Paramodulation with Non-Monotonic Orderings and Simplification

• Published in: Journal of automated reasoning Vol. 50; no. 1; pp. 51 - 98
• Main Authors: Bofill, Miquel, Rubio, Albert
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 2013; Springer; Springer Nature B.V
• Subjects: Applied sciences; Artificial Intelligence; Computer Science; Computer science; control theory; systems; Exact sciences and technology; Language theory and syntactical analysis; Logic and foundations; Logical, boolean and switching functions; Mathematical Logic and Formal Languages; Mathematical Logic and Foundations; Mathematical logic, foundations, set theory; Mathematics; Proof theory and constructive mathematics; Sciences and techniques of general use; Symbolic and Algebraic Manipulation; Theoretical computing; Ordered paramodulation; Equational reasoning; Automated theorem proving; Knuth-Bendix completion; Knuth Bendix; Redundancy; Elimination; Rewriting; Automatic proving; Logical programming; Modeling; Equational theory; Theorem proving; Edge effect; Completeness; Ordering; Proof theory; Compatibility; Rewriting systems; Demodulation
• ISSN: 0168-7433; 1573-0670
• DOI: 10.1007/s10817-011-9244-z

Ordered paramodulation and Knuth-Bendix completion are known to remain complete when using non-monotonic orderings. However, these results do not imply the compatibility of the calculus with essential redundancy elimination techniques such as demodulation, i.e., simplification by rewriting, which constitute the primary mode of computation in most successful automated theorem provers. In this paper we present a complete ordered paramodulation calculus for non-monotonic orderings which is compatible with powerful redundancy notions including demodulation, hence strictly improving the previous results and making the calculus more likely to be used in practice. As a side effect, we obtain a Knuth-Bendix completion procedure compatible with simplification techniques, which can be used for finding, whenever it exists, a convergent term rewrite system for a given set of equations and a (possibly non-totalizable) reduction ordering.