## Dualities between Alternative Semantics for Logic Programming and Nonmonotonic Reasoning (1998)

Venue: | Journal of Automated Reasoning |

Citations: | 88 - 8 self |

### BibTeX

@INPROCEEDINGS{Baral98dualitiesbetween,

author = {Chitta R. Baral and V. S. Subrahmanian},

title = {Dualities between Alternative Semantics for Logic Programming and Nonmonotonic Reasoning},

booktitle = {Journal of Automated Reasoning},

year = {1998},

pages = {69--86},

publisher = {MIT press}

}

### Years of Citing Articles

### OpenURL

### Abstract

The Gelfond-Lifschitz operator [GL88] associated with a logic program (and likewise the operator associated with default theories by Reiter) exhibits oscillating behavior. In the case of logic programs, there is always at least one finite, non-empty collection of Herbrand interpretations around which the Gelfond-Lifschitz [GL88] operator "bounces around". The same phenomenon occurs with default logic when Reiter's operator \Gamma \Delta is considered. Based on this, a "stable class" semantics and "extension class" semantics was proposed in [BS90]. The main advantage of this semantics was that it was defined for all logic programs (and default theories), and that this definition was modelled using the standard operators existing in the literature such as Reiter's \Gamma \Delta operator. In this paper, our primary aim is to prove that there is a very interesting duality between stable class theory and the well founded semantics for logic programming. In the stable class semantics, class...

### Citations

1855 |
Foundations of Logic Programming
- Lloyd
- 1987
(Show Context)
Citation Context ...(I) = T P I " !, i.e. F P (I) is the least Herbrand model of the negation free logic program P I . We assume that readers are familiar with the operator T P associated with the logic program P . =-=(cf. [L87]-=-). Definition 2.1 (Gelfond and Lifschitz) I is a stable model of P iff I = F P (I). Proposition 2.1 (Baral and Subrahmanian) Let P be any logic program. Then: F P is anti-monotone, i.e. if I 1 ` I 2 ,... |

1492 | The stable model semantics for logic programming
- Gelfond, Lifschitz
- 1988
(Show Context)
Citation Context ...onotonic Reasoning Chitta R. Baral and V.S. Subrahmanian Department of Computer Science University of Maryland College Park, MD 20742 U.S.A. September 21, 1998 Abstract The Gelfond-Lifschitz operator =-=[GL88]-=- associated with a logic program (and likewise the operator associated with default theories by Reiter) exhibits oscillating behavior. In the case of logic programs, there is always at least one finit... |

1422 |
A Logic for Default Reasoning
- Reiter
- 1980
(Show Context)
Citation Context ... class corresponding to the well-founded semantics of the program. Note, however, that there may be other strict stable classes of cardinality 2. 3 Default theories Default logic introduced by Reiter =-=[Rei80]-=- forms one of the most important formalisms for non-monotonic reasoning. Recently, the relationship between default logics and other forms of non-monotonic reasoning have been studied intensely (in pa... |

439 |
Semantical considerations on nonmonotonic logic
- Moore
- 1985
(Show Context)
Citation Context ...y for strong auto-epistemic logic, the logic of iterative expansions introduced by Marek and Truszczynski [MT89b], may be studied. 4 Autoepistemic theories Autoepistemic logic was introduced by Moore =-=[Moo85]-=-. Its relationship with logic program semantics has been extensively studied in the literature [GL88, MS88, MT89b]. Its relationship with other non-monotonic logics like default logic [MS88] and circu... |

336 | Logic programs with classical negation - Gelfond, Lifschitz |

221 |
Unfounded Sets and Well-founded Semantics for General Logic
- Gelder, Ross, et al.
- 1989
(Show Context)
Citation Context ... Introduction Various alternative semantics for logic programming with non-monotonic modes of negation have been proposed. Of these, the most popular semantics thus far are the well-founded semantics =-=[VRS88]-=- and the stable model semantics [GL88]. In this paper, we study the operator (we call it F P ) mapping interpretations to interpretations defined by Gelfond and Joint appointment with the University o... |

209 | The alternating fixpoint of logic programs with negation - Gelder - 1989 |

148 |
On the relation between default and autoepistemic logic
- Konolige
(Show Context)
Citation Context ...nt formalisms for non-monotonic reasoning. Recently, the relationship between default logics and other forms of non-monotonic reasoning have been studied intensely (in particular the work of Konolige =-=[Kon88]-=- and the work of Marek and Truszczynski [MT89a, Mar89] show that default and auto-epistemic logics are not that different after all). More recently, the relationship between logic program semantics an... |

96 |
Nonmonotonic logic II: non-monotonic modal theories
- McDermott
- 1982
(Show Context)
Citation Context ...nce rules. By K we denote the modal logic based on the axiom K, T denotes the logic based on axioms K and T, S4 is the logic based on K, T and 4, and S5 is based on K, T, 4 and 5. McDermott and Doyle =-=[McD82]-=- were the first ones to systematically study nonmonotonic reasoning within modal logic. Let S be a modal logic. By Cn S we mean the consequence operator for modal logic S, where S is any of the modal ... |

78 |
Power domains
- Smyth
- 1978
(Show Context)
Citation Context ...ams, and the stable class semantics both select certain minimal (w.r.t. certain orderings) stable classes. We show here that under two well-known orderings on power domains (Hoare and Smyth orderings =-=[Smy78]-=-) the well-founded semantics corresponds precisely to stable classes that are minimal w.r.t. Hoare's ordering. We show that this phenomenon also occurs in default logic and for suitable structures in ... |

63 |
General logical databases and programs: Default logic semantics and strati cation
- Bidoit, Froidevaux
- 1991
(Show Context)
Citation Context ...lowing two theorems formalize these relationships. Theorem 7 [BS90] M is a stable class of a program P iff E = fCn(M i ) j M i 2 Mg is an extension class of tr 1 (P ). 2 3 tr1 was first introduced in =-=[BF88]. The-=-orem 8 [BS90] Suppose M is a collection of interpretations. M is a stable class of program P iff there exists an extension class E of tr 2 (P ), such that M = fE i " AT j E i 2 Eg is an extension... |

56 |
Relating autoepistemic and default logics
- Marek, TruszczyĆski
- 1989
(Show Context)
Citation Context ...ic programming continue to hold for default theories. We show how the same technique may be applied to "strong" auto-epistemic logic: the logic of strong expansions proposed by Marek and Tru=-=szczynski [MT89a]-=-. 1 Introduction Various alternative semantics for logic programming with non-monotonic modes of negation have been proposed. Of these, the most popular semantics thus far are the well-founded semanti... |

52 |
Stable semantics for logic programs and default reasoning
- Marek, Truszczynski
- 1999
(Show Context)
Citation Context ...efault and auto-epistemic logics are not that different after all). More recently, the relationship between logic program semantics and non-monotonic logics has been studied by Marek and Truszczynski =-=[MT89b]-=- and by Marek and Subrahmanian [MS88]. In all these cases, correspondences are established between certain structures called extensions in default logic, and certain classes of models of logic program... |

51 |
Stable and extension class theory for logic programs and default logics
- Baral, Subrahmanian
- 1992
(Show Context)
Citation Context ...es around". The same phenomenon occurs with default logic when Reiter's operator \Gamma \Delta is considered. Based on this, a "stable class" semantics and "extension class" s=-=emantics was proposed in [BS90]-=-. The main advantage of this semantics was that it was defined for all logic programs (and default theories), and that this definition was modelled using the standard operators existing in the literat... |

34 |
The Relationship between Stable, Supported, Default and Autoepistemic Semantics for General Logic Programs. Theoretical Computer Science 103,365386
- Marek, Subrahmanian
- 1992
(Show Context)
Citation Context ...ot that different after all). More recently, the relationship between logic program semantics and non-monotonic logics has been studied by Marek and Truszczynski [MT89b] and by Marek and Subrahmanian =-=[MS88]-=-. In all these cases, correspondences are established between certain structures called extensions in default logic, and certain classes of models of logic programs. However, default theories may not ... |

26 | Autoepistemic modal logics
- Shvarts
(Show Context)
Citation Context ...All other results related to iterative expansions, iterative expansion classes hold. We call the set flfp(F 2 N;A ); gfp(F 2 N;A )g as the N \Gammawell-founded semantics. The logic K45 Shvarts proves =-=[SH90]-=- that Moore's expansions coincide with K45-expansions. As noted in the last section the function defined by Moore to specify expansions is not antimonotonic and can not be used to define a well-founde... |

15 |
Three-Valued Formalizations of Non-Monotonic Reasoning and Logic Programming
- Przymusinski
- 1989
(Show Context)
Citation Context ...pistemic logic. An additional advantage is that we may, based on our intended applications, choose different orderings (e.g. orderings based on cardinality) on the set of stable classes. Przymusinski =-=[Prz89]-=- has defined a well-founded semantics for default logics and autoepistemic logics. However, these semantics are based on the construction of new three valued reformulations of default and auto-epistem... |

12 | Stable theories in autoepistemic logic - Marek - 1989 |