Connections and higher-order logic

Theorem proving is difficult and deals with complex phenomena. The difficulties seem to be compounded when one works with higher-order logic, but the rich expressive power of Church's formulation [10] [3] of this language makes research on theorem proving in this realm very worthwhile. In order to make significant progress on this problem, we need to try many approaches and ideas, and explore many questions. A highly relevant question is "What makes a logical formula valid?".