Lecture 32: Ordering

The use of orders to eliminate redundancy is critical in theorem proving, particularly when equality is present. We introduce various properties we would like orders to have an introduce the lexicographic path ordering which is based on a precedence among function symbols and constants.

Reading

• Pages 9-12 of the draft chapter Paramodulation-Based Theorem Proving of the Handbook of Automated Reasoning by R. Nieuwenhuis and A. Rubio.

Key Concepts

• Stable order
• Monotonic order
• Subterm property
• Rewrite ordering
• Reduction order
• Simplification order
• Lexicographic path order

Links

• Previous lecture: Residuating Equality Constraints
• Next lecture: Ground Superposition