A universal magnification theorem for higher-order caustic singularities

Universal Higher Order Grammar

We examine the class of languages that can be defined entirely in terms of provability in an extension of the sorted type theory (Tyn) by embedding the logic of phonologies, without introduction of special types for syntactic entities. This class is proven to precisely coincide with the class of logically closed languages that may be thought of as functions from expressions to sets of logically...

Higher - Order Automated Theorem Proving for NaturalLanguage

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 uniication (HOU). This extended form of HOU is used to compute the licensing conditions for corrections.

Higher-Order Automated Theorem Proving

The history of building automated theorem provers for higher-order logic is almost as old as the field of deduction systems itself. The first successful attempts to mechanize and implement higher-order logic were those of Huet [13] and Jensen and Pietrzykowski [17]. They combine the resolution principle for higher-order logic (first studied in [1]) with higher-order unification. The unification...

Higher-Order Automated Theorem Provers

Agent-based Blackboard Architecture for a Higher-Order Theorem Prover

The automated theorem prover Leo was one of the first systems able to prove theorems in higher-order logic. Since the first version of Leo many other systems emerged and outperformed Leo and its successor Leo-II. The Leo-III project’s aim is to develop a new prover reclaiming the lead in the area of higher-order theorem proving. Current competitive theorem provers sequentially manipulate sets o...