All the formulas of LTL can be transformed into negation normal form, where
- all negations appear only in front of the atomic propositions,
- only other logical operators true, false, ∧, and ∨ can appear, and
- only the temporal operators X, U, and R can appear.
Using the above equivalences for negation propagation, it is possible to derive the normal form. This normal form allows R, true, false, and ∧ to appear in the formula, which are not fundamental operators of LTL. Note that the transformation to the negation normal form does not blow up the size of the formula. This normal form is useful in translation from LTL to Büchi automaton.
Read more about this topic: Linear Temporal Logic
Famous quotes containing the words negation, normal and/or form:
“An “unemployed” existence is a worse negation of life than death itself.”
—José Ortega Y Gasset (1883–1955)
“To try to control a nine-month-old’s clinginess by forcing him away is a mistake, because it counteracts a normal part of the child’s development. To think that the child is clinging to you because he is spoiled is nonsense. Clinginess is not a discipline issue, at least not in the sense of correcting a wrongdoing.”
—Lawrence Balter (20th century)
“In full view of his television audience, he preached a new religion—or a new form of Christianity—based on faith in financial miracles and in a Heaven here on earth with a water slide and luxury hotels. It was a religion of celebrity and showmanship and fun, which made a mockery of all puritanical standards and all canons of good taste. Its standard was excess, and its doctrines were tolerance and freedom from accountability.”
—New Yorker (April 23, 1990)