Herein we close the question of the equivalence of shiny and strongly polite theories by establishing that, for theories with a decidable quantifier-free satisfiability problem, the set of many-sorted shiny theories coincides with the set of many-sorted strongly polite theories. Capitalizing on this equivalence, we obtain a Nelson–Oppen combination theorem for many-sorted shiny theories.
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We would like to thank the anonymous reviewers for their helpful comments. This work was partially supported by Fundação para a Ciência e a Tecnologia by way of Grant UID/MAT/04561/2013 to Centro de Matemática, Aplicações Fundamentais e Investigação Operacional of Universidade de Lisboa (CMAF-CIO). Furthermore, FC acknowledges the support from the DP-PMI and FCT (Portugal) through scholarship SRFH/BD/52243/2013.
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Casal, F., Rasga, J. Many-Sorted Equivalence of Shiny and Strongly Polite Theories. J Autom Reasoning 60, 221–236 (2018). https://doi.org/10.1007/s10817-017-9411-y
- Nelson–Oppen method
- Combination of satisfiability procedures
- Shiny theories
- Polite theories
- Strongly polite theories
- First-order logic
- Many-sorted logic