A truth-conditional formulation of Karttunen's account of presupposition

Karttunen's seminal 1973 article Presuppositions of compound sentences, lays the groundwork for the elegant and fruitful theory of this subject which he subsequently presented in (1974). In (1973, pp. 185–8), however, he fallaciously argued that the regularities he discovered concerning the behavior of and, or, and if ... then in English cannot be embodied in any three-valued logic giving a truth-functional interpretation to these connectives. The present paper refutes Karttunen's argument by exhibiting an interpretation with the desired properties, and shows further how the full articulation of his 1974 system can be developed naturally within a truth-conditional semantics for English if bivalence is abandoned — contrary to what Karttunen expected.