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Interpolation in the Inquisitive Hierarchy

  • Josef v. H. Doyle
  • Wesley Fussner
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Abstract

We show that each of the infinitely many extensions of the basic inquisitive logic has the Craig interpolation property, and deduce from this that each of these extensions also has the Beth definability property. These results stand in contrast to existing characterizations of interpolation within lattices of extensions, in which the distribution of logics with interpolation is sparse.

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Cite

BibTeXRIS
BibTeX
@misc{doyle2026interpolation,
  title = {{Interpolation in the Inquisitive Hierarchy}},
  author = {Josef v. H. Doyle and Wesley Fussner},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32366},
  eprint = {2610.32366},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32366},
}
RIS
TY  - UNPB
TI  - Interpolation in the Inquisitive Hierarchy
AU  - Josef v. H. Doyle
AU  - Wesley Fussner
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32366
UR  - https://arxiv.org/abs/2610.32366
AB  - We show that each of the infinitely many extensions of the basic inquisitive logic has the Craig interpolation property, and deduce from this that each of these extensions also has the Beth definability property. These results stand in contrast to existing characterizations of interpolation within lattices of extensions, in which the distribution of logics with interpolation is sparse.
ER  -