Embedding Minimal Knowledge into Autoepistemic Logic

Riccardo Rosati.
In Proceedings of the Fifth Conference of the Italian Association for Artificial Intelligence (AI*IA'97), Lecture Notes in Artificial Intelligence, pages 231-241, Springer, 1997.

Abstract:

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.

Bibtex entry:

@String{AI*IA-97 = "Proceedings of the Fifth Conference of the Italian Association for Artificial Intelligence (AI*IA'97)"}

@String{LNAI = "Lecture Notes in Artificial Intelligence"}

@String{SV = "Springer"}

@Inproceedings{Rosa97c,
author = "Riccardo Rosati",
title = "Embedding Minimal Knowledge into Autoepistemic Logic",
booktitle = AI*IA-97,
pages = "231--241",
publisher = SV,
series = LNAI,
year = 1997,
}