## An Assumption-Based Framework for Non-Monotonic Reasoning (1993)

Venue: | Proc. 2nd International Workshop on Logic Programming and Non-monotonic Reasoning |

Citations: | 59 - 14 self |

### BibTeX

@INPROCEEDINGS{Bondarenko93anassumption-based,

author = {Andrei Bondarenko and Francesca Toni and Robert A. Kowalski},

title = {An Assumption-Based Framework for Non-Monotonic Reasoning},

booktitle = {Proc. 2nd International Workshop on Logic Programming and Non-monotonic Reasoning},

year = {1993},

pages = {171--189},

publisher = {MIT Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

The notion of assumption-based framework generalises and refines the use of abduction to give a formalisation of non-monotonic reasoning. In this framework, a sentence is a non-monotonic consequence of a theory if it can be derived monotonically from a theory extended by means of acceptable assumptions. The notion of acceptability for such assumptions is formulated in terms of their ability successfully to "counterattack" any "attacking" set of assumptions. One set of assumptions is said to "attack" another if the first set monotonically implies a consequence which is inconsistent with an assumption in the second set. This argumentation-theoretic criterion of acceptability is based on notions first introduced for logic programming and used to give a unified account of such diverse semantics for logic programming as stable models, partial stable models, preferred extensions, stable theories, well-founded semantics, and stationary semantics. The new framework makes it possible to general...

### Citations

1492 | The stable model semantics for logic programming
- Gelfond, Lifschitz
- 1988
(Show Context)
Citation Context ...his paper, this semantics corresponds to many of the semantics which have been proposed for different formalisms for non-monotonic reasoning, including the stable model semantics of logic programming =-=[8]-=-, and extensions in default logic [18], autoepistemic logic [15] and non-monotonic modal logic [14]. Intuitively, a consistent set of assumptions is stable if it attacks every assumption it does not c... |

1422 |
A Logic for Default Reasoning
- Reiter
- 1980
(Show Context)
Citation Context ... to many of the semantics which have been proposed for different formalisms for non-monotonic reasoning, including the stable model semantics of logic programming [8], and extensions in default logic =-=[18]-=-, autoepistemic logic [15] and non-monotonic modal logic [14]. Intuitively, a consistent set of assumptions is stable if it attacks every assumption it does not contain. Definition 2.8 A set of assump... |

772 | On the acceptability of arguments and its fundamental role in non-monotonic reasoning, logic programming and n-person games
- Dung
- 1995
(Show Context)
Citation Context ...1993). 2 This work was done while the author was a visitor at Imperial College 1 other formalisms for non-monotonic reasoning. The new framework was inspired by Dung's general argumentation framework =-=[6]-=-, but is formulated differently as a generalisation of the abductive frameworks of Poole [16] and Eshghi and Kowalski [7]. The new framework generalises the approach of [16] and shows how any monotoni... |

536 | Abductive logic programming
- Kakas, Kowalski, et al.
- 1992
(Show Context)
Citation Context ...rk, the assumption-based framework investigated in this paper generalises the notion of attacking and counterattacking sets of assumptions introduced for logic programming by Kakas, Kowalski and Toni =-=[13]-=-. It also defines a new notion of counterattack which improves upon previous definitions. The framework makes it possible to generalise various improvements first introduced for the semantics of logic... |

439 |
Semantical considerations on nonmonotonic logic
- Moore
- 1985
(Show Context)
Citation Context ...which have been proposed for different formalisms for non-monotonic reasoning, including the stable model semantics of logic programming [8], and extensions in default logic [18], autoepistemic logic =-=[15]-=- and non-monotonic modal logic [14]. Intuitively, a consistent set of assumptions is stable if it attacks every assumption it does not contain. Definition 2.8 A set of assumptions \Delta is stable (wi... |

370 |
A logical framework for default reasoning
- Poole, Goebel, et al.
- 1987
(Show Context)
Citation Context ...lisms for non-monotonic reasoning. The new framework was inspired by Dung's general argumentation framework [6], but is formulated differently as a generalisation of the abductive frameworks of Poole =-=[16]-=- and Eshghi and Kowalski [7]. The new framework generalises the approach of [16] and shows how any monotonic logic can be extended to a non-monotonic logic by appropriately identifying a set of candid... |

336 |
Logic programs with classical negation
- Gelfond, Lifschitz
(Show Context)
Citation Context ... : : ; l n l where l 2 HB e , l 1 ; : : : ; l n 2 Lit e , and ns0, and of the form l; not l ? where l 2HB e , ffl Ab = fnot l j l 2 HB e g. The negation denoted by : is called "classical" ne=-=gation in [9]. However,-=- in this paper we use the term "explicit" negation, because clauses of extended logic programs are treated more like inference rules than like classical implications. The instance of the def... |

221 |
Unfounded Sets and Well-founded Semantics for General Logic
- Gelder, Ross, et al.
- 1989
(Show Context)
Citation Context ...nterattacks any attack against that assumption. A set of assumptions is grounded if it is minimally complete. In logic programming the notion of groundedness corresponds to the well-founded semantics =-=[20, 4]-=-. Definition 2.6 A set of assumptions \Delta is complete (with respect to a theory T ) if and only if ffl T [ \Delta is consistent, and ffl \Delta = fff j ff 2 Ab and 8 A` Ab, if A attacks fffg, then ... |

203 |
Abduction compared with negation as failure
- Eshghi, Kowalski
(Show Context)
Citation Context ...ning. The new framework was inspired by Dung's general argumentation framework [6], but is formulated differently as a generalisation of the abductive frameworks of Poole [16] and Eshghi and Kowalski =-=[7]-=-. The new framework generalises the approach of [16] and shows how any monotonic logic can be extended to a non-monotonic logic by appropriately identifying a set of candidate assumptions and specifyi... |

199 | Preferred Subtheories: An Extended Logical Framework for Default Reasoning
- Brewka
- 1989
(Show Context)
Citation Context ...ted. Consequently, the framework defined in section 3 is a special case of the framework presented here. This framework is related to the extension of Poole's abductive framework introduced by Brewka =-=[2]-=-. One major difference between our approaches is that Brewka defines preference between abducibles whereas we define preferences more generally between formulae of the language. Further work is necess... |

127 | Stable models and non-determinism in logic programs with negation
- SaccĂ , Zaniolo
- 1990
(Show Context)
Citation Context ...n a set of assumptions \Delta, P [ \Delta is a preferred extension in the sense of [4] (and P [ \Delta is an admissible scenario [4]) of P if and only if Th(P [ \Delta)" Lit is a partial stable m=-=odel [19]-=- of P if and only if \Delta is preferred (\Delta is admissible respectively) with respect to P . This theorem is an immediate consequence of results presented by Dung in [4, 6], together with results ... |

109 |
Generalized stable models: a semantics for abduction
- Kakas, Mancarella
- 1990
(Show Context)
Citation Context ...kly stable [11], which is a mistake. 10 Note that in this approach the integrity constraints I are used only to check consistency, and not to create attacks. The generalised stable model semantics of =-=[10]-=- is a special case of the general definition of stability. Theorem 4.1 Given an abductive logic program hP; Ab 0 ; Ii, M is a generalised stable model [10] of hP; Ab 0 ; Ii if and only if there is a s... |

96 | Nonmonotonic logic II: non-monotonic modal theories - McDermott - 1982 |

57 |
Stationary semantics for disjunctive logic programs and deductive databases
- Przymusinski
- 1990
(Show Context)
Citation Context ...t M = E"HB; (b) given a set of assumptions \Delta, P [ \Delta is a complete scenario [4] (and Th(P [ \Delta)"Lit is a well-founded model [20]) of P if and only if P [ \Delta is a stationary =-=expansion [17]-=- of P if and only if \Delta is complete (grounded respectively) with respect to P ; (c) given a set of assumptions \Delta, P [ \Delta is a preferred extension in the sense of [4] (and P [ \Delta is an... |

33 |
Negation as hypothesis: an abductive foundation for logic programming
- Dung
- 1991
(Show Context)
Citation Context ...nterattacks any attack against that assumption. A set of assumptions is grounded if it is minimally complete. In logic programming the notion of groundedness corresponds to the well-founded semantics =-=[20, 4]-=-. Definition 2.6 A set of assumptions \Delta is complete (with respect to a theory T ) if and only if ffl T [ \Delta is consistent, and ffl \Delta = fff j ff 2 Ab and 8 A` Ab, if A attacks fffg, then ... |

27 |
Stable theories for logic programs
- Kakas, Mancarella
(Show Context)
Citation Context ...framework. The interpretation of negative literals as abducibles was first presented in [7], and was the basis for the preferred extension semantics [4], the stable theory and acceptability semantics =-=[11]-=-, and the argumentation-theoretic interpretation for the semantics of logic programming presented in [13]. The instance of the definition 2.2 of attack for the assumption-based framework h(L; R); Abi ... |

23 |
Well-founded reasoning with classical negation
- Dung, Ruamviboonsuk
- 1991
(Show Context)
Citation Context ... E of the theory P [ fl / p; :p j l 2 HB e , and p 2 HBg in the corresponding assumption-based framework and M = E"HB e . 4.3.2 The Dung and Ruamviboonsuk semantics Dung and Ruamviboonsuk's seman=-=tics [5]-=- is a special case of admissibility semantics with counterattacks 1 where extended logic programs are further extended by the integrity constraints f?/ p; :p j p 2 HBg. Theorem 4.3 Given an extended l... |

19 | Preferred extensions are partial stable models - Kakas, Mancarella - 1992 |

10 |
Normal logic programs as open positive programs
- Brogi, Lamma, et al.
(Show Context)
Citation Context ... P if and only if \Delta is preferred (\Delta is admissible respectively) with respect to P . This theorem is an immediate consequence of results presented by Dung in [4, 6], together with results in =-=[3]-=- and [12]. The following example shows that preferred extensions are better than stable models. 7 Example 3.1 The program fp / not pg has no stable extension, but it has a preferred extension correspo... |

2 |
Abductive systems for non-monotonic reasoning
- Bondarenko
- 1991
(Show Context)
Citation Context ...mptions \Delta and A, in the assumption-based framework corresponding to D, A attacks \Delta if and only if T [ A ` :OE, for some M OE 2 \Delta. The following theorem is a consequence of a theorem in =-=[1]. The-=-orem 5.1 E is an extension [18] of a default theory (T ; D) if and only if there is a stable extension E 0 of T in the assumption-based framework corresponding to D and E = E 0 " L 0 . As we have... |