New foundations for imperative logic I: Logical connectives, consistency, and quantifiers

Abstract. Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: “kiss me and hug me ” is the conjunction of “kiss me ” with “hug me”. This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives is true exactly if both conjuncts are true, the conjunction of two imperatives is satisfied exactly if both conjuncts are satisfied⎯what more is there to say? Much more, I argue. “If you love me, kiss me”, a conditional imperative, mixes a declarative antecedent (“you love me”) with an imperative consequent (“kiss me”); it is satisfied if you love and kiss me, violated if you love but don’t kiss me, and avoided if you don’t love me. So we need a logic of three-valued imperatives which mixes declaratives with imperatives. I develop such a logic. 1