Fragments Of First Order Logic

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Fragments of First-Order Logic

Author : Ian Pratt-Hartmann
Publisher : Oxford University Press
ISBN 13 : 0192867962
Total Pages : 673 pages
Book Rating : 4.1/5 (928 download)

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Book Synopsis Fragments of First-Order Logic by : Ian Pratt-Hartmann

Download or read book Fragments of First-Order Logic written by Ian Pratt-Hartmann and published by Oxford University Press. This book was released on 2023-02-18 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: A sentence of first-order logic is satisfiable if it is true in some structure, and finitely satisfiable if it is true in some finite structure. The question arises as to whether there exists an algorithm for determining whether a given formula of first-order logic is satisfiable, or indeed finitely satisfiable. This question was answered negatively in 1936 by Church and Turing (for satisfiability) and in 1950 by Trakhtenbrot (for finite satisfiability).In contrast, the satisfiability and finite satisfiability problems are algorithmically solvable for restricted subsets---or, as we say, fragments---of first-order logic, a fact which is today of considerable interest in Computer Science. This book provides an up-to-date survey of the principal axes of research, charting the limits of decision in first-order logic and exploring the trade-off between expressive power and complexity of reasoning. Divided into three parts, the book considers for which fragments of first-order logic there is an effective method for determining satisfiability or finite satisfiability. Furthermore, if these problems are decidable for some fragment, what is their computational complexity? Part I focusses on fragments defined by restricting the set of available formulas. Topics covered include the Aristotelian syllogistic and its relatives, the two-variable fragment, the guarded fragment, the quantifier-prefix fragments and the fluted fragment. Part II investigates logics with counting quantifiers. Starting with De Morgan's numerical generalization of the Aristotelian syllogistic, we proceed to the two-variable fragment with counting quantifiers and its guarded subfragment, explaining the applications of the latter to the problem of query answering in structured data. Part III concerns logics characterized by semantic constraints, limiting the available interpretations of certain predicates. Taking propositional modal logic and graded modal logic as our cue, we return to the satisfiability problem for two-variable first-order logic and its relatives, but this time with certain distinguished binary predicates constrained to be interpreted as equivalence relations or transitive relations. The work finishes, slightly breaching the bounds of first-order logic proper, with a chapter on logics interpreted over trees.

Extensions of First-Order Logic

Author : Maria Manzano
Publisher : Cambridge University Press
ISBN 13 : 9780521354356
Total Pages : 414 pages
Book Rating : 4.3/5 (543 download)

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Book Synopsis Extensions of First-Order Logic by : Maria Manzano

Download or read book Extensions of First-Order Logic written by Maria Manzano and published by Cambridge University Press. This book was released on 1996-03-29 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to many-sorted logic as an extension of first-order logic.

The Classical Decision Problem

Author : Egon Börger
Publisher : Springer Science & Business Media
ISBN 13 : 9783540423249
Total Pages : 500 pages
Book Rating : 4.4/5 (232 download)

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Book Synopsis The Classical Decision Problem by : Egon Börger

Download or read book The Classical Decision Problem written by Egon Börger and published by Springer Science & Business Media. This book was released on 2001-08-28 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive treatment of the classical decision problem of mathematical logic and of the role of the classical decision problem in modern computer science. The text presents a revealing analysis of the natural order of decidable and undecidable cases and includes a number of simple proofs and exercises.

Rewriting Techniques and Applications

Author : Robert Nieuwenhuis
Publisher : Springer Science & Business Media
ISBN 13 : 3540402543
Total Pages : 527 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Rewriting Techniques and Applications by : Robert Nieuwenhuis

Download or read book Rewriting Techniques and Applications written by Robert Nieuwenhuis and published by Springer Science & Business Media. This book was released on 2003-05-27 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the14thInternationalConferenceon RewritingTechniquesandApplications (RTA2003). It was held June 9-11, 2003 in Valencia, Spain, as part of RDP, theFederatedConferenceonRewriting,- ductionandProgramming, together with the International Conference on Typed Lambda Calculi and Applications (TLCA2003), the International Workshop on First-order Theorem Proving (FTP2003), the annual meeting of the IFIP Working Group 1.6 on Term Rewriting, the International Workshop on Rule- Based Programming (RULE2003), the International Workshop on Uni?cation (UNIF2003), the International Workshop on Functional and (Constraint) Logic Programming (WFLP2003), the International Workshop on Reduction Stra- gies in Rewriting and Programming (WRS2003), and the International Wo- shop on Termination (WST2003). RTA is the major forum for the presentation of research on all aspects of rewr- ing. Previous RTA conferences were held in Dijon (1985), Bordeaux (1987), Chapel Hill (1989), Como (1991), Montreal (1993), Kaiserslautern (1995), New Brunswick, NJ (1996), Sitges, Barcelona (1997), Tsukuba (1998), Trento (1999), Norwich (2000), Utrecht (2001), and Copenhagen (2002). This year, there were 61 submissions of which 57 regular research papers and 4 system descriptions, with authors from institutions in France (19.6 authors of submitted papers, of which 11.3 were accepted), USA (6.5 of 9), UK (3.5 of 4.5), Japan(3of6),Germany(2.5 of 4),TheNetherlands(2.2 of 5.2),Spain(1.5 of 4), Austria (1 of 1), Israel (0.5 of 2.5), Portugal (0 of 1), Algeria (0 of 1), Denmark (0 of 1), Canada (0 of 1), Brazil (0 of 0.6), and Poland (0 of 0.5).

Many-Dimensional Modal Logics: Theory and Applications

Author : A. Kurucz
Publisher : Elsevier
ISBN 13 : 008053578X
Total Pages : 767 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Many-Dimensional Modal Logics: Theory and Applications by : A. Kurucz

Download or read book Many-Dimensional Modal Logics: Theory and Applications written by A. Kurucz and published by Elsevier. This book was released on 2003-10-21 with total page 767 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects.To study the computational behaviour of many-dimensional modal logics is the main aim of this book. On the one hand, it is concerned with providing a solid mathematical foundation for this discipline, while on the other hand, it shows that many seemingly different applied many-dimensional systems (e.g., multi-agent systems, description logics with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) fit in perfectly with this theoretical framework, and so their computational behaviour can be analyzed using the developed machinery.We start with concrete examples of applied one- and many-dimensional modal logics such as temporal, epistemic, dynamic, description, spatial logics, and various combinations of these. Then we develop a mathematical theory for handling a spectrum of 'abstract' combinations of modal logics - fusions and products of modal logics, fragments of first-order modal and temporal logics - focusing on three major problems: decidability, axiomatizability, and computational complexity. Besides the standard methods of modal logic, the technical toolkit includes the method of quasimodels, mosaics, tilings, reductions to monadic second-order logic, algebraic logic techniques. Finally, we apply the developed machinery and obtained results to three case studies from the field of knowledge representation and reasoning: temporal epistemic logics for reasoning about multi-agent systems, modalized description logics for dynamic ontologies, and spatio-temporal logics.The genre of the book can be defined as a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). On the other hand, well-known results from modal and first-order logic are formulated without proofs and supplied with references to accessible sources.The intended audience of this book is logicians as well as those researchers who use logic in computer science and artificial intelligence. More specific application areas are, e.g., knowledge representation and reasoning, in particular, terminological, temporal and spatial reasoning, or reasoning about agents. And we also believe that researchers from certain other disciplines, say, temporal and spatial databases or geographical information systems, will benefit from this book as well.Key Features:• Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science• Written by internationally leading researchers in the field of pure and applied logic• Combines mathematical theory of modal logic and applications in artificial intelligence and computer science• Numerous open problems for further research• Well illustrated with pictures and tables

First Order Categorical Logic

Author : M. Makkai
Publisher : Springer
ISBN 13 : 3540371001
Total Pages : 317 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis First Order Categorical Logic by : M. Makkai

Download or read book First Order Categorical Logic written by M. Makkai and published by Springer. This book was released on 2006-11-15 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt:

First-Order Dynamic Logic

Author : D. Harel
Publisher :
ISBN 13 : 9783662174500
Total Pages : 152 pages
Book Rating : 4.1/5 (745 download)

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Book Synopsis First-Order Dynamic Logic by : D. Harel

Download or read book First-Order Dynamic Logic written by D. Harel and published by . This book was released on 2014-01-15 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Metamathematics of First-Order Arithmetic

Author : Petr Hájek
Publisher : Cambridge University Press
ISBN 13 : 1107168414
Total Pages : 475 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Metamathematics of First-Order Arithmetic by : Petr Hájek

Download or read book Metamathematics of First-Order Arithmetic written by Petr Hájek and published by Cambridge University Press. This book was released on 2017-03-02 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: A much-needed monograph on the metamathematics of first-order arithmetic, paying particular attention to fragments of Peano arithmetic.

Decidability of Logical Theories and Their Combination

Author : João Rasga
Publisher : Springer Nature
ISBN 13 : 3030565548
Total Pages : 185 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Decidability of Logical Theories and Their Combination by : João Rasga

Download or read book Decidability of Logical Theories and Their Combination written by João Rasga and published by Springer Nature. This book was released on 2020-10-20 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a self-contained introduction to decidability of first-order theories and their combination. The technical material is presented in a systematic and universal way and illustrated with plenty of examples and a range of proposed exercises. After an overview of basic first-order logic concepts, the authors discuss some model-theoretic notions like embeddings, diagrams, and elementary substructures. The text then goes on to explore an applicable way to deduce logical consequences from a given theory and presents sufficient conditions for a theory to be decidable. The chapters that follow focus on quantifier elimination, decidability of the combination of first-order theories and the basics of computability theory. The inclusion of a chapter on Gentzen calculus, cut elimination, and Craig interpolation, as well as a chapter on combination of theories and preservation of decidability, help to set this volume apart from similar books in the field. Decidability of Logical Theories and their Combination is ideal for graduate students of Mathematics and is equally suitable for Computer Science, Philosophy and Physics students who are interested in gaining a deeper understanding of the subject. The book is also directed to researchers that intend to get acquainted with first-order theories and their combination.

Modal Logic

Author : Patrick Blackburn
Publisher : Cambridge University Press
ISBN 13 : 1316101959
Total Pages : 574 pages
Book Rating : 4.3/5 (161 download)

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Book Synopsis Modal Logic by : Patrick Blackburn

Download or read book Modal Logic written by Patrick Blackburn and published by Cambridge University Press. This book was released on 2002-08-22 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Model-Theoretic Logics

Author : J. Barwise
Publisher : Cambridge University Press
ISBN 13 : 1107168252
Total Pages : 912 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Model-Theoretic Logics by : J. Barwise

Download or read book Model-Theoretic Logics written by J. Barwise and published by Cambridge University Press. This book was released on 2017-03-02 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together several directions of work in model theory between the late 1950s and early 1980s.

Handbook of Modal Logic

Author : Patrick Blackburn
Publisher : Elsevier
ISBN 13 : 9780080466668
Total Pages : 1260 pages
Book Rating : 4.4/5 (666 download)

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Book Synopsis Handbook of Modal Logic by : Patrick Blackburn

Download or read book Handbook of Modal Logic written by Patrick Blackburn and published by Elsevier. This book was released on 2006-11-03 with total page 1260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Graph Transformations

Author : Hartmut Ehrig
Publisher : Springer
ISBN 13 : 3540302034
Total Pages : 462 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Graph Transformations by : Hartmut Ehrig

Download or read book Graph Transformations written by Hartmut Ehrig and published by Springer. This book was released on 2004-11-11 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: ICGT 2004 was the 2nd International Conference on Graph Transformation, following the first one in Barcelona (2002), and a series of six international workshops on graph grammars with applications in computer science between 1978 and 1998. ICGT 2004 was held in Rome (Italy), Sept. 29-Oct. 1, 2004 under the auspices of the European Association for Theoretical Computer Science (EATCS), the European Association of Software Science and Technology (EASST), and the IFIP WG 1.3, Foundations of Systems Specification. The scope of the conference concerned graphical structures of various kinds (like graphs, diagrams, visual sentences and others) that are useful when describing complex structures and systems in a direct and intuitive way. These structures are often augmented with formalisms that add to the static description a further dimension, allowing for the modelling of the evolution of systems via all kinds of transformations of such graphical structures. The field of graph transformation is concerned with the theory, applications, and implementation issues of such formalisms. The theory is strongly related to areas such as graph theory and graph algorithms, formal language and parsing theory, the theory of concurrent and distributed systems, formal specification and verification, logic, and semantics. The application areas include all those fields of computer science, information processing,engineering,and the natural sciences where static and dynamic m- elling using graphical structures and graph transformations, respectively, play important roles. In many of these areas tools based on graph transformation technology have been implemented and used

The Calculus of Computation

Author : Aaron R. Bradley
Publisher : Springer Science & Business Media
ISBN 13 : 3540741135
Total Pages : 375 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis The Calculus of Computation by : Aaron R. Bradley

Download or read book The Calculus of Computation written by Aaron R. Bradley and published by Springer Science & Business Media. This book was released on 2007-09-18 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written with graduate and advanced undergraduate students in mind, this textbook introduces computational logic from the foundations of first-order logic to state-of-the-art decision procedures for arithmetic, data structures, and combination theories. The textbook also presents a logical approach to engineering correct software. Verification exercises are given to develop the reader's facility in specifying and verifying software using logic. The treatment of verification concludes with an introduction to the static analysis of software, an important component of modern verification systems. The final chapter outlines courses of further study.

Logic and Its Applications

Author : Md. Aquil Khan
Publisher : Springer
ISBN 13 : 9783662587706
Total Pages : 0 pages
Book Rating : 4.5/5 (877 download)

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Book Synopsis Logic and Its Applications by : Md. Aquil Khan

Download or read book Logic and Its Applications written by Md. Aquil Khan and published by Springer. This book was released on 2019-02-05 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the refereed proceedings of the 8th Indian Conference on Logic and Its Applications, ICLA 2019, held in Delhi, India, in March 2019. The volume contains 13 full revised papers along with 6 invited talks presented at the conference. The aim of this conference series is to bring together researchers from a wide variety of fields in which formal logic plays a significant role. Areas of interest include mathematical and philosophical logic, computer science logic, foundations and philosophy of mathematics and the sciences, use of formal logic in areas of theoretical computer science and artificial intelligence, logic and linguistics, and the relationship between logic and other branches of knowledge. Of special interest are studies in systems of logic in the Indian tradition, and historical research on logic.

Computer Science Logic

Author : European Association for Computer Science Logic. Conference
Publisher : Springer Science & Business Media
ISBN 13 : 3540282319
Total Pages : 577 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Computer Science Logic by : European Association for Computer Science Logic. Conference

Download or read book Computer Science Logic written by European Association for Computer Science Logic. Conference and published by Springer Science & Business Media. This book was released on 2005-08-09 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 19th International Workshop on Computer Science Logic, CSL 2005, held as the 14th Annual Conference of the EACSL in Oxford, UK in August 2005. The 33 revised full papers presented together with 4 invited contributions were carefully reviewed and selected from 108 papers submitted. All current aspects of logic in computer science are addressed ranging from mathematical logic and logical foundations to methodological issues and applications of logics in various computing contexts. The volume is organized in topical sections on semantics and logics, type theory and lambda calculus, linear logic and ludics, constraints, finite models, decidability and complexity, verification and model checking, constructive reasoning and computational mathematics, and implicit computational complexity and rewriting.

Logic Programming and Automated Reasoning

Author : Harald Ganzinger
Publisher : Springer
ISBN 13 : 3540482423
Total Pages : 404 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Logic Programming and Automated Reasoning by : Harald Ganzinger

Download or read book Logic Programming and Automated Reasoning written by Harald Ganzinger and published by Springer. This book was released on 2007-07-12 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the papers presented at the Sixth International Conference on Logic for Programming and Automated Reasoning (LPAR'99), held in Tbilisi, Georgia, September 6-10, 1999, and hosted by the University of Tbilisi. Forty-four papers were submitted to LPAR'99. Each of the submissions was reviewed by three program committee members and an electronic program com mittee meeting was held via the Internet. Twenty-three papers were accepted. We would like to thank the many people who have made LPAR'99 possible. We are grateful to the following groups and individuals: to the program committee and the additional referees for reviewing the papers in a very short time, to the organizing committee, and to the local organizers of the INTAS workshop in Tbilisi in April 1994 (Khimuri Rukhaia, Konstantin Pkhakadze, and Gela Chankvetadze). And last but not least, we would like to thank Konstantin - rovin, who maintained the program committee Web page; Uwe Waldmann, who supplied macros for these proceedings and helped us to install some programs for the electronic management of the program committee work; and Bill McCune, who implemented these programs.