Аналог теоремы Макинсона для нормальных модальных логик с оператором Сегерберга.

Abstract

We prove the analogue of Makinson s theorem ([Makinson, 1971]) for normal modal logics with the Segerberg operator, i. e. logics with two unary modalities: the usual ‘‘necessity” operator $\square$ and the operator $\square^*$, defined by the “Segerberg axioms”, $\square^*\phi\longleftrightarrow\phi\&\square\square^*$ and $\phi\&\square^*(\phi\rightarrow\square\phi)\rightarrow\square^*\phi$. (The Segerberg operator is widely known as one of the modalities of propositional dynamic logic.) As the corollary of the proven result we get a simple decidability procedure for effectively axiomatizable normal logics with the Segerberg operator.