CERES in higher-order logic

CERES in higher-order logic

We define a generalization CERES of the first-order cut-elimination method CERES to higher-order logic. At the core of CERES lies the computation of an (unsatisfiable) set of sequents CS(π) (the characteristic sequent set) from a proof π of a sequent S. A refutation of CS(π) in a higher-order resolution calculus can be used to transform cut-free parts of π (the proof projections) into a cut-fre...

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