Extensions of First-Order Logic PDF Download

Author: Maria Manzano
Publisher: Cambridge University Press
ISBN: 9780521354356
Category : Computers
Languages : en
Pages : 414

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Book Description
An introduction to many-sorted logic as an extension of first-order logic.

Author: H.-D. Ebbinghaus
Publisher: Springer Science & Business Media
ISBN: 1475723555
Category : Mathematics
Languages : en
Pages : 290

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Book Description
This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.

Author: Zoran Majkic
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110981467
Category : Computers
Languages : en
Pages : 425

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Book Description
This book introduces the properties of conservative extensions of First Order Logic (FOL) to new Intensional First Order Logic (IFOL). This extension allows for intensional semantics to be used for concepts, thus affording new and more intelligent IT systems. Insofar as it is conservative, it preserves software applications and constitutes a fundamental advance relative to the current RDB databases, Big Data with NewSQL, Constraint databases, P2P systems, and Semantic Web applications. Moreover, the many-valued version of IFOL can support the AI applications based on many-valued logics.

Author: Shawn Hedman
Publisher: OUP Oxford
ISBN: 0191586773
Category : Mathematics
Languages : en
Pages : 452

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Book Description
The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, this text covers the fundamental topics in classical logic in an extremely clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, and model theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course.

Author: Philippe Besnard
Publisher: Springer Science & Business Media
ISBN: 3662056895
Category : Computers
Languages : en
Pages : 221

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Book Description
This book is written for those who are interested in a fonnalization of human reasoning, especially in order to build "intelligent" computer systems. Thus, it is mainly designed for the Artificial Intelligence community, both students and researchers, although it can be useful for people working in related fields like cognitive psychology. The major theme is not Artificial Intelligence applications, although these are discussed throughout in sketch fonn. Rather, the book places a heavy emphasis on the fonnal development of default logic, results and problems. Default logic provides a fonnalism for an important part of human reasoning. Default logic is specifically concerned with common sense reasoning, which has recently been recognized in the Artificial Intelligence literature to be of fundamental importance for knowledge representation. Previously, fonnalized reasoning systems failed in real world environments, though succeeding with an acceptable ratio in well-defined environments. This situation enabled empirical explorations and the design of systems without theoretical justification. In particular, they could not be compared since there was no basis to judge their respective merits. Default logic turned out to be very fruitful by proving the correctness of some of them. We hope that this book will initiate other successful developments in default logic.

Author: Stewart Shapiro
Publisher: Clarendon Press
ISBN: 0191524018
Category : Mathematics
Languages : en
Pages : 302

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Book Description
The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed development of higher-order logic, including a comprehensive discussion of its semantics. Professor Shapiro demonstrates the prevalence of second-order notions in mathematics is practised, and also the extent to which mathematical concepts can be formulated in second-order languages . He shows how first-order languages are insufficient to codify many concepts in contemporary mathematics, and thus that higher-order logic is needed to fully reflect current mathematics. Throughout, the emphasis is on discussing the philosophical and historical issues associated with this subject, and the implications that they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic as might be gained from a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in this subject.

Author: C. Maria Keet
Publisher:
ISBN: 9781848902954
Category : Computer software
Languages : en
Pages : 344

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Book Description
An Introduction to Ontology Engineering introduces the student to a comprehensive overview of ontology engineering, and offers hands-on experience that illustrate the theory. The topics covered include: logic foundations for ontologies with languages and automated reasoning, developing good ontologies with methods and methodologies, the top-down approach with foundational ontologies, and the bottomup approach to extract content from legacy material, and a selection of advanced topics that includes Ontology-Based Data Access, the interaction between ontologies and natural languages, and advanced modelling with fuzzy and temporal ontologies. Each chapter contains review questions and exercises, and descriptions of two group assignments are provided as well. The textbook is aimed at advanced undergraduate/postgraduate level in computer science and could fi t a semester course in ontology engineering or a 2-week intensive course. Domain experts and philosophers may fi nd a subset of the chapters of interest, or work through the chapters in a different order. Maria Keet is an Associate Professor with the Department of Computer Science, University of Cape Town, South Africa. She received her PhD in Computer Science in 2008 at the KRDB Research Centre, Free University of Bozen-Bolzano, Italy. Her research focus is on knowledge engineering with ontologies and Ontology, and their interaction with natural language and conceptual data modelling, which has resulted in over 100 peer-reviewed publications. She has developed and taught multiple courses on ontology engineering and related courses at various universities since 2009.

Author: Robert L. Rogers
Publisher: Elsevier
ISBN: 1483257975
Category : Mathematics
Languages : en
Pages : 248

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Book Description
Mathematical Logic and Formalized Theories: A Survey of Basic Concepts and Results focuses on basic concepts and results of mathematical logic and the study of formalized theories. The manuscript first elaborates on sentential logic and first-order predicate logic. Discussions focus on first-order predicate logic with identity and operation symbols, first-order predicate logic with identity, completeness theorems, elementary theories, deduction theorem, interpretations, truth, and validity, sentential connectives, and tautologies. The text then tackles second-order predicate logic, as well as second-order theories, theory of definition, and second-order predicate logic F2. The publication takes a look at natural and real numbers, incompleteness, and the axiomatic set theory. Topics include paradoxes, recursive functions and relations, Gödel's first incompleteness theorem, axiom of choice, metamathematics of R and elementary algebra, and metamathematics of N. The book is a valuable reference for mathematicians and researchers interested in mathematical logic and formalized theories.

Author: John Harrison
Publisher: Cambridge University Press
ISBN: 0521899575
Category : Computers
Languages : en
Pages : 703

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Book Description
A one-stop reference, self-contained, with theoretical topics presented in conjunction with implementations for which code is supplied.

Author: Alexandra Silva
Publisher: Springer Nature
ISBN: 3030888533
Category : Philosophy
Languages : en
Pages : 435

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Book Description
Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 27th Workshop on Logic, Language, Information and Communication, WoLLIC 2021, Virtual Event, in October 2021. The 25 full papers presented included 6 invited lectures were fully reviewed and selected from 50 submissions. The idea is to have a forum which is large enough in the number of possible interactions between logic and the sciences related to information and computation.