-fibred languages which allow formulae to apply to themselves. The book also studies sufficient conditions for transferring properties of the component logics into properties of the combined system.
Automated Deduction In Classical And Non Classical Logics
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Author : Ricardo Caferra
language : en
Publisher: Springer
Release Date : 2003-07-31
Automated Deduction In Classical And Non Classical Logics written by Ricardo Caferra and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-31 with Computers categories.
This volume presents a collection of thoroughly reviewed revised full papers on automated deduction in classical, modal, and many-valued logics, with an emphasis on first-order theories. Five invited papers by prominent researchers give a consolidated view of the recent developments in first-order theorem proving. The 14 research papers presented went through a twofold selection process and were first presented at the International Workshop on First-Order Theorem Proving, FTP'98, held in Vienna, Austria, in November 1998. The contributed papers reflect the current status in research in the area; most of the results presented rely on resolution or tableaux methods, with a few exceptions choosing the equational paradigm.