## Abstract

Autoepistemic logic is one of the principal modes of nonmonotonicreasoning. It unifies several other modes of nonmonotonic reasoning andhas important application in logic programming. In the paper, a theoryof autoepistemic logic is developed. This paper starts with a briefsurvey of some of the previously known results. Then, the nature ofnonmonotonicity is studied by investigating how membership ofautoepistemic statements in autoepistemic theories depends on theunderlying objective theory. A notion similar to set-theoretic forcingis introduced. Expansions of autoepistemic theories are alsoinvestigated. Expansions serve as sets of consequences of anautoepistemic theory and they can also be used to define semantics forlogic programs with negation. Theories that have expansions arecharacterized, and a normal form that allows the description of allexpansions of a theory is introduced. Our results imply algorithms todetermine whether a theory has a unique expansion. Sufficient conditions1991 that imply existence of a unique expansion arediscussed. The definition of stratified theories is extended and (undersome additional assumptions) efficient algorithms for testing whether atheory is stratified are proposed. The theorem characterizing expansionsis applied to two classes of theories, K_{1}-theoriesand ae-programs. In each case, simple hypergraph characterization ofexpansions of theories from each of these classes is given. Finally,connections with stable model semantics for logic programs with negationis discussed. In particular, it is proven that the problem of existenceof stable models is NP-complete.

Original language | English |
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Pages (from-to) | 587-618 |

Number of pages | 32 |

Journal | Journal of the ACM (JACM) |

Volume | 38 |

Issue number | 3 |

DOIs | |

State | Published - Jan 7 1991 |

## ASJC Scopus subject areas

- Software
- Control and Systems Engineering
- Information Systems
- Hardware and Architecture
- Artificial Intelligence