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 (SIC)-I-2, 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.
Admissibility of Π2-Inference Rules: interpolation, model completion, and contact algebras / N. Bezhanishvili, L. Carai, S. Ghilardi, L. Landi. - In: ANNALS OF PURE AND APPLIED LOGIC. - ISSN 0168-0072. - 174:1(2023 Jan), pp. 103169.1-103169.31. [10.1016/j.apal.2022.103169]
Admissibility of Π2-Inference Rules: interpolation, model completion, and contact algebras
L. Carai
Secondo
;S. GhilardiPenultimo
;
2023
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 (SIC)-I-2, 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.File | Dimensione | Formato | |
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