The word tautology was used by the ancient Greeks to describe a statement that was asserted to be true merely by virtue of saying the same thing twice, a pejorative meaning … 展开

Propositional logic begins with propositional variables, atomic units that represent concrete propositions. A formula consists of propositional variables connected by logical … 展开

The problem of determining whether a formula is a tautology is fundamental in propositional logic. If there are n variables occurring in a formula then … 展开

An axiomatic system is complete if every tautology is a theorem (derivable from axioms). An axiomatic system is sound if every theorem is a tautology. 展开

A formula of propositional logic is a tautology if the formula itself is always true, regardless of which valuation is used for the propositional variables. There are infinitely many tautologies.
In many of the following examples A represents the statement … 展开

There is a general procedure, the substitution rule, that allows additional tautologies to be constructed from a given tautology (Kleene 1967 … 展开

The problem of constructing practical algorithms to determine whether sentences with large numbers of propositional variables are tautologies is an area of contemporary … 展开