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Jankov - style formulas and refutation systems

Citkin A.

Reports on Mathematical Logic

2013

Vol. 48

67--80

The paper studies the logics which algebraic se- mantics comprises of the Hilbert algebras endowed with additional operations - the regular algebras. With any fnite subdirectly irre- ducible regular algebra one can associate a Jankov formula. In its turn, the Jankov formulas can be used as anti-axioms for a refutation system. It is proven that a logic has a complete refutation system based on Jankov formulas if and only if this logic enjoys fnite model property. Also, such a refutation system is fnite, that is, it contains a fnite number of axioms and anti-axioms, if and and only if the logic is tabular.