Being Polite Is Not Enough (and Other Limits of Theory Combination)

Guilherme V. Toledo; Benjamin Przybocki; Yoni Zohar

doi:10.1007/978-3-031-99984-0_2

Being Polite Is Not Enough (and Other Limits of Theory Combination)

Guilherme V. Toledo, Benjamin Przybocki, Yoni Zohar

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In the Nelson–Oppen combination method for satisfiability modulo theories, the combined theories must be stably infinite; in gentle combination, one theory has to be gentle, and the other has to satisfy a similar yet weaker property; in shiny combination, only one has to be shiny (smooth, with a computable minimal model function and the finite model property); and for polite combination, only one has to be strongly polite (smooth and strongly finitely witnessable). For each combination method, we prove that if any of its assumptions are removed, then there is no general method to combine an arbitrary pair of theories satisfying the remaining assumptions. We also prove new theory combination results that weaken the assumptions of gentle and shiny combination.

Original language	English
Title of host publication	Automated Deduction - CADE 30 - 30th International Conference on Automated Deduction, 2025, Proceedings
Editors	Clark Barrett, Uwe Waldmann
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	17-34
Number of pages	18
ISBN (Print)	9783031999833
DOIs	https://doi.org/10.1007/978-3-031-99984-0_2
State	Published - 2025
Event	30th International Conference on Automated Deduction, CADE 2025 - Stuttgart, Germany Duration: 28 Jul 2025 → 31 Jul 2025

Publication series

Name	Lecture Notes in Computer Science
Volume	15943 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	30th International Conference on Automated Deduction, CADE 2025
Country/Territory	Germany
City	Stuttgart
Period	28/07/25 → 31/07/25

Bibliographical note

Publisher Copyright:
© The Author(s) 2025.

Access to Document

10.1007/978-3-031-99984-0_2

Cite this

V. Toledo, G., Przybocki, B., & Zohar, Y. (2025). Being Polite Is Not Enough (and Other Limits of Theory Combination). In C. Barrett, & U. Waldmann (Eds.), Automated Deduction - CADE 30 - 30th International Conference on Automated Deduction, 2025, Proceedings (pp. 17-34). (Lecture Notes in Computer Science; Vol. 15943 LNAI). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-99984-0_2

V. Toledo, Guilherme ; Przybocki, Benjamin ; Zohar, Yoni. / Being Polite Is Not Enough (and Other Limits of Theory Combination). Automated Deduction - CADE 30 - 30th International Conference on Automated Deduction, 2025, Proceedings. editor / Clark Barrett ; Uwe Waldmann. Springer Science and Business Media Deutschland GmbH, 2025. pp. 17-34 (Lecture Notes in Computer Science).

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V. Toledo, G, Przybocki, B & Zohar, Y 2025, Being Polite Is Not Enough (and Other Limits of Theory Combination). in C Barrett & U Waldmann (eds), Automated Deduction - CADE 30 - 30th International Conference on Automated Deduction, 2025, Proceedings. Lecture Notes in Computer Science, vol. 15943 LNAI, Springer Science and Business Media Deutschland GmbH, pp. 17-34, 30th International Conference on Automated Deduction, CADE 2025, Stuttgart, Germany, 28/07/25. https://doi.org/10.1007/978-3-031-99984-0_2

Being Polite Is Not Enough (and Other Limits of Theory Combination). / V. Toledo, Guilherme; Przybocki, Benjamin; Zohar, Yoni.
Automated Deduction - CADE 30 - 30th International Conference on Automated Deduction, 2025, Proceedings. ed. / Clark Barrett; Uwe Waldmann. Springer Science and Business Media Deutschland GmbH, 2025. p. 17-34 (Lecture Notes in Computer Science; Vol. 15943 LNAI).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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V. Toledo G, Przybocki B, Zohar Y. Being Polite Is Not Enough (and Other Limits of Theory Combination). In Barrett C, Waldmann U, editors, Automated Deduction - CADE 30 - 30th International Conference on Automated Deduction, 2025, Proceedings. Springer Science and Business Media Deutschland GmbH. 2025. p. 17-34. (Lecture Notes in Computer Science). doi: 10.1007/978-3-031-99984-0_2