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Conference Paper

Superposition and Chaining for Totally Ordered Divisible Abelian Groups (Extended Abstract)

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Waldmann,  Uwe       
Automation of Logic, MPI for Informatics, Max Planck Society;
Programming Logics, MPI for Informatics, Max Planck Society;

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Citation

Waldmann, U. (2001). Superposition and Chaining for Totally Ordered Divisible Abelian Groups (Extended Abstract). In R. Goré, A. Leitsch, & T. Nipkow (Eds.), Automated reasoning: First International Joint Conference, IJCAR 2001 (pp. 226-241). Berlin, Germany: Springer.


Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-3249-2
Abstract
We present a calculus for first-order theorem proving in the presence of the axioms of totally ordered divisible abelian groups. The calculus extends previous superposition or chaining calculi for divisible torsion-free abelian groups and dense total orderings without endpoints. As its predecessors, it is refutationally complete and requires neither explicit inferences with the theory axioms nor variable overlaps. It offers thus an efficient way of treating equalities and inequalities between additive terms over, e.g., the rational numbers within a first-order theorem prover.