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Two-variable logic : ウィキペディア英語版 | Two-variable logic
In mathematical logic and computer science, two-variable logic is the fragment of first-order logic where formulae can be written using only two different variables. This fragment is usually studied without function symbols. == Decidability ==
One of the main points is that some important problems about two-variable logic, such as satisfiability and finite satisfiability, are decidable. This result generalizes results about the decidability of fragments of two-variable logic, such as certain description logics; however, some fragments of two-variable logic enjoy a much lower computational complexity for their satisfiability problems. By contrast, for the three-variable fragment of first-order logic without function symbols, satisfiability is undecidable.〔A. S. Kahr, Edward F. Moore and Hao Wang. ''Entscheidungsproblem Reduced to the ∀ ∃ ∀ Case'', 1962, noting that their ∀ ∃ ∀ formulas use only three variables.〕
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