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.
Read more about this topic: Sahlqvist Formula
Famous quotes containing the word definition:
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (1842–1910)
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)