Progress in the Development of Automated Theorem Proving for Higher-Order Logic
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Terminating Tableaux for the Basic Fragment of Simple Type Theory
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Analytic Tableaux for Higher-Order Logic with Choice
Journal of Automated Reasoning
Combining and automating classical and non-classical logics in classical higher-order logics
Annals of Mathematics and Artificial Intelligence
Higher-order aspects and context in SUMO
Web Semantics: Science, Services and Agents on the World Wide Web
Formal probabilistic analysis of cyber-physical transportation systems
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part III
Formal verification of cyber-physical systems: coping with continuous elements
ICCSA'13 Proceedings of the 13th international conference on Computational Science and Its Applications - Volume 1
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Many mathematical and computational concepts can be represented in a natural way using higher-order logic. Consequently, higher-order logic has become an important topic of research. /Automated Reasoning in Higher-Order Logic/ presents both a theoretical analysis of fragments of higher-order logic as well as a complete automated search procedure for an extensional form of higher-order logic. The first part of the book provides a detailed presentation of the theory (syntax and semantics) of fragments of higher-order logic. The fragments differ in the amount of extensionality and set comprehension principles included. Three families of sequent calculi are defined and proven sound and complete with respect to appropriate model classes. Using the model constructions in the book, different versions of Cantor's theorem are determined to not be provable in certain fragments. In fact, some versions of Cantor's theorem are independent of other versions (in sufficiently weak fragments). In the second part of the book, an automated proof procedure for extensional type theory is described. Proving completeness of such a higher-order search procedure is a nontrivial task. The book provides such a completeness proof by first proving completeness of the ground case and then proving appropriate lifting results. /Automated Reasoning in Higher-Order Logic/ is an essential document for researchers in higher-order logic and higher-order theorem proving. The book is also essential reading for programmers implementing or extending higher-order search procedures. Users of higher-order theorem provers can use the book to improve their understanding of the underlying logical systems.