Normal Forms in Intensional Logic

In this note, it is shown, following up on a conjecture of Joyce Friedman and David Warren in 1980, and in contrast with what is commonly assumed, that the reduction of applied λ-terms in Richard Montague’s intensional logic does not need to conflict with other possible reductions. For a confluent reduction, one only needs to access more rules than just the λ-reduction alone. In addition, we need to draw from principles, such as λ-Application Distribution and λ-Argument Exploitation, and suitably adjust the concept of a normal form.