Sahlqvist Formula - Definition

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 AB, 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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