Dual Tableaux Foundations, Methodology, Case Studies [Paperback]

This book presents logical foundations of dual tableaux together with a number of their applications both to logics traditionally dealt with in mathematics and philosophy (such as modal, intuitionistic, relevant, and many-valued logics) and to various applied theories of computational logic (such as temporal reasoning, spatial reasoning, fuzzy-set-based reasoning, rough-set-based reasoning, order-of magnitude reasoning, reasoning about programs, threshold logics, logics of conditional decisions). The distinguishing feature of most of these applications is that the corresponding dual tableaux are built in a relational language which provides useful means of presentation of the theories. In this way modularity of dual tableaux is ensured. We do not need to develop and implement each dual tableau from scratch, we should only extend the relational core common to many theories with the rules specific for a particular theory.Providing a reference for researchers and students, this volume presents the fundamental concepts of dual tableaux, and a wide scope of applications. These include logic methods used in mathematics and philosophy, as well as applied theories of computational logic.1. Dual Tableau for Classical First-Order Logic.- 2. Dual Tableaux for Logics of Classical Algebras of Binary.- 3. Theories of Point Relations and Relational Model Checking .- 4. Dual Tableaux for Peirce Algebras.- 5. Dual Tableaux for Fork Algebras .- 6. Dual Tableaux for Relational Databases .- Part III. Relational Reasoning in Traditional Non-classical Logics.- 7. Dual Tableaux for Classical Modal Logics.- 8. Dual Tableaux for Some Logics Based on Intuitionism.- 9. Dual Tableaux for Relevant Logics.- 10. Dual Tableaux for Many-valued Logics.- Part IV. Relational Reasoning in Logics of Information and Data.- Analysis.- 11. Dual Tableaux for Information Logics of Plain Frames .- 12. Dual Tableaux for Information Logics of Relative Frames.- 13. Dual Tableau for Formal Concept Analysis.- 14. l3*