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Combining Non-Stably Infinite Theories
Journal article   Open access

Combining Non-Stably Infinite Theories

Cesare Tinelli and Calogero G Zarba
Electronic notes in theoretical computer science, Vol.86(1), pp.35-48
05/2003
DOI: 10.1016/S1571-0661(04)80651-0
url
https://doi.org/10.1016/S1571-0661(04)80651-0View
Published (Version of record) Open Access

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. 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 provide a new combination method that can combine any theory that is not stably infinite with another theory, provided that the latter is what we call a shiny theory. Examples of shiny theories include the theory of equality, the theory of partial orders, and the theory of total orders. An interesting consequence of our results is that any decision procedure for the satisfiability of quantifier-free Σ-formulae in a Σ-theory T can always be extended to accept inputs over an arbitrary signature Ω ⊇ Σ.

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