An introduction to mathematical logic and type theory: to truth through proof
An introduction to mathematical logic and type theory: to truth through proof
The clausal theory of types
Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
Extensional Higher-Order Resolution
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
Constrained resolution: a complete method for higher-order logic.
Constrained resolution: a complete method for higher-order logic.
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
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
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This paper presents two approaches to primitive equality treatment in higher-order (HO) automated theorem proving: a calculus EP adapting traditional first-order (FO) paramodulation [RW69], and a calculus ERUE adapting FO RUE-Resolution [Dig79] to classical type theory, i.e., HO logic based on Church's simply typed λ-calculus. EP and ERUE extend the extensional HO resolution approach ER [BK98a]. In order to reach Henkin completeness without the need for additional extensionality axioms both calculi employ new, positive extensionality rules analogously to the respective negative ones provided by ER that operate on unification constraints. As the extensionality rules have an intrinsic and unavoidable difference-reducing character the HO paramodulation approach loses its pure term-rewriting character. On the other hand examples demonstrate that the extensionality rules harmonise quite well with the difference-reducing HO RUE-resolution idea.