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Modal Logic

Modal Logic Author Patrick Blackburn
ISBN-10 9781316101957
Release 2002-08-22
Pages
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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.



Basic Proof Theory

Basic Proof Theory Author A. S. Troelstra
ISBN-10 0521779111
Release 2000-07-27
Pages 417
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Introduction to proof theory and its applications in mathematical logic, theoretical computer science and artificial intelligence.



Epistemic Logic for AI and Computer Science

Epistemic Logic for AI and Computer Science Author J.-J. Ch. Meyer
ISBN-10 0521602807
Release 2004-03-25
Pages 372
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A broad introduction to the subject; many exercises with full solutions are provided.



Extensions of First Order Logic

Extensions of First Order Logic Author Maria Manzano
ISBN-10 0521354358
Release 1996-03-29
Pages 388
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This book introduces some extensions of classical first-order logic and applies them to reasoning about computer programs. The extensions considered are: second-order logic, many-sorted logic, w-logic, modal logic type theory and dynamic logic. These have wide applications in various areas of computer science, philosophy, natural language processing and artificial intelligence. Researchers in these areas will find this book a useful introduction and comparative treatment.



Modal Logic

Modal Logic Author Nino B. Cocchiarella
ISBN-10 0199710635
Release 2008-08-04
Pages 288
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In this text, a variety of modal logics at the sentential, first-order, and second-order levels are developed with clarity, precision and philosophical insight. All of the S1-S5 modal logics of Lewis and Langford, among others, are constructed. A matrix, or many-valued semantics, for sentential modal logic is formalized, and an important result that no finite matrix can characterize any of the standard modal logics is proven. Exercises, some of which show independence results, help to develop logical skills. A separate sentential modal logic of logical necessity in logical atomism is also constructed and shown to be complete and decidable. On the first-order level of the logic of logical necessity, the modal thesis of anti-essentialism is valid and every de re sentence is provably equivalent to a de dicto sentence. An elegant extension of the standard sentential modal logics into several first-order modal logics is developed. Both a first-order modal logic for possibilism containing actualism as a proper part as well as a separate modal logic for actualism alone are constructed for a variety of modal systems. Exercises on this level show the connections between modal laws and quantifier logic regarding generalization into, or out of, modal contexts and the conditions required for the necessity of identity and non-identity. Two types of second-order modal logics, one possibilist and the other actualist, are developed based on a distinction between existence-entailing concepts and concepts in general. The result is a deeper second-order analysis of possibilism and actualism as ontological frameworks. Exercises regarding second-order predicate quantifiers clarify the distinction between existence-entailing concepts and concepts in general. Modal Logic is ideally suited as a core text for graduate and undergraduate courses in modal logic, and as supplementary reading in courses on mathematical logic, formal ontology, and artificial intelligence.



Temporal Logics in Computer Science

Temporal Logics in Computer Science Author Stéphane Demri
ISBN-10 9781107028364
Release 2016-09-30
Pages 780
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A comprehensive, modern and technically precise exposition of the theory and main applications of temporal logics in computer science.



Advanced Topics in Bisimulation and Coinduction

Advanced Topics in Bisimulation and Coinduction Author Davide Sangiorgi
ISBN-10 9781139502900
Release 2011-10-13
Pages
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Coinduction is a method for specifying and reasoning about infinite data types and automata with infinite behaviour. In recent years, it has come to play an ever more important role in the theory of computing. It is studied in many disciplines, including process theory and concurrency, modal logic and automata theory. Typically, coinductive proofs demonstrate the equivalence of two objects by constructing a suitable bisimulation relation between them. This collection of surveys is aimed at both researchers and Master's students in computer science and mathematics and deals with various aspects of bisimulation and coinduction, with an emphasis on process theory. Seven chapters cover the following topics: history, algebra and coalgebra, algorithmics, logic, higher-order languages, enhancements of the bisimulation proof method, and probabilities. Exercises are also included to help the reader master new material.



First Order Modal Logic

First Order Modal Logic Author M. Fitting
ISBN-10 9789401152921
Release 2012-12-06
Pages 292
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This is a thorough treatment of first-order modal logic. The book covers such issues as quantification, equality (including a treatment of Frege's morning star/evening star puzzle), the notion of existence, non-rigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both Fregean and Russellian paradigms.



Handbook of Modal Logic

Handbook of Modal Logic Author Patrick Blackburn
ISBN-10 0080466664
Release 2006-11-03
Pages 1260
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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



Algebra and Coalgebra in Computer Science

Algebra and Coalgebra in Computer Science Author Andrea Corradini
ISBN-10 9783642229442
Release 2011-08-27
Pages 420
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This book constitutes the refereed proceedings of the 4th International Conference on Algebra and Coalgebra in Computer Science, CALCO 2011, held in Winchester, UK, in August/September 2011. The 21 full papers presented together with 4 invited talks were carefully reviewed and selected from 41 submissions. The papers report results of theoretical work on the mathematics of algebras and coalgebras, the way these results can support methods and techniques for software development, as well as experience with the transfer of the resulting technologies into industrial practice. They cover topics in the fields of abstract models and logics, specialized models and calculi, algebraic and coalgebraic semantics, and system specification and verification. The book also includes 6 papers from the CALCO-tools Workshop, colocated with CALCO 2011 and dedicated to tools based on algebraic and/or coalgebraic principles.



Computer Science Theory and Applications

Computer Science   Theory and Applications Author Volker Diekert
ISBN-10 9783540745099
Release 2007-08-15
Pages 420
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This book features the refereed proceedings of the 2nd International Symposium on Computer Science in Russia held in September 2007. The 35 papers cover theory track deals with algorithms, protocols, and data structures; complexity and cryptography; formal languages, automata and their applications to computer science; computational models and concepts; proof theory; and applications of logic to computer science. Many applications are presented.



Formal Methods in Artificial Intelligence

Formal Methods in Artificial Intelligence Author Allan Ramsay
ISBN-10 0521424216
Release 1991-07-26
Pages 292
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This book covers the background of classical logic, including the major meta-theorems, and the state of the art in theorem proving.



Modal Logic for Open Minds

Modal Logic for Open Minds Author Johan van Benthem
ISBN-10 NWU:35556040094005
Release 2010
Pages 381
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In this work, the author provides an introduction to the field of modal logic, outlining its major ideas and emploring the numerous ways in which various academic fields have adopted it.



Introduction to Coalgebra

Introduction to Coalgebra Author Bart Jacobs
ISBN-10 9781316833971
Release 2016-10-27
Pages
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The area of coalgebra has emerged within theoretical computer science with a unifying claim: to be the mathematics of computational dynamics. It combines ideas from the theory of dynamical systems and from the theory of state-based computation. Although still in its infancy, it is an active area of research that generates wide interest. Written by one of the founders of the field, this book acts as the first mature and accessible introduction to coalgebra. It provides clear mathematical explanations, with many examples and exercises involving deterministic and non-deterministic automata, transition systems, streams, Markov chains and weighted automata. The theory is expressed in the language of category theory, which provides the right abstraction to make the similarity and duality between algebra and coalgebra explicit, and which the reader is introduced to in a hands-on manner. The book will be useful to mathematicians and (theoretical) computer scientists and will also be of interest to mathematical physicists, biologists and economists.



An Introduction to Substructural Logics

An Introduction to Substructural Logics Author Greg Restall
ISBN-10 9781135111311
Release 2002-09-11
Pages 400
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This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. An Introduction to Substrucural Logics is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda Both students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading.



Products of topological modal logics

Products of topological modal logics Author Darko Sarenac
ISBN-10 STANFORD:36105127120314
Release 2006
Pages 238
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Products of topological modal logics has been writing in one form or another for most of life. You can find so many inspiration from Products of topological modal logics also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Products of topological modal logics book for free.



Dynamic Logic

Dynamic Logic Author David Harel
ISBN-10 0262263025
Release 2000-09-29
Pages 476
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Among the many approaches to formal reasoning about programs, Dynamic Logic enjoys the singular advantage of being strongly related to classical logic. Its variants constitute natural generalizations and extensions of classical formalisms. For example, Propositional Dynamic Logic (PDL) can be described as a blend of three complementary classical ingredients: propositional calculus, modal logic, and the algebra of regular events. In First-Order Dynamic Logic (DL), the propositional calculus is replaced by classical first-order predicate calculus. Dynamic Logic is a system of remarkable unity that is theoretically rich as well as of practical value. It can be used for formalizing correctness specifications and proving rigorously that those specifications are met by a particular program. Other uses include determining the equivalence of programs, comparing the expressive power of various programming constructs, and synthesizing programs from specifications.This book provides the first comprehensive introduction to Dynamic Logic. It is divided into three parts. The first part reviews the appropriate fundamental concepts of logic and computability theory and can stand alone as an introduction to these topics. The second part discusses PDL and its variants, and the third part discusses DL and its variants. Examples are provided throughout, and exercises and a short historical section are included at the end of each chapter.