Consensus theorem

It is the conjunction of all the unique literals of the terms, excluding the literal that appears unnegated in one term and negated in the other.

includes a term that is negated in

(or vice versa), the consensus term

is false; in other words, there is no consensus term.

The conjunctive dual of this equation is:

The consensus is the conjunction of the two terms, omitting both

[2] The consensus is undefined if there is more than one opposition.

For the conjunctive dual of the rule, the consensus

The RHS can be derived from the LHS simply through the conjunction elimination inference rule.

In Boolean algebra, repeated consensus is the core of one algorithm for calculating the Blake canonical form of a formula.

[2] In digital logic, including the consensus term in a circuit can eliminate race hazards.

[3] The concept of consensus was introduced by Archie Blake in 1937, related to the Blake canonical form.

[4] It was rediscovered by Samson and Mills in 1954[5] and by Quine in 1955.

[6] Quine coined the term 'consensus'.

Robinson used it for clauses in 1965 as the basis of his "resolution principle".