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Combining Nonstably Infinite Theories

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Abstract

The Nelson–Oppen combination method combines decision procedures for first-order theories over disjoint signatures into a single decision procedure for the union theory. In order to be correct, the method requires that the component theories be stably infinite. This restriction makes the method inapplicable to many interesting theories such as, for instance, theories having only finite models.

In this paper, we describe two extensions of the Nelson–Oppen method that address the problem of combining theories that are not stably infinite. In our extensions, the component decision procedures exchange not only equalities between shared variables but also certain cardinality constraints.

Applications of our results include the combination of theories having only finite models, as well as the combination of nonstably infinite theories with the theory of equality, the theories of total and partial orders, and the theory of lattices with maximum and minimum.

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Authors and Affiliations

  1. Department of Computer Science, The University of Iowa, 14 MacLean Hall, Iowa City, IA, 52242, USA

    Cesare Tinelli

  2. Department of Computer Science, University of New Mexico, MSC01 1130, Albuquerque, NM, 87131, USA

    Calogero G. Zarba

Authors
  1. Cesare Tinelli
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  2. Calogero G. Zarba
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Correspondence to Cesare Tinelli.

Additional information

Calogero G. Zarba: Work done by this author at Stanford University and later at LORIA and INRIA-Lorraine.

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Tinelli, C., Zarba, C.G. Combining Nonstably Infinite Theories. J Autom Reasoning 34, 209–238 (2005). https://doi.org/10.1007/s10817-005-5204-9

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