Embedding minimal knowledge into autoepistemic logic

  • Riccardo Rosati
Knowledge Representation 1
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1321)


We investigate the epistemological properties of MKNF, Lifschitz's logic of minimal knowledge and negation as failure. In particular, we show that the expressive power of MKNF is equivalent to Moore's autoepistemic logic (AEL), by defining an embedding of MKNF into AEL and vice versa. We also prove that the negation as failure modality not of MKNF exactly corresponds to the negative introspection operator in AEL. The two previous results imply that MKNF's minimal knowledge modality K can be represented by means of negation as failure not, i.e. MKNF theories admit an equivalent representation in terms of unimodal theories using the not operator only. This in turn implies that negation as failure is “more expressive” than minimal knowledge.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Riccardo Rosati
    • 1
  1. 1.Dipartimento di Informatica e SistemisticaUniversity di Roma “La Sapienza”RomaItaly

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