Infinitary calculus for a restricted first-order linear temporal logic without contraction on quantified formulas

Abstract

An infinitary calculus for a restricted fragment of the first-order linear temporal logic is considered. We prove that for this fragment one can construct the infinitary calculusG Lω * without contraction on predicate formulas. The calculusG Lω * possesses the following properties: (1) the succedent rule for the existential quantifier is included into the corresponding axiom; (2) the premise of the antecedent rule for the universal quantifier does not contain a duplicate of the main formula. The soundness and completness ofG Lω * are also proved.