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Commemorating the 50th anniversary of the first time a mathematical theorem was proven by a computer system, Freek Wiedijk initiated the present book in 2004 by inviting formalizations of a proof of the irrationality of the square root of two from scientists using various theorem proving systems. The 17 systems included in this volume are among the most relevant ones for the formalization of mathematics. The systems are showcased by presentation of the formalized proof and a description in the form of answers to a standard questionnaire. The 17 systems presented are HOL, Mizar, PVS, Coq, Otter/Ivy, Isabelle/Isar, Alfa/Agda, ACL2, PhoX, IMPS, Metamath, Theorema, Leog, Nuprl, Omega, B method, and Minlog.

Proof theory --- Algebra --- Algèbre --- Data processing. --- Computer programs. --- Logiciels --- Computer programs --- Computer Science --- Mechanical Engineering - General --- Engineering & Applied Sciences --- Mathematics --- Mechanical Engineering --- Physical Sciences & Mathematics --- Information Technology --- Artificial Intelligence --- Computer science. --- Software engineering. --- Mathematical logic. --- Artificial intelligence. --- Computer Science. --- Artificial Intelligence (incl. Robotics). --- Software Engineering. --- Mathematical Logic and Formal Languages. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Computer software engineering --- Engineering --- Informatics --- Science --- Artificial Intelligence. --- Proof theory - Data processing --- Algebra - Computer programs

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The database industry is clearly a multi-billion, world-wide, all-encompassing part of the software world. This is part thanks to the standardization of query languages in the form of SQL. And yet, it is well known that SQL has significant shortcomings. Quantifiers in Action: Generalized Quantification in Query, Logical and Natural Languages analyzes one of those shortcomings, the way in which quantification is dealt with in SQL. It is well known that most query languages are simply versions of First Order Logic (FOL). GQs are an extension of the idea of quantifier in FOL. Hence, GQs can be a meaningful extension of the treatment of quantification in query languages. Even though studied within the theoretical community up until now, GQs can be successfully applied, and are a perfect example of a practical theory within databases. This book provides a brief background in logic and introduces the concept of GQs, and then develops a query language based on GQs, called QLGQ. Using QLGQ, the reader explores the efficient implementation of the concept, always a primary consideration in databases. This professional book also includes several extensions, for use with documents employing question and answer techniques. Quantifiers in Action: Generalized Quantification in Query, Logical and Natural Languages is the result of several years of research funded by NSF through a CAREER Award. It is designed for practitioners and researchers that work within the database management field. This volume is also suitable for graduate-level students in computer science.

Categories (Mathematics). --- Categories (Mathematics) --- Engineering & Applied Sciences --- Mathematics --- Algebra --- Mathematical Theory --- Computer Science --- Physical Sciences & Mathematics --- Category theory (Mathematics) --- Computer science. --- Computer communication systems. --- Programming languages (Electronic computers). --- Database management. --- Information storage and retrieval. --- Computer Science. --- Database Management. --- Programming Languages, Compilers, Interpreters. --- Information Storage and Retrieval. --- Information Systems Applications (incl. Internet). --- Computer Communication Networks. --- Ordered algebraic structures --- Sheaf theory --- Congresses. --- Congresses --- Information storage and retrieva. --- Data base management --- Data services (Database management) --- Database management services --- DBMS (Computer science) --- Generalized data management systems --- Services, Database management --- Systems, Database management --- Systems, Generalized database management --- Electronic data processing --- Informatics --- Science --- Information storage and retrieval systems. --- Automatic data storage --- Automatic information retrieval --- Automation in documentation --- Computer-based information systems --- Data processing systems --- Data storage and retrieval systems --- Discovery systems, Information --- Information discovery systems --- Information processing systems --- Information retrieval systems --- Machine data storage and retrieval --- Mechanized information storage and retrieval systems --- Computer systems --- Electronic information resources --- Data libraries --- Digital libraries --- Information organization --- Information retrieval --- Algèbre homologique --- Topologie algébrique --- Algebraic topology --- Algebra, Homological --- Application software. --- Communication systems, Computer --- Computer communication systems --- Data networks, Computer --- ECNs (Electronic communication networks) --- Electronic communication networks --- Networks, Computer --- Teleprocessing networks --- Data transmission systems --- Digital communications --- Electronic systems --- Information networks --- Telecommunication --- Cyberinfrastructure --- Network computers --- Application computer programs --- Application computer software --- Applications software --- Apps (Computer software) --- Computer software --- Computer languages --- Computer program languages --- Computer programming languages --- Machine language --- Languages, Artificial --- Distributed processing --- Analyse fonctionnelle --- Functional analysis --- Algèbre homologique. --- Topologie algébrique. --- Algèbre homologique --- Topologie algébrique --- Algebraic topology. --- Algebra, Homological. --- Catégories (mathématiques) --- Functional analysis. --- Geometrie algebrique --- Cohomologie --- Programming languages (Electronic computers) --- Computer networks.