Automated reasoning with ordinary assertions and default assumptions

In this paper, we explain the use of PPC NAT, a three-valued first-order object logic (PPC) implemented in Isabelle, for reasoning with undefined expressions. This kind of expressions can be found in default logic where deductions are divided from facts (which are true) together with a set of assumptions (defaults), which can be true. The main features of our system are: the ability to formalize default assumptions and to reason about them automatically.