Weakened Negative Introspection

A new weakened scheme for negative introspection in autoepistemic reasoning is proposed. The scheme is formulated proof-theoretically in terms of enumer-ations of formulae. The resulting sets of conclusions based on this negative introspec-tion principle, cautious autoepistemic expansions, generalize Moore style stable expansions such that every set of premises has a cautious expansion. A nitary characterization is developed for cautious expansions. The elimination of weakly grounded cautious expansions yields a subclass of cautious expansions: the N-grounded cautious expansions. The least N-grounded cautious expansion is shown to be unique and the intersection of all N-grounded cautious expansions. This is in contrast with Moore style stable expansions. The least N-grounded cautious expansion can be constructed iteratively as the least xed point of a monotonic operator. Such a construction is exceptional, since autoepistemic expansions are nonconstructive in general. It is also shown that cautious autoepistemic logic is decidable. A comparison is made with some other schemes of weakened negative introspection. The given set of examples demonstrates that the proposed negative introspection principle is stronger than, e.g., that of the well-founded semantics.