Admissibility of Π<sub>2</sub>-inference rules: Interpolation, model completion, and contact algebras

Admissibility of Π₂-inference rules: Interpolation, model completion, and contact algebras

Authors	N. Bezhanishvili L. Carai S. Ghilardi L. Landi
Publication date	01-2023
Journal	Annals of Pure and Applied Logic
Article number	103169
Volume \| Issue number	174 \| 1
Number of pages	31
Organisations	Interfacultary Research - Institute for Logic, Language and Computation (ILLC)
Abstract	We devise three strategies for recognizing admissibility of non-standard inference rules via interpolation, uniform interpolation, and model completions. We apply our machinery to the case of symmetric implication calculus S²IC, where we also supply a finite axiomatization of the model completion of its algebraic counterpart, via the equivalent theory of contact algebras. Using this result we obtain a finite basis for admissible Π₂-rules.
Document type	Article
Language	English
Published at	https://doi.org/10.48550/arXiv.2201.06076 https://doi.org/10.1016/j.apal.2022.103169
Downloads	2201.06076 (Submitted manuscript) 1-s2.0-S0168007222000847-main (Final published version)
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