 Logics where LEM fails are not themselves hard to come by. Among many such logics are a number of three-valued logics that allow sentences to take a third value over and above true and false. Sentences like Liar sentences take the third value. One of the most commonly applied logics is the Strong Kleene logic \(K_3\). We do not go into the details of \(K_3\) here, but only note the properties of \(K_3\) we need. (For more details, see the entry on  many-valued logic,  or Priest 2008.) First and foremost, we have:   \[\not\vdash_{K3} A \vee \neg A.\]   LEM fails. In fact, there are no logical truths (or valid sentences) according to \(K_3\). (We return to this on the topic of a ‘suitable conditional’ below.)