  The goal of computational logic is to allow us to model computation as well
as to reason about it. We argue that a computational logic must be able to
model interactive computation. We show that first-order logic cannot model
interactive computation due to the incompleteness of interaction. We show that
interactive computation is necessarily paraconsistent, able to model both a
fact and its negation, due to the role of the world (environment) in
determining the course of the computation. We conclude that paraconsistency is
a necessary property for a logic that can model interactive computation.
