Autoepistemic Logics of Closed Beliefs and Logic Programming

Moore's autoepistemic logic AEL proved to be a very successful approach to formalizing non-monotonic reasoning and logic programming. However, AEL also has some important drawbacks, e.g., quite \reasonable" theories are often inconsistent in AEL, it does not always lead to the expected, intended semantics and it cannot be eeectively computed even for very simple classes of theories. In this paper we propose a more general approach to autoepistemic reasoning by introducing Autoepistemic Logics of Closed Beliefs AEL cl , where j = cl denotes a speciic negative introspection inference operator (\closed world assumption") on which negative introspection in this logic is based. Negative introspection determines which formulae in autoepistemic logic are disbelieved, or, putting it diierently, negation of which for-mulae can be assumed by default. It determines therefore the set of closed world beliefs derivable in a given autoepistemic logic. Moore's autoepistemic logic AEL is a special case of AEL cl obtained when the negative introspection operator j = cwa , based on CWA, is used as j = cl , i.e., AEL AEL cwa. The proposed logics provide a natural and mathematically elegant framework where by choosing diierent negative introspection operators j = cl we obtain diierent au-toepistemic logics AEL cl whose properties reeect the properties of the operator j = cl. We substantiate this claim by investigating in the class of logic programs the Autoepis-temic Logic of Closed Beliefs AEL circ , in which the negative introspection operator j = circ is based on McCarthy's circumscription CIRC, and comparing it to the original Moore's autoepistemic logic AEL = AEL cwa , in which the negative introspection operator j = cwa is based on Reiter's CWA. Our results show that AEL circ represents a new and attractive autoepistemic logic which eliminates the drawbacks of the original Moore's AEL mentioned above. Moreover, in the class of logic programs, AEL circ naturally deenes the well-founded semantics thus showing that the well-founded semantics can also be viewed as being based on autoepistemic logic.