MULTIVALUED AUTOEPISTEMIC LOGIC

We generalize Moore's autoepistemic logic to multi-valued autoepistemi c logic, where the set of truth-values can be any complete lattice. Mu lti-valued autoepistemic extensions can be characterized by admissible belief interpretations which are the conrete approximations of extens ions and are appropriate to be computed and manipulated. We prove that multi-valued autoepistemic extensions are exactly the theories of max imal multivalued Kripke models. The class of stratified theories is in vestigated and it is shown that stratified theories have exactly one m ulti-valued autoepistemic extension. Finally we present a sequent calc ulus for multi-valued logic which serves as a tool for a decision proc edure for multi-valued autoepistemic logic.