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Relation algebras are algebras arising from the study of binary relations.They form a part of the field of algebraic logic, and have applications in proof theory, modal logic, and computer science. This research text uses combinatorial games to study the fundamental notion of representations of relation algebras. Games allow an intuitive and appealing approach to the subject, and permit substantial advances to be made. The book contains many new results and proofs not published elsewhere. It should be invaluable to graduate students and researchers interested in relation algebras and g

Mathematical logic --- Relation algebras. --- Game theory. --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Algebra of relations --- Algebras, Relation --- Relational algebras --- Relations, Algebra of --- Algebraic logic

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This monograph details several different methods for constructing simple relation algebras, many of which are new with this book. By drawing these seemingly different methods together, all are shown to be aspects of one general approach, for which several applications are given. These tools for constructing and analyzing relation algebras are of particular interest to mathematicians working in logic, algebraic logic, or universal algebra, but will also appeal to philosophers and theoretical computer scientists working in fields that use mathematics. The book is written with a broad audience in mind and features a careful, pedagogical approach; an appendix contains the requisite background material in relation algebras. Over 400 exercises provide ample opportunities to engage with the material, making this a monograph equally appropriate for use in a special topics course or for independent study. Readers interested in pursuing an extended background study of relation algebras will find a comprehensive treatment in author Steven Givant’s textbook, Introduction to Relation Algebras (Springer, 2017).

Relation algebras. --- Algebraic logic. --- Algebra of relations --- Algebras, Relation --- Relational algebras --- Relations, Algebra of --- Mathematics. --- Algebra. --- Mathematical logic. --- Mathematical Logic and Foundations. --- Logic, Symbolic and mathematical --- Algebraic logic --- Logic, Symbolic and mathematical. --- Mathematics --- Mathematical analysis --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism

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This volume contains the proceedings of the 7th International Seminar on - lational Methods in Computer Science (RelMiCS 7) and the 2nd International Workshop onApplications ofKleeneAlgebra.Thecommonmeetingtookplacein Bad Malente (near Kiel), Germany,from May May 12–17,2003.Its purpose was to bring together researchers from various subdisciplines of Computer Science, Mathematics and related ?elds who use the calculi of relations and/or Kleene algebra as methodological and conceptual tools in their work. This meeting is the joint continuation of two di?erent series of meetings. Previous RelMiCS seminars were held in Schloss Dagstuhl (Germany) in J- uary 1994, Parati (Brazil) in July 1995, Hammamet (Tunisia) in January 1997, Warsaw (Poland) in September 1998, Quebec (Canada) in January 2000, and Oisterwijk (The Netherlands) in October 2001. The ?rst workshop on appli- tions of Kleene algebra was also held in Schloss Dagstuhl in February 2001. To join these two events in a common meeting was mainly motivated by the s- stantialcommoninterestsandoverlapofthetwocommunities.Wehopethatthis leads to fruitful interactions and opens new and interesting research directions.

Algebraic logic --- Relation algebras --- Symbolic and Algebraic Manipulation. --- Algebra of relations --- Algebras, Relation --- Relational algebras --- Relations, Algebra of --- Mathematics. --- Software engineering. --- Computer logic. --- Mathematical logic. --- Computer science --- Artificial intelligence. --- Number theory. --- Number Theory. --- Mathematical Logic and Formal Languages. --- Software Engineering. --- Logics and Meanings of Programs. --- Artificial Intelligence (incl. Robotics). --- Logic, Symbolic and mathematical --- Computer science. --- Logic design. --- Algebra --- Artificial Intelligence. --- Data processing. --- 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 --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Switching theory --- Computer software engineering --- Engineering --- Informatics --- Science --- Number study --- Numbers, Theory of --- Computer science—Mathematics. --- Computer science logic --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Algebraic logic - Congresses --- Relation algebras - Congresses

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This book constitutes the proceedings of the 19th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2021, which took place in Marseille, France, during November 2-5, 2021. The 29 papers presented in this book were carefully reviewed and selected from 35 submissions. They deal with the development and dissemination of relation algebras, Kleene algebras, and similar algebraic formalisms. Topics covered range from mathematical foundations to applications as conceptual and methodological tools in computer science and beyond. .

Lògica algebraica --- Informàtica --- Enginyeria --- Càlcul intensiu (Informàtica) --- Disseny de sistemes --- Història de la informàtica --- Geometria computacional --- Informàtica tova --- Processament de dades --- Programació (Ordinadors) --- Sistemes informàtics --- Teledocumentació --- Tractament del llenguatge natural (Informàtica) --- Automatització d'arxius --- Automatització de biblioteques --- Automatització de museus --- Indústria informàtica --- Teoria de la informació --- Lògica algèbrica --- Lògica matemàtica --- Àlgebra de Boole --- Computer science --- Algebraic logic --- Relation algebras --- Mathematics --- Algebra of relations --- Algebras, Relation --- Relational algebras --- Relations, Algebra of --- Logic, Symbolic and mathematical --- Logic programming. --- Computer science—Mathematics. --- Computer science. --- Mathematical logic. --- Logic in AI. --- Mathematics of Computing. --- Theory of Computation. --- Mathematical Logic and Foundations. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Informatics --- Science --- Computer programming

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This book constitutes the proceedings of the 12 International Conference on Relational and Algebraic Methods in Computer Science, RAMICS 2011, held in Rotterdam, The Netherlands, in May/June 2011. This conference merges the RelMICS (Relational Methods in Computer Science) and AKA (Applications of Kleene Algebra) conferences, which have been a main forum for researchers who use the calculus of relations and similar algebraic formalisms as methodological and conceptual tools.  Relational and algebraic methods and software tools turn out to be useful for solving problems in social choice and game theory. For that reason this conference included a special track on Computational Social Choice and Social Software. The 18 papers included were carefully reviewed and selected from 27 submissions. In addition the volume contains 2 invited tutorials and 5 invited talks.

Computer science --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Computer Science --- Mathematical Theory --- Relation algebras --- Algebra of relations --- Algebras, Relation --- Relational algebras --- Relations, Algebra of --- Computer science. --- Software engineering. --- Computer logic. --- Mathematical logic. --- Artificial intelligence. --- Computer simulation. --- Computer Science. --- Mathematical Logic and Formal Languages. --- Symbolic and Algebraic Manipulation. --- Logics and Meanings of Programs. --- Software Engineering. --- Simulation and Modeling. --- Artificial Intelligence (incl. Robotics). --- Mathematics. --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- 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 --- Fifth generation computers --- Neural computers --- Computer mathematics --- Discrete mathematics --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Computer science logic --- Logic, Symbolic and mathematical --- Computer software engineering --- Engineering --- Informatics --- Science --- Algebraic logic --- Algebra --- Logic design. --- Artificial Intelligence. --- Data processing. --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Switching theory --- Computer science—Mathematics. --- Machine theory. --- Formal Languages and Automata Theory. --- Computer Science Logic and Foundations of Programming. --- Computer Modelling. --- Abstract automata --- Abstract machines --- Automata --- Mathematical machine theory --- Algorithms --- Recursive functions --- Robotics