**Sahlqvist Formula**

In modal logic, **Sahlqvist formulas** are a certain kind of modal formula with remarkable properties. The **Sahlqvist correspondence theorem** states that every Sahlqvist formula is canonical, and corresponds to a first-order definable class of Kripke frames.

Sahlqvist's definition characterizes a decidable set of modal formulas with first-order correspondents. Since it is undecidable, by Chagrova's theorem, whether an arbitrary modal formula has a first-order correspondent, there are formulas with first-order frame conditions that are not Sahlqvist (see the examples below). Hence Sahlqvist formulas define only a (decidable) subset of modal formulas with first-order correspondents.

Read more about Sahlqvist Formula: Definition, Examples of Sahlqvist Formulas, Examples of Non-Sahlqvist Formulas, Kracht's Theorem

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