 Succeeding the work of Kripke, many attempts have been made to construct languages containing their own truth predicate and not suffering from the revenge problem of strengthened liars. Many of these attempts have focused on modifying or extending the underlying strong three-valued logic, e.g. modifying the semantics of the conditional (Field, 2003, 2008) or allowing an unbounded number of truth-values (Cook, 2007; Schlenker, 2010; Tourville and Cook, 2016). 