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arXiv · 2201.06076

Admissibility of $\Pi_2$-Inference Rules: interpolation, model completion, and contact algebras

Nick Bezhanishvili·Luca Carai·Silvio Ghilardi·Lucia Landi
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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 $\mathsf{S^2IC}$, 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 $\Pi_2$-rules.

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Nick Bezhanishvili, Luca Carai, Silvio Ghilardi, Lucia Landi. 2022-01-16. Admissibility of $\Pi_2$-Inference Rules: interpolation, model completion, and contact algebras. https://arxiv.org/abs/2201.06076

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