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Yankov Characteristic Formulas (An Algebraic Account)

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V.A. Yankov on Non-Classical Logics, History and Philosophy of Mathematics

Part of the book series: Outstanding Contributions to Logic ((OCTR,volume 24))

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Abstract

The Yankov (characteristic) formulas were introduced by V. Yankov in 1963. Nowadays, the Yankov (or frame) formulas are used in virtually every branch of propositional logic: intermediate, modal, fuzzy, relevant, many-valued, etc. All these different logics have one thing in common: in one form or the other, they admit the deduction theorem. From a standpoint of algebraic logic, this means that their corresponding varieties have a ternary deductive (TD) term. It is natural to extend the notion of a characteristic formula to such varieties and, thus, to apply this notion to an even broader class of logics, namely, the logics in which the algebraic semantic is a variety with a TD term.

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Notes

  1. 1.

    In Troelstra (1965) the logics \(\boldsymbol{L}_1\) and \(\boldsymbol{L}_2\) are called independent just in case if they are incomparable, i.e. \(\boldsymbol{L}_1 \nsubseteq \boldsymbol{L}_2\) and \(\boldsymbol{L}_2 \nsubseteq \boldsymbol{L}_1\).

  2. 2.

    These algebras are due to Wroński (1974) and Blok (1977); in Jankov (1968a) the different algebras were employed.

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    Alex Citkin

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    Alex Citkin

  2. Hellenic Open University, Athens, Greece

    Ioannis M. Vandoulakis

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Citkin, A. (2022). Yankov Characteristic Formulas (An Algebraic Account). In: Citkin, A., Vandoulakis, I.M. (eds) V.A. Yankov on Non-Classical Logics, History and Philosophy of Mathematics. Outstanding Contributions to Logic, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-031-06843-0_5

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