Dual Tableaux: Foundations Methodology Case Studies The 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. 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. Dual Tableau for a Fuzzy Logic 15. Dual Tableaux for Logics of Order of Magnitude Reasoning Part V. Relational Reasoning about Time Space and Action 16. Dual Tableaux for Temporal Logics 17. Dual Tableaux for Interval Temporal Logics 18. Dual Tableaux for Spatial Reasoning 19. Dual Tableaux for Logics of Programs Part VI. Beyond Relational Theories 20. Dual Tableaux for Threshold Logics 21. Signed Dual Tableau for G¨odel Dummett Logic 22. Dual Tableaux for First Order Post Logics 23. Dual Tableau for Propositional Logic with Identity 24. Dual Tableaux for Logics of Conditional Decisions 25. Methodological Principles of Dual Tableaux References Index.