Craig interpolation theorem fails in bi-intuitionistic predicate logic
- In this article we show that bi-intuitionistic predicate logic lacks the Craig Interpolation Property. We proceed by adapting the counterexample given by Mints, Olkhovikov and Urquhart for intuitionistic predicate logic with constant domains [13]. More precisely, we show that there is a valid implication \(\phi \rightarrow \psi\) with no interpolant. Importantly, this result does not contradict the unfortunately named "Craig interpolation" theorem established by Rauszer in [24] since that article is about the property more correctly named "deductive interpolation" (see Galatos, Jipsen, Kowalski and Ono’s use of this term in [5]) for global consequence. Given that the deduction theorem fails for bi-intuitionistic logic with global consequence, the two formulations of the property are not equivalent.
| Author: | Grigory OlkhovikovORCiDGND, Guillermo BadiaORCiDGND |
|---|---|
| URN: | urn:nbn:de:hbz:294-106716 |
| DOI: | https://doi.org/10.1017/S1755020322000296 |
| Parent Title (English): | The review of symbolic logic |
| Publisher: | Cambridge University Press |
| Place of publication: | Cambridge |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2024/01/18 |
| Date of first Publication: | 2022/08/12 |
| Publishing Institution: | Ruhr-Universität Bochum, Universitätsbibliothek |
| Tag: | Craig Interpolation Theorem; bi-asimulation; bi-intuitionistic predicate logic |
| First Page: | 1 |
| Last Page: | 23 |
| Institutes/Facilities: | Institut für Philosophie I |
| open_access (DINI-Set): | open_access |
| faculties: | Fakultät für Philosophie und Erziehungswissenschaft |
| Licence (English): |  Creative Commons - CC BY 4.0 - Attribution 4.0 International |
