Independence in higher-order subclassical logic.

Higher Order Independence in Matroids

One may regard vectors in a finite dimensional vector space as being linear forms in a polynomial ring in an obvious way. A collection of linear forms satisfying various linear dependence relations can become independent when each of the forms is raised to the k-th power. In this paper we prove that a certain class of matroids satisfies a " higher order " independence property of this kind. The...

Axiomatizing first-order consequences in independence logic

Independence logic, introduced in [5], cannot be effectively axiomatized. However, first-order consequences of independence logic sentences can be axiomatized. In this article we give an explicit axiomatization and prove that it is complete in this sense. The proof is a generalization of the similar result for dependence logic introduced in [8].

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...