Abstract
The paper presents Hilbert-style systems and sequent calculi for some weaker versions of common sense modal predicate calculus. The main results are the strong completeness results for the Hilbert-style systems and cut elimination theorems for the sequent calculi.
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Acknowledgment
We are extremely grateful to Jeremy Seligman for circulating his draft on CMPC and discussing it. We also thank Tomoyuki Yamada for helpful comments and discussions. The work of the second author was partially supported by JSPS KAKENHI Grant-in-Aid for Scientific Research (C) Grant Number 19K12113, JSPS KAKENHI Grant-in-Aid for Scientific Research (B) Grant Number 17H02258, and JSPS Core-to-Core Program (A. Advanced Research Networks).
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Sawasaki, T., Sano, K. (2020). Proof-Theoretic Results of Common Sense Modal Predicate Calculi. In: Liao, B., Wáng, Y. (eds) Context, Conflict and Reasoning. Logic in Asia: Studia Logica Library. Springer, Singapore. https://doi.org/10.1007/978-981-15-7134-3_10
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DOI: https://doi.org/10.1007/978-981-15-7134-3_10
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