Many-Sorted Equivalence of Shiny and Strongly Polite Theories

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Abstract

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.

Keywords

Nelson–Oppen method Combination of satisfiability procedures Shiny theories Polite theories Strongly polite theories First-order logic Many-sorted logic 

Notes

Acknowledgements

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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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Dep. Matemática, Instituto Superior TécnicoU LisboaLisbonPortugal
  2. 2.Centro de Matemática, Aplicações Fundamentais e Investigação Operacional (CMAF-CIO)U LisboaLisbonPortugal

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