Rules of Inference
Like all connectives in first-order logic, the biconditional has rules of inference that govern its use in formal proofs.
Read more about this topic: Logical Biconditional
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“As no one can tell what was the Roman pronunciation, each nation makes the Latin conform, for the most part, to the rules of its own language; so that with us of the vowels only A has a peculiar sound.”
—Henry David Thoreau (1817–1862)
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“Rules and particular inferences alike are justified by being brought into agreement with each other. A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend. The process of justification is the delicate one of making mutual adjustments between rules and accepted inferences; and in the agreement achieved lies the only justification needed for either.”
—Nelson Goodman (b. 1906)