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Characteristic Inference Rules

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Abstract

The goal of this paper is to generalize a notion of quasi-characteristic inference rule (by using finite partial algebras instead of finite subdirectly irreducible algebras) in the following way: with every finite partial algebra we associate a (multiple-conclusion) rule, and study the properties of these rules. We prove that any equivalential logic can be axiomatized by such rules. We further discuss the correlations between characteristic rules of the finite partial algebras and canonical rules. Then, with every algebra we associate a set of characteristic rules that correspond to each finite partial subalgebra of this algebra. Finally, we demonstrate that in many respects these sets enjoy the same properties as regular quasi-characteristic rules.

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    Alex Citkin

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Citkin, A. Characteristic Inference Rules. Log. Univers. 9, 27–46 (2015). https://doi.org/10.1007/s11787-015-0116-x

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