Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
An introduction to mathematical logic and type theory: to truth through proof
An introduction to mathematical logic and type theory: to truth through proof
The clausal theory of types
Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Solving the multiple instance problem with axis-parallel rectangles
Artificial Intelligence
Machine Learning
Classification of Individuals with Complex Structure
ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning
Learning comprehensible theories from structured data
Advanced lectures on machine learning
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This paper presents a case for the use of higher-order logic as a foundation for computational logic. A suitable polymorphically-typed, 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 examples, as is the technique of programming with abstractions. The paper concludes by placing the results in the wider context of previous and current research in the use of higher-order logic in computational logic.