Dual Tableaux: Foundations, Methodology, Case Studies

Description

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. Front Matter....Pages i-xvi Front Matter....Pages 1-1 Dual Tableau for Classical First-Order Logic....Pages 3-31 Dual Tableaux for Logics of Classical Algebras of Binary Relations....Pages 33-67 Theories of Point Relations and Relational Model Checking....Pages 69-82 Front Matter....Pages 83-83 Dual Tableaux for Peirce Algebras....Pages 85-103 Dual Tableaux for Fork Algebras....Pages 105-120 Dual Tableaux for Relational Databases....Pages 121-139 Front Matter....Pages 141-141 Dual Tableaux for Classical Modal Logics....Pages 143-160 Dual Tableaux for Some Logics Based on Intuitionism....Pages 161-176 Dual Tableaux for Relevant Logics....Pages 177-194 Dual Tableaux for Many-Valued Logics....Pages 195-213 Front Matter....Pages 215-215 Dual Tableaux for Information Logics of Plain Frames....Pages 217-235 Dual Tableaux for Information Logics of Relative Frames....Pages 237-249 Dual Tableau for Formal Concept Analysis....Pages 251-261 Dual Tableau for a Fuzzy Logic....Pages 263-275 Dual Tableaux for Logics of Order of Magnitude Reasoning....Pages 277-287 Front Matter....Pages 289-289 Dual Tableaux for Temporal Logics....Pages 291-313 Dual Tableaux for Interval Temporal Logics....Pages 315-327 Dual Tableaux for Spatial Reasoning....Pages 329-358 Dual Tableaux for Logics of Programs....Pages 359-382 Front Matter....Pages 383-383 Dual Tableaux for Threshold Logics....Pages 385-396 Front Matter....Pages 383-383 Signed Dual Tableau for Gödel–Dummett Logic....Pages 397-406 Dual Tableaux for First-Order Post Logics....Pages 407-416 Dual Tableau for Propositional Logic with Identity....Pages 417-431 Dual Tableaux for Logics of Conditional Decisions....Pages 433-452 Front Matter....Pages 453-453 Methodological Principles of Dual Tableaux....Pages 455-493 Back Matter....Pages 495-523