  A. Tarski proposed the study of infinitary consequence operations as the
central topic of mathematical logic. He considered monotonicity to be a
property of all such operations. In this paper, we weaken the monotonicity
requirement and consider more general operations, inference operations. These
operations describe the nonmonotonic logics both humans and machines seem to be
using when infering defeasible information from incomplete knowledge. We single
out a number of interesting families of inference operations. This study of
infinitary inference operations is inspired by the results of Kraus, Lehmann
and Magidor on finitary nonmonotonic operations, but this paper is
self-contained.
