Using decision procedures with a higher-order logic

Abstract

In automated reasoning, there is a perceived trade-off between expressiveness and automation. Higher-order logic is typically viewed as expressive but resistant to automation, in contrast with firstorder logic and its fragments. We argue that higher-order logic and its variants actually achieve a happy medium between expressiveness and automation, particularly when used as a front-end to a wide range of decision procedures and deductive procedures. We illustrate the discussion with examples from PVS, but some of the observations apply to other variants of higher-order logic as well.