Proof Theory Of Modal Logic PDF Download
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Author | : Heinrich Wansing |
Publisher | : Springer Science & Business Media |
Total Pages | : 317 |
Release | : 2013-06-29 |
Genre | : Philosophy |
ISBN | : 9401727988 |
Download Proof Theory of Modal Logic Book in PDF, ePub and Kindle
Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.
Author | : M. Fitting |
Publisher | : Springer Science & Business Media |
Total Pages | : 574 |
Release | : 1983-04-30 |
Genre | : Mathematics |
ISBN | : 9789027715739 |
Download Proof Methods for Modal and Intuitionistic Logics Book in PDF, ePub and Kindle
"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.
Author | : Torben Braüner |
Publisher | : Springer Science & Business Media |
Total Pages | : 240 |
Release | : 2010-11-17 |
Genre | : Philosophy |
ISBN | : 9400700024 |
Download Hybrid Logic and its Proof-Theory Book in PDF, ePub and Kindle
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 | : Heinrich Wansing |
Publisher | : |
Total Pages | : 334 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9789401727990 |
Download Proof Theory of Modal Logic Book in PDF, ePub and Kindle
Author | : M. Fitting |
Publisher | : Springer Science & Business Media |
Total Pages | : 563 |
Release | : 2013-04-18 |
Genre | : Philosophy |
ISBN | : 9401727945 |
Download Proof Methods for Modal and Intuitionistic Logics Book in PDF, ePub and Kindle
"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.
Author | : Heinrich Wansing |
Publisher | : Springer Science & Business Media |
Total Pages | : 259 |
Release | : 2013-03-14 |
Genre | : Philosophy |
ISBN | : 9401712808 |
Download Displaying Modal Logic Book in PDF, ePub and Kindle
The present monograph is a slightly revised version of my Habilitations schrift Proof-theoretic Aspects of Intensional and Non-Classical Logics, successfully defended at Leipzig University, November 1997. It collects work on proof systems for modal and constructive logics I have done over the last few years. The main concern is display logic, a certain refinement of Gentzen's sequent calculus developed by Nuel D. Belnap. This book is far from offering a comprehensive presentation of generalized sequent systems for modal logics broadly conceived. The proof-theory of non-classical logics is a rapidly developing field, and even the generalizations of the ordinary notion of sequent listed in Chapter 1 can hardly be presented in great detail within a single volume. In addition to further investigating the various approaches toward generalized Gentzen systems, it is important to compare them and to discuss their relative advantages and disadvantages. An initial attempt at bringing together work on different kinds of proof systems for modal logics has been made in [188]. Another step in the same direction is [196]. Since Chapter 1 contains introductory considerations and, moreover, every remaining chapter begins with some surveying or summarizing remarks, in this preface I shall only emphasize a relation to philosophy that is important to me, register the sources of papers that have entered this book in some form or another, and acknowledge advice and support.
Author | : Jean Goubault-Larrecq |
Publisher | : Springer Science & Business Media |
Total Pages | : 448 |
Release | : 2001-11-30 |
Genre | : Computers |
ISBN | : 9781402003684 |
Download Proof Theory and Automated Deduction Book in PDF, ePub and Kindle
Interest in computer applications has led to a new attitude to applied logic in which researchers tailor a logic in the same way they define a computer language. In response to this attitude, this text for undergraduate and graduate students discusses major algorithmic methodologies, and tableaux and resolution methods. The authors focus on first-order logic, the use of proof theory, and the computer application of automated searches for proofs of mathematical propositions. Annotation copyrighted by Book News, Inc., Portland, OR
Author | : Sally Popkorn |
Publisher | : Cambridge University Press |
Total Pages | : 340 |
Release | : 1994-12-08 |
Genre | : Mathematics |
ISBN | : 052146482X |
Download First Steps in Modal Logic Book in PDF, ePub and Kindle
This is a first course in propositional modal logic, suitable for mathematicians, computer scientists and philosophers. Emphasis is placed on semantic aspects, in the form of labelled transition structures, rather than on proof theory.
Author | : Patrick Blackburn |
Publisher | : Elsevier |
Total Pages | : 1260 |
Release | : 2006-11-03 |
Genre | : Mathematics |
ISBN | : 9780080466668 |
Download Handbook of Modal Logic Book in PDF, ePub and Kindle
The Handbook of Modal Logic contains 20 articles, which collectively introduce contemporary modal logic, survey current research, and indicate the way in which the field is developing. The articles survey the field from a wide variety of perspectives: the underling theory is explored in depth, modern computational approaches are treated, and six major applications areas of modal logic (in Mathematics, Computer Science, Artificial Intelligence, Linguistics, Game Theory, and Philosophy) are surveyed. The book contains both well-written expository articles, suitable for beginners approaching the subject for the first time, and advanced articles, which will help those already familiar with the field to deepen their expertise. Please visit: http://people.uleth.ca/~woods/RedSeriesPromo_WP/PubSLPR.html - Compact modal logic reference - Computational approaches fully discussed - Contemporary applications of modal logic covered in depth
Author | : George Boolos |
Publisher | : Cambridge University Press |
Total Pages | : 0 |
Release | : 2009-01-08 |
Genre | : Mathematics |
ISBN | : 9780521092975 |
Download The Unprovability of Consistency Book in PDF, ePub and Kindle
The Unprovability of Consistency is concerned with connections between two branches of logic: proof theory and modal logic. Modal logic is the study of the principles that govern the concepts of necessity and possibility; proof theory is, in part, the study of those that govern provability and consistency. In this book, George Boolos looks at the principles of provability from the standpoint of modal logic. In doing so, he provides two perspectives on a debate in modal logic that has persisted for at least thirty years between the followers of C. I. Lewis and W. V. O. Quine. The author employs semantic methods developed by Saul Kripke in his analysis of modal logical systems. The book will be of interest to advanced undergraduate and graduate students in logic, mathematics and philosophy, as well as to specialists in those fields.