Theory path orderings

Stuber, Jürgen

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Theory path orderings

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Stuber, Jürgen
Programming Logics, MPI for Informatics, Max Planck Society;

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Citation

Stuber, J. (1999). Theory path orderings. In P. Narendran, & M. Rusinowitch (Eds.), Proceedings of the 10th International Conference on Rewriting Techniques and Applications (RTA-99) (pp. 148-162). Berlin, Germany: Springer.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-36A3-5

Abstract

We introduce the notion of a theory path ordering~(TPO), which simplifies the construction of term orderings for superposition theorem proving in algebraic theories. To achieve refutational completeness of such calculi we need total, $E$-compatible and $E$-antisymmetric simplification quasi-orderings. The construction of a TPO takes as its ingredients a status function for interpreted function symbols and a precedence that makes the interpreted function symbols minimal. The properties of the ordering then follow from related properties of the status function. Theory path orderings generalize associative path orderings.