Higher - Order Automated Theorem Proving for NaturalLanguage

Automated Higher-order Reasoning in Quantales

We present an approach to bring reasoning in quantales into the realm of automated theorem proving. We use the TPTP Problem Library for this purpose which by a recent approach now integrates fully automated higher-order theorem provers. In particular, we give an encoding of quantales in the new typed higher-order form and show how to prove theorems about quantales fully automatically.

Higher-Order Automated Theorem Proving for Natural Language Semantics

This paper describes a tableau-based higher-order theorem prover Hot and an application to natural language semantics. In this application, Hot is used to prove equivalences using world knowledge during higher-order unii-cation (HOU). This extended form of HOU is used to compute the licensing conditions for corrections.

Automated Theorem Proving in First-Order Logic Modulo: On the Difference between Type Theory and Set Theory

Resolution modulo is a first-order theorem proving method that can be applied both to first-order presentations of simple type theory (also called higher-order logic) and to set theory. When it is applied to some first-order presentations of type theory, it simulates exactly higherorder resolution. In this note, we compare how it behaves on type theory and on set theory. Higher-order theorem pr...

Higher-Order Automated Theorem Provers

Comparing Approaches To Resolution Based Higher-Order Theorem Proving

We investigate several approaches to resolution based automated theorem proving in classical higher-order logic (based on Church’s simply typed λ-calculus) and discuss their requirements with respect to Henkin completeness and full extensionality. In particular we focus on Andrews’ higher-order resolution (Andrews 1971), Huet’s constrained resolution (Huet 1972), higher-order E-resolution, and ...