Syntactic proofs for Yablo’s paradoxes in temporal logic

Abstract

Temporal logic is of importance in theoretical computer science for its application in formal verification, to state requirements of hardware or software systems. Linear temporal logic is an appropriate logical environment to formalize Yablo’s paradox which is seemingly non-self-referential and basically has a sequential structure. We give a brief review of Yablo’s paradox and its various versions. Formalization of these paradoxes yields some theorems in Linear Temporal Logic (LTL) for which we give syntactic proofs using an appropriate axiomatization of LTL.