, Note that (15) is ill-typed for two reasons now: the first x is a variable not assumed anywhere and the term bark(x, e) is ill-typed as well. Employing dependent event types in the Montagovian semantics (i.e., in C e as described in Sect. 4.1), would still leave a small possibility of some formally legal but incorrect semantics. For instance, one might consider the following semantics for (8): (16) (#) ?e : Event. ¬?x : e. dog(x) & bark(e) Note that, although (16) is incorrect, it is still well-typed because e is just an event, not an event with x as agent. 9 This, however, 14) ¬?x : Dog. ?e : Evt A (x). bark(x, e) (15) (#) ?e : Evt A (x). ¬?x : Dog. bark(x, e)
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