Definition
Sahlqvist formulas are built up from implications, where the consequent is positive and the antecedent is of a restricted form.
- A boxed atom is a propositional atom preceded by a number (possibly 0) of boxes, i.e. a formula of the form (often abbreviated as for ).
- A Sahlqvist antecedent is a formula constructed using ∧, ∨, and from boxed atoms, and negative formulas (including the constants ⊥, ⊤).
- A Sahlqvist implication is a formula A → B, where A is a Sahlqvist antecedent, and B is a positive formula.
- A Sahlqvist formula is constructed from Sahlqvist implications using ∧ and (unrestricted), and using ∨ on formulas with no common variables.
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