  Turner’s idea is to treat Caused as a modal operator [ c ], making this the basis of a modal nonmonotonic logic. In the preferred models of this logic, the caused propositions coincide with the propositions that are true, and this must be the only possibility consistent with the extensional part of the model. To make this more explicit, recall that in the possible worlds interpretation of S5, it is possible to identify possible worlds with state descriptions, which we can represent as sets I of literals (atomic formulas and their negations). Making this identification, then, we can think of a model as a pair &lt;I, S&gt;, where S is a set of interpretations (complete, consistent sets of literals) including I. The modal operator [ c ] is given the standard semantics: where S is a set of interpretations and where I ∈ S,  S ⊨I [ c  ] A if and only if  S ⊨I′ A for all I′ ∈S. &lt;I, S&gt; satisfies a set of formulas T if and only if S ⊨I A for all A ∈ T.