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This textbook provides a first introduction to mathematical logic which is closely attuned to the applications of logic in computer science. In it the authors emphasize the notion that deduction is a form of computation. Whilst all the traditional subjects of logic are covered thoroughly: syntax, semantics, completeness, and compactness; much of the book deals with less traditional topics such as resolution theorem proving, logic programming and non-classical logics - modal and intuitionistic - which are becoming increasingly important in computer science. No previous exposure to logic is assumed and so this will be suitable for upper level undergraduates or beginning graduate students in computer science or mathematics.From reviews of the first edition: "... must surely rank as one of the most fruitful textbooks introduced into computer science ... We strongly suggest it as a textbook ..." SIGACT News
Automata Theory and its Applications is a uniform treatment of the theory of finite state machines on finite and infinite strings and trees. Many books deal with automata on finite strings, but there are very few expositions that prove the fundamental results of automata on infinite strings and trees. These results have important applications to modeling parallel computation and concurrency, the specification and verification of sequential and concurrent programs, databases, operating systems, computational complexity, and decision methods in logic and algebra. Thus, this textbook fills an important gap in the literature by exposing early fundamental results in automata theory and its applications. Beginning with coverage of all standard fundamental results regarding finite automata, the book deals in great detail with BA1/4chi and Rabin automata and their applications to various logical theories such as S1S and S2S, and describes game-theoretic models of concurrent operating and communication systems. The book is self-contained with numerous examples, illustrations, exercises, and is suitable for a two-semester undergraduate course for computer science or mathematics majors, or for a one-semester graduate course/seminar. Since no advanced mathematical background is required, the text is also useful for self-study by computer science professionals who wish to understand the foundations of modern formal approaches to software development, validation, and verification.
This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2018, held in Deerfield Beach, FL, USA, in January 2018. The 22 revised full papers were carefully reviewed and selected from 22 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logics; logical foundations of database theory; equational logic and term rewriting; lambda andcombinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple-agent system logics; logics of proof and justification; non-monotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; and other logics in computer science.
The theory of finite automata on finite stings, infinite strings, and trees has had a dis tinguished history. First, automata were introduced to represent idealized switching circuits augmented by unit delays. This was the period of Shannon, McCullouch and Pitts, and Howard Aiken, ending about 1950. Then in the 1950s there was the work of Kleene on representable events, of Myhill and Nerode on finite coset congruence relations on strings, of Rabin and Scott on power set automata. In the 1960s, there was the work of Btichi on automata on infinite strings and the second order theory of one successor, then Rabin's 1968 result on automata on infinite trees and the second order theory of two successors. The latter was a mystery until the introduction of forgetful determinacy games by Gurevich and Harrington in 1982. Each of these developments has successful and prospective applications in computer science. They should all be part of every computer scientist's toolbox. Suppose that we take a computer scientist's point of view. One can think of finite automata as the mathematical representation of programs that run us ing fixed finite resources. Then Btichi's SIS can be thought of as a theory of programs which run forever (like operating systems or banking systems) and are deterministic. Finally, Rabin's S2S is a theory of programs which run forever and are nondeterministic. Indeed many questions of verification can be decided in the decidable theories of these automata.
This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2013, held in San Diego, CA, USA in January 2013. The volume presents 29 revised refereed papers carefully selected by the program committee. The scope of the Symposium is broad and includes constructive mathematics and type theory; logic, automata and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logic; logical foundations of database theory; equational logic and term rewriting; lambda and combinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple agent system logics; logics of proof and justification; nonmonotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; and other logics in computer science.
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.
The Symposium on Logical Foundations of Computer Science series provides a forum for the fast-growing body of work in the logical foundations of computer science, e.g., those areas of fundamental theoretical logic related to computer science. The LFCS series began with "Logic at Botik," Pereslavl-Zalessky,1989, which was co-organized by Albert R. Meyer (MIT) and Michael Taitslin (Tver). After that, organization passed to Anil Nerode. Currently LFCS is governed by a Steering Committee consisting of Anil Nerode (General Chair), Stephen Cook, Dirk van Dalen, Yuri Matiyasevich, John McCarthy, J. Alan Robinson, Gerald Sacks, and Dana Scott. The 2009 Symposium on Logical Foundations of Computer Science (LFCS 2009) took place in Howard Johnson Plaza Resort, Deer?eld Beach, Florida, USA, during January 3-6. This volume contains the extended abstracts of talks selected by the Program Committee for presentation at LFCS 2009. The scope of the symposium is broad and contains constructive mathematics and type theory; automata and automatic structures; computability and r- domness; logical foundations of programming; logical aspects of computational complexity; logic programmingand constraints;automated deduction and int- active theorem proving; logical methods in protocol and program veri?cation; logical methods in program speci?cation and extraction; domain theory l- ics; logical foundations of database theory; equational logic and term rewriting; lambda andcombinatorycalculi;categoricallogicandtopologicalsemantics;l- ear logic; epistemic and temporal logics; intelligent and multiple agent system logics; logics of proof and justi?cation; nonmonotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics;
Hybrid systems are interacting networks of digital and continuous systems. - brid systems arise throughout business and industry in areas such as interactive distributed simulation, trac control, plant process control, military command and control, aircraft and robot design, and path planning. Three of the fun- mental problems that hybrid systems theory should address are: How to model physical and information systems as hybrid systems; how to verify that their - havior satis es program or performance specic ations; and how to extract from performancespeci cationsforanetworkofphysicalsystemsandtheirsimulation models digital control programs which will force the network to obey its perf- mance speci cation. This rapidly developing area is at the interface of control, engineeringandcomputer science. Methods under developmentareextensionsof thosefromdiverseareassuchasprogramveri cation, concurrentanddistributed processes, logic programming, logics of programs, discrete event simulation, c- culus of variations, optimization, di erential geometry, Lie algebras, automata theory, dynamical systems, etc. When the rst LNCS volume Hybrid Systems was published in 1993, the e ect was to focus the attention of researchers worldwide on developing theory andengineeringtoolsapplicabletohybridsystemsinwhichcontinuousprocesses interact with digital programs in real time. At the time of publication of this fth volume, there is general agreement that this is an important area in which mathematics, control engineering, and computer science can be fruitfully c- bined. There are now hybrid system sections in many engineering and computer scienceinternationalmeetings, hybridsystems researchgroupsin manyuniver- ties and industrial laboratories, and also other excellent series of hybrid systems conferenc
This book constitutes the thoroughly refereed post-conference documentation of the Fourth International Conference on Hybrid Systems held in Ithaca, NY, USA, in October 1996. The volume presents 19 carefully revised full papers selected from numerous submissions. Hybrid systems research focuses on modeling, design, and validation of interacting systems (plants) and computer programs (control automata). This volume is devoted to hybrid systems models, formal verification, computer simulation, goal reachability, algorithms for extracting hybrid control programs, and application models for avionics, highway traffic control, and air traffic control.
This book constitutes the refereed proceedings of the 4th
International Conference on Logic Programming and Nonmonotonic
Reasoning, LPNMR '97, held in Dagstuhl Castle, Germany, in July
1997.
This book constitutes the refereed proceedings of the 4th
International Symposium on Logical Foundations of Computer Science,
LFCS'97, held in Yaroslavl, Russia, in July 1997.
This book documents the scientific outcome of the Third
International Workshop on Hybrid Systems, held in Ithaca, NY, USA,
in October 1994. It presents a selection of carefully reviewed and
revised full papers chosen from the workshop contribution and is
the successor to LNCS 736, the seminal "Hybrid Systems" volume
edited by Grossman, Nerode, Ravn, and Rischel.
This volume contains the revised refereed papers accepted for
presentation at the Third International Conference on Logic
Programming and Nonmonotonic Reasoning, LPNMR '95, held in
Lexington, KY, USA in June 1995 under the sponsorship of the
Association for Logic Programming.
This volume presents the refereed papers accepted for the
international symposium Logical Foundations of Computer Science
'94, Logic at St. Petersburg, held in St. Petersburg, Russia in
July 1994. The symposium was the third in a series of joint efforts
of logicians from both the former Soviet Union and the West.
Hybrid systems are networks of interacting digital and analog devices. Control systems for inherently unstable aircraft and computer aided manufacturing are typical applications for hybrid systems, but due to the rapid development of processor and circuit technology modern cars and consumer electronics use software to control physical processes. The identifying characteristic of hybrid systems is that they incorporate both continuous components governed by differential equations and also digital components - digital computers, sensors, and actuators controlled by programs. This volume of invited refereed papers is inspired by a workshop on the Theory of Hybrid Systems, held at the Technical University, Lyngby, Denmark, in October 1992, and by a prior Hybrid Systems Workshop, held at Cornell University, USA, in June 1991, organized by R.L. Grossman and A. Nerode. Some papers are the final versions of papers presented at these workshops and some are invited papers from other researchers who were not able to attend these workshops.
This volume presents the papers selected for the Symposium Logic at Tver '92, held at Sokol, near Tver, Russia in July 1992. It is the second in a series of international symposia on logical foundations of computer science held in Russia. The meeting is a joint effort of scholars from both the former Soviet Union and the West, and indicates a new era of international cooperation. Sponsors of the meeting include: the Association for Computing Machinery, the Association for Symbolic Logic, andthe Committee on Mathematical Foundations of Computer Science of IEEE. The book is a unique source of information on the state of computer science research in the former Soviet Union and presents important discoveries in the area of logical foundations of computer science.
The courses given at the 1st C.I.M.E. Summer School of 1988 dealt with the main areas on the borderline between applied logic and theoretical computer science. These courses are recorded here in five expository papers: S. Homer: The Isomorphism Conjecture and its Generalization.- A. Nerode: Some Lectures on Intuitionistic Logic.- R.A. Platek: Making Computers Safe for the World. An Introduction to Proofs of Programs. Part I. - G.E. Sacks: Prolog Programming.- A. Scedrov: A Guide to Polymorphic Types.
This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2022, held in Deerfield Beach, FL, USA, in January 2022. The 23 revised full papers were carefully reviewed and selected from 35 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logics; logical foundations of database theory; equational logic and term rewriting; lambda and combinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple-agent system logics; logics of proof and justification; non-monotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; other logics in computer science.
This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2020, held in Deerfield Beach, FL, USA, in January 2020. The 17 revised full papers were carefully reviewed and selected from 30 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logics; logical foundations of database theory; equational logic and term rewriting; lambda and combinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple-agent system logics; logics of proof and justification; non-monotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; other logics in computer science.
This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2016, held in Deerfield Beach, FL, USA in January 2016. The 27 revised full papers were carefully reviewed and selected from 46 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logics; logical foundations of database theory; equational logic and term rewriting; lambda and combinatory calculi; categorical logic and topological semantics; linear logic; epistemic and temporal logics; intelligent and multiple-agent system logics; logics of proof and justification; non-monotonic reasoning; logic in game theory and social software; logic of hybrid systems; distributed system logics; mathematical fuzzy logic; system design logics; and other logics in computer science.
This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2007, held in New York, NY, USA in June 2007. The volume presents 36 revised refereed papers carefully selected by the program committee. All current aspects of logic in computer science are addressed, including constructive mathematics and type theory, logical foundations of programming, logical aspects of computational complexity, logic programming and constraints, automated deduction and interactive theorem proving, logical methods in protocol and program verification and in program specification and extraction, domain theory logics, logical foundations of database theory, equational logic and term rewriting, lambda and combinatory calculi, categorical logic and topological semantics, linear logic, epistemic and temporal logics, intelligent and multiple agent system logics, logics of proof and justification, nonmonotonic reasoning, logic in game theory and social software, logic of hybrid systems, distributed system logics, system design logics, as well as other logics in computer science.
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