## Autoepistemic Logics of Closed Beliefs and Logic Programming (1995)

Venue: | Proceedings of the First International Workshop on Logic Programming and Non-monotonic Reasoning |

Citations: | 22 - 10 self |

### BibTeX

@INPROCEEDINGS{Przymusinski95autoepistemiclogics,

author = {Teodor C. Przymusinski},

title = {Autoepistemic Logics of Closed Beliefs and Logic Programming},

booktitle = {Proceedings of the First International Workshop on Logic Programming and Non-monotonic Reasoning},

year = {1995},

pages = {3--20},

publisher = {MIT Press}

}

### OpenURL

### Abstract

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 effectively 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 specific 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 differently, negation of which formulae 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 specia...

### Citations

1520 | The Stable Model Semantics for Logic Programming
- Gelfond, Lifschitz
- 1988
(Show Context)
Citation Context ...commonsense, non-monotonic reasoning [Kon87, Gel88, Lif89, MT88]. It also plays an important role in logic programming [Prz88b, Prz89], where it is used to define the so called stable model semantics =-=[GL88]. However,-=- Moore's autoepistemic logic AEL also has some important drawbacks: ffl Quite "reasonable" theories are often inconsistent in AEL [Mor88, Prz91b]; ffl Even for consistent theories AEL does n... |

857 | The well-founded semantics for general logic programs
- Gelder, Ross, et al.
- 1991
(Show Context)
Citation Context ...c in the size of the program. 4. For any logic program T , the semantics introduced by its unique least stable autoepistemic expansion e T in AEL circ always coincides with the well-founded semantics =-=[VGRS90]-=- which has been proven to be equivalent to suitable (3-valued) forms of all major non-monotonic formalisms [Prz91b] and appears to be the most promising semantics for logic programs [PP90, PW91]. 5. A... |

831 |
Circumscription—a form of nonmonotonic reasoning
- McCarthy
- 1980
(Show Context)
Citation Context ...ass of theories comprising of all logic programs, the Autoepistemic Logic of Closed Beliefs AEL circ , in which the negative introspection operator j= circ is based on McCarthy's Circumscription CIRC =-=[McC80]-=-, or - equivalently - on the Extended Closed World Assumption ECWA [Min82, GPP89], and, compared its behavior to the behavior of the original Moore's Autoepistemic Logic AEL = AEL cwa , in which negat... |

622 | Towards a theory of declarative knowledge - Apt, Blair, et al. - 1988 |

447 |
Semantical considerations on nonmonotonic logic
- Moore
- 1985
(Show Context)
Citation Context ...y defines the well-founded semantics thus showing that the well-founded semantics can also be viewed as being based on autoepistemic logic. 1 Introduction Autoepistemic logic AEL, introduced by Moore =-=[Moo85]-=-, proved to be a very successful approach to formalizing commonsense, non-monotonic reasoning [Kon87, Gel88, Lif89, MT88]. It also plays an important role in logic programming [Prz88b, Prz89], where i... |

340 | Logic programs with classical negation - Gelfond, Lifschitz - 1990 |

324 | Computing Circumscription - Lifschitz - 1985 |

192 |
Autoepistemic logic
- Marek, Truszczyński
- 1991
(Show Context)
Citation Context ...PW91]. Moreover, the semantics obtained in this way is computationally intractable. Just the problem of determining whether a propositional program has a stable autoepistemic expansion is NP-complete =-=[MT88]-=-, while computation of the stable semantics is NP-hard [KS89]. It turns out, however, that if instead of using autoepistemic expansions in AEL we use autoepistemic expansions in AEL circ , the above m... |

131 | Negation as Failure Using Tight Derivations for General Logic Programs - Gelder - 1989 |

110 |
On strati autoepistemic theories
- Gelfond
- 1987
(Show Context)
Citation Context ...r 2 Observe, however, that this expansion is different from the one proposed in [Mor88], which contains LCanF ixIt, and thus appears to be somewhat unintuitive. logic programs. Gelfond first proposed =-=[Gel87] to define the semantics of l-=-ogic programs by translating logic programs into corresponding autoepistemic theories obtained by replacing negative premises "��C " by ":LC", i.e., by translating the "ne... |

91 | On the relationship between circumscription and negation as failure - Gelfond, Przymusinska, et al. - 1989 |

72 | On inde data bases and the closed world assumption - Minker - 1982 |

67 |
problems for simple default logics
- Hard
- 1991
(Show Context)
Citation Context ...ationally intractable. Just the problem of determining whether a propositional program has a stable autoepistemic expansion is NP-complete [MT88], while computation of the stable semantics is NP-hard =-=[KS89]-=-. It turns out, however, that if instead of using autoepistemic expansions in AEL we use autoepistemic expansions in AEL circ , the above mentioned drawbacks are eliminated and, moreover, we obtain a ... |

67 | On the declarative semantics of stratified deductive databases and logic programs - PRZYMUSINSKI - 1987 |

54 | Semantic Issues in Deductive Databases and Logic Programs
- Przymusinska, Przymusinski
- 1990
(Show Context)
Citation Context ...e previous section. Let us recall that a logic program P is a set of clauses of the form A / B 1s: : :sBms��C 1s: : :s��C n where m; ns0 and A, B i 's and C i 's are atoms. Without loss of gen=-=erality [PP90] we -=-can assume that the program has been instantiated and thus consists of a (possibly infinite) set of propositional clauses. However, the negation symbol ��C in program clauses does not denote the c... |

53 | Stable semantics for logic programs and default theories - Marek, Truszcynski - 1989 |

34 | Three-Valued Non-Monotonic Formalisms And Semantics of Logic Programs. Artificial intelligence, 49, 309–343. (Extended abstract appeared in: Three-valued non-monotonic formalisms and logic programming
- Przymusinski
- 1991
(Show Context)
Citation Context ...epistemic expansion e T in AEL circ always coincides with the well-founded semantics [VGRS90] which has been proven to be equivalent to suitable (3-valued) forms of all major non-monotonic formalisms =-=[Prz91b]-=- and appears to be the most promising semantics for logic programs [PP90, PW91]. 5. Analogous results apply to the much broader class of all disjunctive logic programs or disjunctive deductive databas... |

33 |
On closed-world data bases
- Reiter
- 1978
(Show Context)
Citation Context ... special case, namely, Moore's AEL coincides with the Autoepistemic Logic of Closed Beliefs AEL cwa in which the negative introspection operator j= cwa , based on Reiter's Closed World Assumption CWA =-=[Rei78]-=-, is used: AEL j AEL cwa : The proposed logics provide a natural and mathematically elegant framework where by choosing different negative introspection inference operators j= cl we obtain different a... |

32 | On the adequacy of predicate circumscription for closed-world reasoning - Etherington, Mercer, et al. - 1985 |

32 | Autoepistemic logic and formalization of commonsense reasoning - Gelfond - 1989 |

28 | Between circumscription and autoepistemic logic - Lifschitz - 1989 |

18 | Non-monotonic formalisms and logic programming - Przymusinski - 1989 |

16 | On the relation between default theories and autoepistemic logic - Konolige - 1988 |

13 | Well--founded semantics: Theory and implementation - Przymusinski, Warren - 1992 |

9 | C.: On the relationship between nonmonotonic reasoning and logic programming - Przymusinski - 1988 |

8 |
Autoepistemic stable closures and contradiction resolution
- Morris
- 1989
(Show Context)
Citation Context ... believes that he can fix it. It is easy to see that this theory does not have any stable autoepistemic expansions in Moore's AEL, in spite of the fact that it seems to have a reasonable meaning (cf. =-=[Mor88]-=-). Therefore, in AEL = AEL cwa the theory T is inconsistent. On the other hand, T has precisely one stable autoepistemic expansion T in AEL circ , namely: T = T [ fLBrokenCarg obtained by adding to T ... |

8 | Well-founded completions of logic programs
- Przymusinski
- 1991
(Show Context)
Citation Context ...unded model: M P = f��Abnormal; Runs; ��SendF orRepairs; ��Brokeng:2 For a more detailed discussion of the relationship between autoepistemic logic and wellfounded semantics the reader is =-=referred to [Prz91c]-=-. Acknowledgments The author is grateful to Kurt Konolige, Mirek Truszczynski and to anonymous referees for their helpful comments. The author acknowledges support from the National Science Foundation... |

1 |
Semantics of disjunctive deductive databases
- Przymusinski
- 1991
(Show Context)
Citation Context ...d appears to be the most promising semantics for logic programs [PP90, PW91]. 5. Analogous results apply to the much broader class of all disjunctive logic programs or disjunctive deductive databases =-=[Prz91a]-=-. The significance of our results is at least twofold: ffl The new Autoepistemic Logic of Closed Beliefs AEL circ (based on circumscription CIRC) espouses a much more regular behavior than Moore's AEL... |