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In [[mathematical logic]] and [[computer science]], '''two-variable logic''' is the [[fragment (logics)|fragment]] of [[first-order logic]] where [[formula (logics)|formulae]] can be written using only two different [[variable (logics)|variable]]s. This fragment is usually studied without [[function symbol]]s, and one of its main points is that some important problems about it, such as [[satisfiability (logics)|satisfiability]] and [[finite satisfiability (logics)|finite satisfiability]], are [[decidability (computer science)|decidable]].
What is more, the two-variable fragment of first-order logic with no function symbols is known to be decidable even with the addition of [[counting quantifiers]]. This is a more powerful result, as counting quantifiers for high numerical values are not expressible in that logic.
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