A sequent calculus for a first order linear temporal logic with equality
We consider a first order temporal logic of linear discrete time with temporal modalities ○ (“next”), D (“always in the future”) which includes equality, time-dependant predicate as well as time-dependant function symbols. It is known that this logic is not finitary axiomatizable. We present an infinite cut-free Gentzen-style calculus for the logic. The inference rules for equality which have no counterparts in sequent calculi for first order predicate logic with equality are introduced. Soundness and completeness are proved for the calculus.
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