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Two-Variable First-Order Logic with Equivalence Closure
Ist Teil von
SIAM journal on computing, 2014-01, Vol.43 (3), p.1012-1063
Ort / Verlag
Philadelphia: Society for Industrial and Applied Mathematics
Erscheinungsjahr
2014
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
We consider the satisfiability and finite satisfiability problems for extensions of the two-variable fragment of first-order logic in which an equivalence closure operator can be applied to a fixed number of binary predicates. We show that the satisfiability problem for two-variable, first-order logic with equivalence closure applied to two binary predicates is in 2-NExpTime, and we obtain a matching lower bound by showing that the satisfiability problem for two-variable first-order logic in the presence of two equivalence relations is 2-NExpTime-hard. The logics in question lack the finite model property; however, we show that the same complexity bounds hold for the corresponding finite satisfiability problems. We further show that the satisfiability (${=}$ finite satisfiability) problem for the two-variable fragment of first-order logic with equivalence closure applied to a single binary predicate is NExpTime-complete. [PUBLICATION ABSTRACT]