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We show that intuitionistic quantifiers admit the following temporalinterpretation: $\forall x A$ is true at a world $w$ iff $A$ is true at everyobject in the domain of every future world, and $\exists x A$ is true at $w$iff $A$ is true at some object in the domain of some past world. For thispurpose we work with a predicate version of the well-known tense propositionallogic $\sf S4.t$. The predicate logic $\sf Q^\circ S4.t$ is obtained byweakening the axioms of the standard predicate extension $\sf QS4.t$ of $\sfS4.t$ along the lines Corsi weakened $\sf QK$ to $\sf Q^\circ K$. The G\"odeltranslation embeds the predicate intuitionistic logic $\sf IQC$ into $\sf QS4$fully and faithfully. We provide a temporal version of the G\"odel translationand prove that it embeds $\sf IQC$ into $\sf Q^\circ S4.t$ fully andfaithfully; that is, we show that a sentence is provable in $\sf IQC$ iff itstranslation is provable in $\sf Q^\circ S4.t$. Faithfulness is proved usingsyntactic methods, while we prove fullness utilizing the generalized Kripkesemantics of Corsi.

Temporal interpretation of intuitionistic quantifiers