First Steps In Modal Logic

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First Steps In Modal Logic

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Author : Sally Popkorn
language : en
Publisher: Cambridge University Press
Release Date : 1994-12-08

First Steps In Modal Logic written by Sally Popkorn 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 1994-12-08 with Mathematics categories.

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.

The Unprovability Of Consistency

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Author : George Boolos
language : en
Publisher: Cambridge University Press
Release Date : 1979-04-30

The Unprovability Of Consistency written by George Boolos 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 1979-04-30 with Mathematics categories.

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.

Modal Logic

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Author : Patrick Blackburn
language : en
Publisher: Cambridge University Press
Release Date : 2001

Modal Logic written by Patrick Blackburn 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 2001 with Computers categories.

This is an advanced 2001 textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s. Researchers in areas ranging from economics to computational linguistics have since realised its worth. The book is for novices and for more experienced readers, with two distinct tracks clearly signposted at the start of each chapter. The development is mathematical; prior acquaintance with first-order logic and its semantics is assumed, and familiarity with the basic mathematical notions of set theory is required. The authors focus on the use of modal languages as tools to analyze the properties of relational structures, including their algorithmic and algebraic aspects, and applications to issues in logic and computer science such as completeness, computability and complexity are considered. Three appendices supply basic background information and numerous exercises are provided. Ideal for anyone wanting to learn modern modal logic.

Handbook Of Modal Logic

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Author : Patrick Blackburn
language : en
Publisher: Elsevier
Release Date : 2006-11-03

Handbook Of Modal Logic written by Patrick Blackburn and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-03 with Mathematics categories.

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

Finite Model Theory And Its Applications

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Author : Erich Grädel
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-04

Finite Model Theory And Its Applications written by Erich Grädel 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 2007-06-04 with Computers categories.

Finite model theory,as understoodhere, is an areaof mathematicallogic that has developed in close connection with applications to computer science, in particular the theory of computational complexity and database theory. One of the fundamental insights of mathematical logic is that our understanding of mathematical phenomena is enriched by elevating the languages we use to describe mathematical structures to objects of explicit study. If mathematics is the science of patterns, then the media through which we discern patterns, as well as the structures in which we discern them, command our attention. It isthis aspect oflogicwhichis mostprominentin model theory,“thebranchof mathematical logic which deals with the relation between a formal language and its interpretations”. No wonder, then, that mathematical logic, and ?nite model theory in particular, should ?nd manifold applications in computer science: from specifying programs to querying databases, computer science is rife with phenomena whose understanding requires close attention to the interaction between language and structure. This volume gives a broadoverviewof some central themes of ?nite model theory: expressive power, descriptive complexity, and zero–one laws, together with selected applications to database theory and arti?cial intelligence, es- cially constraint databases and constraint satisfaction problems. The ?nal chapter provides a concise modern introduction to modal logic,which emp- sizes the continuity in spirit and technique with ?nite model theory.

Logic For Applications

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Author : Anil Nerode
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Logic For Applications written by Anil Nerode 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 2012-12-06 with Computers categories.

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 re cent dramatic growth in the applications oflogic to computer science. Thus, our choice oftopics has been heavily influenced by such applications. Of course, we cover the basic traditional topics: syntax, semantics, soundnes5, completeness and compactness as well as a few more advanced results such as the theorems of Skolem-Lowenheim and Herbrand. Much ofour 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 PRO LOG. We deal extensively with the mathematical foundations ofall three ofthese subjects. In addition, we include two chapters on nonclassical logics - modal and intuitionistic - that are becoming increasingly important in computer sci ence. We develop the basic material on the syntax and semantics (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 in troduced for classical logic. We indicate how it can easily be adapted to various other special types of modal logics. A number of more advanced topics (includ ing nonmonotonic logic) are also briefly introduced both in the nonclassical logic chapters and in the material on Logic Programming and PROLOG.

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.

The Combined Power Of Research Education And Dissemination

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Author : Mike Hinchey
language : en
Publisher: Springer Nature
Release Date : 2024-10-22

The Combined Power Of Research Education And Dissemination written by Mike Hinchey and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-22 with Computers categories.

Starting with a Laurea in Ingegneria Elettronica and a PhD in Computer and Systems Engineering at the Politecnico di Torino, Tiziana has stayed faithful to her love of organized management of composable functionalities in software and systems, with building blocks and MDD, and she strives for coherence and alignment in complex systems through verification, model checking and workflow synthesis. Her quest for simplicity spans technologies (low-code/no-code; ITSy project), business (Business Model Canvas; tools for innovative business models) and disciplines with her concept of the Digital Thread, a metaphor for IT-mediated interoperation of reusable and ideally verified tools and systems in new platforms where reuse, repurposing and evolution are supported by design. Her most recent initiative, R@ISE, aims at opening the world of IT production and adaptation to a wider range of users and professions. Tiziana is a cofounder and managing editor of the International Journal on Software Tools for Technology Transfer, she cofounded the ISoLA conference, and cofounded METAFrame Technologies serving as CEO. She is a Fellow of the Society for Design and Process Science and a Fellow and President of the Irish Computer Society. Throughout her career Tiziana’s successes have been motivated by how best to advance science and engineering through the implementation of techniques in challenging applications, and the contributions in this volume by leading researchers are representative of a community that shares this drive.

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.

The Logic Of Provability

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Author : George Boolos
language : en
Publisher: Cambridge University Press
Release Date : 1995-04-28

The Logic Of Provability written by George Boolos 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 1995-04-28 with Mathematics categories.

Boolos, a pre-eminent philosopher of mathematics, investigates the relationship between provability and modal logic.