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Ordered chaining calculi for first-order theories of transitive relations

Authors:

Harald GanzingerAuthors Info & Claims

Journal of the ACM (JACM), Volume 45, Issue 6

Pages 1007 - 1049

https://doi.org/10.1145/293347.293352

Published: 01 November 1998 Publication History

Abstract

We propose inference systems for binary relations that satisfy composition laws such as transitivity. Our inference mechanisms are based on standard techniques from term rewriting and represent a refinement of chaining methods as they are used in the context of resolution-type theorem proving. We establish the refutational completeness of these calculi and prove that our methods are compatible with the usual simplification techniques employed in refutational theorem provers, such as subsumption or tautology deletion. Various optimizations of the basic chaining calculus will be discussed for theories with equality and for total orderings. A key to the practicality of chaining methods is the extent to which so-called variable chaining can be avoided. We demonstrate that rewrite techniques considerably restrict variable chaining and that further restrictions are possible if the transitive relation under consideration satisfies additional properties, such as symmetry. But we also show that variable chaining cannot be completely avoided in general.

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Index Terms

Ordered chaining calculi for first-order theories of transitive relations
1. Computing methodologies
2. Theory of computation

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Publication History

Published: 01 November 1998

Published in JACM Volume 45, Issue 6

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Korovin KKovács LReger GSchoisswohl JVoronkov A(2023)ALASCA: Reasoning in Quantified Linear ArithmeticTools and Algorithms for the Construction and Analysis of Systems10.1007/978-3-031-30823-9_33(647-665)Online publication date: 22-Apr-2023
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https://dl.acm.org/doi/10.1007/s10817-021-09605-z
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