Higher-Order Logic and Disquotational Truth

Disquotational Truth and Analyticity

The uniform reflection principle for the theory of uniform T-sentences is added to PA. The resulting system is justified on the basis of a disquotationalist theory of truth where the provability predicate is conceived as a special kind of analyticity. The system is equivalent to the system ACA of arithmetical comprehension. If the truth predicate is also allowed to occur in the sentences that a...

Executing Higher Order Logic

We report on the design of a prototyping component for the theorem prover Isabelle/HOL. Specifications consisting of datatypes, recursive functions and inductive definitions are compiled into a functional program. Functions and inductively defined relations can be mixed. Inductive definitions must be such that they can be executed in Prolog style but requiring only matching rather than unificat...

Higher-Order Logic Programming

Higher-Order Computational Logic

This paper presents the case for the use of higher-order logic as a foundation for computational logic. A suitable polymorphicallytyped, higher-order logic is introduced and its syntax and proof theory briefly described. In addition, a metric space of closed terms suitable for knowledge representation purposes is presented. The approach to representing individuals is illustrated with some examp...

Higher order logic