Reasoning In Simple Type Theory
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Reasoning In Simple Type Theory
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Author : Christoph Benzmüller
language : en
Publisher:
Release Date : 2008
Reasoning In Simple Type Theory written by Christoph Benzmüller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Reasoning in Simple Type Theory is a collection of papers that includes reprints of eight seminal papers in this area as well as thirteen new contributed articles. For the reprints we have chosen a paper by Alonzo Church (introducing his simple theory of types), a paper by Leon Henkin (proving completeness of Church's type theory relative to Henkin's semantics) and some of the most important papers by Peter Andrews. The new articles were contributed by Peter Andrews and his students and collaborators as well as a number of researchers his work has influenced. The volume intends to show the historical development of this important area of formal reasoning up to its current state of art and appears in honor of Peter Andrews on his 70th birthday.
Simple Type Theory
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Author : William M. Farmer
language : en
Publisher: Springer Nature
Release Date : 2023-01-01
Simple Type Theory written by William M. Farmer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Computers categories.
This unique textbook, in contrast to a standard logic text, provides the reader with a logic that actually can be used in practice to express and reason about mathematical ideas. The book is an introduction to simple type theory, a classical higher-order version of predicate logic that extends first-order logic. It presents a practice-oriented logic called Alonzo that is based on Alonzo Church's formulation of simple type theory known as Church's type theory. Unlike traditional predicate logics, Alonzo admits undefined expressions. The book illustrates, using Alonzo, how simple type theory is suited ideally for reasoning about mathematical structures and constructing libraries of mathematical knowledge. Topics and features: Offers the first book-length introduction to simple type theory as a predicate logic Provides the reader with a logic that is close to mathematical practice Presents the tools needed to build libraries of mathematical knowledge Employs two semantics, one for mathematics and one for logic Emphasizes the model-theoretic view of predicate logic Includes several important topics, such as definite description and theory morphisms, not usually found in standard logic textbooks Aimed at students of computing and mathematics at the graduate or upper-undergraduate level, this book is also well-suited for mathematicians, computing professionals, engineers, and scientists who need a practical logic for expressing and reasoning about mathematical ideas. William M. Farmer is a Professor in the Department of Computing and Software at McMaster University in Hamilton, Ontario, Canada.
Basic Simple Type Theory
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Author : J. Roger Hindley
language : en
Publisher: Cambridge University Press
Release Date : 1997
Basic Simple Type Theory written by J. Roger Hindley 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 1997 with Computers categories.
Type theory is one of the most important tools in the design of higher-level programming languages, such as ML. This book introduces and teaches its techniques by focusing on one particularly neat system and studying it in detail. By concentrating on the principles that make the theory work in practice, the author covers all the key ideas without getting involved in the complications of more advanced systems. This book takes a type-assignment approach to type theory, and the system considered is the simplest polymorphic one. The author covers all the basic ideas, including the system's relation to propositional logic, and gives a careful treatment of the type-checking algorithm that lies at the heart of every such system. Also featured are two other interesting algorithms that until now have been buried in inaccessible technical literature. The mathematical presentation is rigorous but clear, making it the first book at this level that can be used as an introduction to type theory for computer scientists.
Formal Semantics In Modern Type Theories
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Author : Stergios Chatzikyriakidis
language : en
Publisher: John Wiley & Sons
Release Date : 2021-02-17
Formal Semantics In Modern Type Theories written by Stergios Chatzikyriakidis 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 2021-02-17 with Language Arts & Disciplines categories.
This book studies formal semantics in modern type theories (MTTsemantics). Compared with simple type theory, MTTs have much richer type structures and provide powerful means for adequate semantic constructions. This offers a serious alternative to the traditional settheoretical foundation for linguistic semantics and opens up a new avenue for developing formal semantics that is both model-theoretic and proof-theoretic, which was not available before the development of MTTsemantics. This book provides a reader-friendly and precise description of MTTs and offers a comprehensive introduction to MTT-semantics. It develops several case studies, such as adjectival modification and copredication, to exemplify the attractiveness of using MTTs for the study of linguistic meaning. It also examines existing proof assistant technology based on MTT-semantics for the verification of semantic constructions and reasoning in natural language. Several advanced topics are also briefly studied, including dependent event types, an application of dependent typing to event semantics.
Computational Logic In Multi Agent Systems
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Author : Jürgen Dix
language : en
Publisher: Springer
Release Date : 2010-08-12
Computational Logic In Multi Agent Systems written by Jürgen Dix and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-12 with Computers categories.
This book constitutes the refereed proceedings of the 11th International Workshop on Computational Logic in Multi-Agent Systems, CLIMA-XI, held in Lisbon, Portugal in August 2010. The 14 papers included in this volume were carefully reviewed and selected from 31 submissions. The purpose of the CLIMA workshops is to provide a forum for discussing techniques, based on computational logic, for representing, programming and reasoning about agents and multi-agent systems in a formal way. CLIMA 2010 featured two thematic special sessions on norms and normative multi-agent systems and logics for games and strategic reasoning.
Categorical Logic And Type Theory
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Author : Bart Jacobs
language : en
Publisher: Elsevier Science & Technology
Release Date : 1999
Categorical Logic And Type Theory written by Bart Jacobs and has been published by Elsevier Science & Technology this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.
Computational Logic
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Author : Dov M. Gabbay
language : en
Publisher: Newnes
Release Date : 2014-12-09
Computational Logic written by Dov M. Gabbay and has been published by Newnes this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-09 with Mathematics categories.
Handbook of the History of Logic brings to the development of logic the best in modern techniques of historical and interpretative scholarship. Computational logic was born in the twentieth century and evolved in close symbiosis with the advent of the first electronic computers and the growing importance of computer science, informatics and artificial intelligence. With more than ten thousand people working in research and development of logic and logic-related methods, with several dozen international conferences and several times as many workshops addressing the growing richness and diversity of the field, and with the foundational role and importance these methods now assume in mathematics, computer science, artificial intelligence, cognitive science, linguistics, law and many engineering fields where logic-related techniques are used inter alia to state and settle correctness issues, the field has diversified in ways that even the pure logicians working in the early decades of the twentieth century could have hardly anticipated. Logical calculi, which capture an important aspect of human thought, are now amenable to investigation with mathematical rigour and computational support and fertilized the early dreams of mechanised reasoning: "Calculemus. The Dartmouth Conference in 1956 – generally considered as the birthplace of artificial intelligence – raised explicitly the hopes for the new possibilities that the advent of electronic computing machinery offered: logical statements could now be executed on a machine with all the far-reaching consequences that ultimately led to logic programming, deduction systems for mathematics and engineering, logical design and verification of computer software and hardware, deductive databases and software synthesis as well as logical techniques for analysis in the field of mechanical engineering. This volume covers some of the main subareas of computational logic and its applications. - Chapters by leading authorities in the field - Provides a forum where philosophers and scientists interact - Comprehensive reference source on the history of logic
Automated Deduction Cade 22
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Author : Renate Schmidt
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-07-26
Automated Deduction Cade 22 written by Renate Schmidt 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 2009-07-26 with Computers categories.
This book constitutes the refereed proceedings of the 22nd International Conference on Automated Deduction, CADE-22, held in Montreal, Canada, in August 2009. The 27 revised full papers and 5 system descriptions presented were carefully reviewed and selected from 77 submissions. Furthermore, three invited lectures by distinguished experts in the area were included. The papers are organized in topical sections on combinations and extensions, minimal unsatisfiability and automated reasoning support, system descriptions, interpolation and predicate abstraction, resolution-based systems for non-classical logics, termination analysis and constraint solving, rewriting, termination and productivity, models, modal tableaux with global caching, arithmetic.
Categorical Logic And Type Theory
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Author : B. Jacobs
language : en
Publisher: Gulf Professional Publishing
Release Date : 2001-05-10
Categorical Logic And Type Theory written by B. Jacobs and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-10 with Computers categories.
This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.
Simple Type Theory
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Author : William Michael Farmer
language : en
Publisher:
Release Date : 2023
Simple Type Theory written by William Michael Farmer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Computer science categories.