 (On the entries containing a *, see the supplementary document  Some Formal Theories in the Literature.)  In the case of Restall, commitment to all three operations directly follows from the fact that his theory validates W4 and Modal Criterion. Taylor in fact has no modal theory of facts, but it seems that in a natural modal extension of his theory the previously mentioned acceptance claims should be correct. The restrictions in Taylor’s case are due to the fact that he works with standard first-order languages. Taylor is concerned with giving a theory of the facts “posited” by standard first-order languages, i.e., of the facts which play a role in determining the truth-values of the sentences of that language. Standard first-order languages admit of conjunction and disjunction only on finite collections of sentences, hence the restrictions relative to facts. But clearly, moving to languages in which infinite conjunctions and disjunctions are freely allowed, the restrictions would vanish.