Abstract
We present a way to build-in the linear order theory into the connection method. The approach is an instance of the method developed by U. Petermann for building-in open theories into connection calculi. Connections with linear ordering as background theory are characterized and called cyclic connections. A query language Q and a complete set of such connections with respect to Q are defined and the associated unification problem is proved to be a simultaneous rigid E-unification problem. Although this problem is undecidable, we recall how methods like the equational matings method of J. Gallier et al. or the present cyclic connections method can be used owing to an enumeration procedure of rigid E-unifiers due to B. Beckert.
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Becher, G. (1996). Cyclic connections. In: Miglioli, P., Moscato, U., Mundici, D., Ornaghi, M. (eds) Theorem Proving with Analytic Tableaux and Related Methods. TABLEAUX 1996. Lecture Notes in Computer Science, vol 1071. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61208-4_6
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DOI: https://doi.org/10.1007/3-540-61208-4_6
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