Affiliation:
1. University of Athens
2. University of Victoria
Abstract
We propose a purely extensional semantics for higher-order logic programming. In this semantics program predicates denote sets of ordered tuples, and two predicates are equal iff they are equal as sets. Moreover, every program has a unique minimum Herbrand model which is the greatest lower bound of all Herbrand models of the program and the least fixed-point of an immediate consequence operator. We also propose an SLD-resolution proof system which is proven sound and complete with respect to the minimum Herbrand model semantics. In other words, we provide a purely extensional theoretical framework for higher-order logic programming which generalizes the familiar theory of classical (first-order) logic programming.
Funder
Greek national funds
Operational Program Education and Lifelong Learning of the National Strategic Reference Framework (NSRF) - Research Funding Program: Heracleitus II
European Social Fund
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science
Reference27 articles.
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2. Studies in logic and the foundations of mathematics series;Barendregt H. P.
3. Higher-order semantics and extensionality
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