Background
Propositional logic begins with propositional variables, atomic units that represent concrete propositions. A formula consists of propositional variables connected by logical connectives in a meaningful way, so that the truth of the overall formula can be uniquely deduced from the truth or falsity of each variable. A valuation is a function that assigns each propositional variable either T (for truth) or F (for falsity). So, for example, using the propositional variables A and B, the binary connectives and representing disjunction and conjunction respectively, and the unary connective representing negation, the following formula can be obtained::. A valuation here must assign to each of A and B either T or F. But no matter how this assignment is made, the overall formula will come out true. For if the first conjunction is not satisfied by a particular valuation, then one of A and B is assigned F, which will cause the corresponding later disjunct to be T.
Read more about this topic: Tautology (logic)
Famous quotes containing the word background:
“Silence is the universal refuge, the sequel to all dull discourses and all foolish acts, a balm to our every chagrin, as welcome after satiety as after disappointment; that background which the painter may not daub, be he master or bungler, and which, however awkward a figure we may have made in the foreground, remains ever our inviolable asylum, where no indignity can assail, no personality can disturb us.”
—Henry David Thoreau (1817–1862)
“They were more than hostile. In the first place, I was a south Georgian and I was looked upon as a fiscal conservative, and the Atlanta newspapers quite erroneously, because they didn’t know anything about me or my background here in Plains, decided that I was also a racial conservative.”
—Jimmy Carter (James Earl Carter, Jr.)
“In the true sense one’s native land, with its background of tradition, early impressions, reminiscences and other things dear to one, is not enough to make sensitive human beings feel at home.”
—Emma Goldman (1869–1940)