 More recently, Cantwell (2008) presented a truth table semantics for a system of connexive logic together with a proof-theoretical characterization. The truth tables for negation and implication are taken from Belnap 1970, but Cantwell's three-valued truth table for the conditional can already be found in a paper by William Cooper (1968). Like Cantwell, Cooper wanted to formally model how conditional sentences in the indicative mood and expressed by means of if-then are used in ordinary conversational English. (Whereas Cantwell takes the entire three-element set of truth values as the co-domain of assignment functions for propositional variables, Cooper restricts assignment functions to mappings from the set of propositional variables to the two-element set of classical truth values.)   Cantwell considers a language containing the constantly false proposition ⊥ and the following three-valued truth tables for negation, conjunction, disjunction, and implication with designated values T and − (where ‘T’ stands for truth and ‘F’ for falsity):