Dual Tableaux: Foundations, Methodology, Case Studies Foundations, Methodology, Case Studies

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.

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.