 An account of the co-tenability idea based on possible worlds was further elaborated in the work of Veltman (1976) and Kratzer (1979), in what has come to be known as premise semantics (an expression coined by D. Lewis 1981). Premise semantics can be presented either as providing acceptance conditions or as providing truth conditions. It is compatible with an epistemic as well as with an ontic interpretation of conditionals. The former builds on the idea that the premises represent essentially an agent’s basic beliefs; this is the approach of Veltman (1976) who took inspiration from Ramsey. The latter takes the premises to represent the basic facts of a possible world; this is the approach of Kratzer (1979, 1981), who was inspired by Rescher and Lewis (D. Lewis 1981) and has functions assigning a premise set to every possible world. In any case, the idea of premise semantics is this. Relative to a given set \(\Gamma\) of premises (assigned to a possible world \(w\)), a conditional \(A&gt;B\) is accepted (or true at \(w\)) if and only if for every maximal subset of \(\Gamma'\) of \(\Gamma\) that is consistent with \(A\) it holds that \(\Gamma' \cup \{A\}\) implies \(B\).