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## A Sequent Calculus for Skeptical Default Logic (1997)

Venue: | Proc. of the Int. Conf. on Automated Reasoning with Analytic Tableaux and Related Methods, Springer-Verlag LNCS 1227 |

Citations: | 8 - 1 self |

### Citations

1651 |
A logic for default reasoning.,"
- Reiter
- 1980
(Show Context)
Citation Context ... a brief comparison between the skeptical calculus and the credulous calculus of [6] . 2 Preliminaries 2.1 Propositional Default Logic Here, only some basic notions are recalled; for more details see =-=[34, 22]-=- . Let L be a standard propositional language. A default is an inference rule of the form: ff : fi 1 ; \Delta \Delta \Delta ; fi n fl , sometimes denoted by ff : fi 1 ; \Delta \Delta \Delta ; fi n = f... |

965 | Circumscription—a form of non-monotonic reasoning. - McCarthy - 1980 |

626 | Nonmonotonic reasoning, preferential models and cumulative logics.
- Kraus, Lehmann, et al.
- 1990
(Show Context)
Citation Context ...27, 3, 4, 7, 35, 1, 2, 31, 36]). On the other hand, the proof-theoretic aspects are not yet completely understood. The fundamental papers by Gabbay [14] , Makinson [24] and Kraus, Lehmann and Magidor =-=[19]-=- , focus their attention on general properties of non-monotonic inference, rather than on specific formalisms. In particular, they do not axiomatize any form of non-monotonic assumption making. A simi... |

203 |
Theoretical foundation for non-monotonic reasoning, Part II: Structured non-monotonic theories.
- Gabbay
- 1991
(Show Context)
Citation Context ...g. see [22, 26, 13, 17, 18, 9, 29, 33, 25] and [30, 27, 3, 4, 7, 35, 1, 2, 31, 36]). On the other hand, the proof-theoretic aspects are not yet completely understood. The fundamental papers by Gabbay =-=[14]-=- , Makinson [24] and Kraus, Lehmann and Magidor [19] , focus their attention on general properties of non-monotonic inference, rather than on specific formalisms. In particular, they do not axiomatize... |

198 |
All I know: A study in autoepistemic logic.
- Levesque
- 1990
(Show Context)
Citation Context ...deration holds for the papers by Bochman [5] and Nait Abdallah [28]. The only complete axiomatizations are Levesque's Hilbert-style system for skeptical reasoning in a generalized autoepistemic logic =-=[20]-=-, 2 Olivetti's sequent calculus for minimal entailment [32] , and Bonatti's sequent calculi for credulous reasoning in default logic and normal autoepistemic logic [6] . A novel feature of [6] is the ... |

162 |
On the relation between default and autoepistemic logic.
- Konolige
- 1988
(Show Context)
Citation Context ...esentation and commonsense reasoning, as well as in the theory of programming languages. 1 The semantic and algorithmic aspects of non-monotonic reasoning have been extensively investigated (e.g. see =-=[22, 26, 13, 17, 18, 9, 29, 33, 25]-=- and [30, 27, 3, 4, 7, 35, 1, 2, 31, 36]). On the other hand, the proof-theoretic aspects are not yet completely understood. The fundamental papers by Gabbay [14] , Makinson [24] and Kraus, Lehmann an... |

158 | Embedding defaults into terminological knowledge representation formalisms’,
- Baader, Hollunder
- 1995
(Show Context)
Citation Context ... well as in the theory of programming languages. 1 The semantic and algorithmic aspects of non-monotonic reasoning have been extensively investigated (e.g. see [22, 26, 13, 17, 18, 9, 29, 33, 25] and =-=[30, 27, 3, 4, 7, 35, 1, 2, 31, 36]-=-). On the other hand, the proof-theoretic aspects are not yet completely understood. The fundamental papers by Gabbay [14] , Makinson [24] and Kraus, Lehmann and Magidor [19] , focus their attention o... |

128 |
General theory of cumulative inference
- Makinson
- 1989
(Show Context)
Citation Context ...13, 17, 18, 9, 29, 33, 25] and [30, 27, 3, 4, 7, 35, 1, 2, 31, 36]). On the other hand, the proof-theoretic aspects are not yet completely understood. The fundamental papers by Gabbay [14] , Makinson =-=[24]-=- and Kraus, Lehmann and Magidor [19] , focus their attention on general properties of non-monotonic inference, rather than on specific formalisms. In particular, they do not axiomatize any form of non... |

69 | A Circumscriptive Theorem Prover, - Ginsberg - 1989 |

68 |
Cumulative Default Logic: in defense of nonmonotonic inference rules,
- Brewka
- 1991
(Show Context)
Citation Context ...esentation and commonsense reasoning, as well as in the theory of programming languages. 1 The semantic and algorithmic aspects of non-monotonic reasoning have been extensively investigated (e.g. see =-=[22, 26, 13, 17, 18, 9, 29, 33, 25]-=- and [30, 27, 3, 4, 7, 35, 1, 2, 31, 36]). On the other hand, the proof-theoretic aspects are not yet completely understood. The fundamental papers by Gabbay [14] , Makinson [24] and Kraus, Lehmann an... |

44 |
Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic.
- Lukasiewicz
- 1951
(Show Context)
Citation Context ...l entailment [32] , and Bonatti's sequent calculi for credulous reasoning in default logic and normal autoepistemic logic [6] . A novel feature of [6] is the use of an axiomatic rejection method (cf. =-=[21, 37, 38, 10, 11, 40, 41, 39, 8]-=-) for checking the consistency of the defaults' justifications, and for deriving negative autoepistemic literals (disbeliefs). In the present paper, we proceed along the line of research initiated in ... |

30 | Computing intersection of autoepistemic expansions.
- Marek, Truszczynski
- 1991
(Show Context)
Citation Context ... well as in the theory of programming languages. 1 The semantic and algorithmic aspects of non-monotonic reasoning have been extensively investigated (e.g. see [22, 26, 13, 17, 18, 9, 29, 33, 25] and =-=[30, 27, 3, 4, 7, 35, 1, 2, 31, 36]-=-). On the other hand, the proof-theoretic aspects are not yet completely understood. The fundamental papers by Gabbay [14] , Makinson [24] and Kraus, Lehmann and Magidor [19] , focus their attention o... |

29 | Towards efficient default reasoning
- Niemelä
- 1995
(Show Context)
Citation Context ... well as in the theory of programming languages. 1 The semantic and algorithmic aspects of non-monotonic reasoning have been extensively investigated (e.g. see [22, 26, 13, 17, 18, 9, 29, 33, 25] and =-=[30, 27, 3, 4, 7, 35, 1, 2, 31, 36]-=-). On the other hand, the proof-theoretic aspects are not yet completely understood. The fundamental papers by Gabbay [14] , Makinson [24] and Kraus, Lehmann and Magidor [19] , focus their attention o... |

22 |
A tableaux and Sequent Calculus for Minimal Entailment
- Olivetti
- 1992
(Show Context)
Citation Context ...lah [28]. The only complete axiomatizations are Levesque's Hilbert-style system for skeptical reasoning in a generalized autoepistemic logic [20], 2 Olivetti's sequent calculus for minimal entailment =-=[32]-=- , and Bonatti's sequent calculi for credulous reasoning in default logic and normal autoepistemic logic [6] . A novel feature of [6] is the use of an axiomatic rejection method (cf. [21, 37, 38, 10, ... |

21 | On the relation between autoepistemic logic and circumscription
- Konolige
- 1989
(Show Context)
Citation Context ...esentation and commonsense reasoning, as well as in the theory of programming languages. 1 The semantic and algorithmic aspects of non-monotonic reasoning have been extensively investigated (e.g. see =-=[22, 26, 13, 17, 18, 9, 29, 33, 25]-=- and [30, 27, 3, 4, 7, 35, 1, 2, 31, 36]). On the other hand, the proof-theoretic aspects are not yet completely understood. The fundamental papers by Gabbay [14] , Makinson [24] and Kraus, Lehmann an... |

20 |
Implementing stable semantics by linear programming
- Bell, Nerode, et al.
- 1993
(Show Context)
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15 |
Decision procedure for autoepistemic logic
- Niemelä
- 1988
(Show Context)
Citation Context |

12 |
Implementing Deductive Databases by Linear Programming,
- Bell, Nerode, et al.
- 1991
(Show Context)
Citation Context |

11 |
Tableaux-based characterization and theorem proving for default logic
- Risch, Schwind
- 1994
(Show Context)
Citation Context |

10 |
Proving unprovability
- Tiomkin
- 1988
(Show Context)
Citation Context ...l entailment [32] , and Bonatti's sequent calculi for credulous reasoning in default logic and normal autoepistemic logic [6] . A novel feature of [6] is the use of an axiomatic rejection method (cf. =-=[21, 37, 38, 10, 11, 40, 41, 39, 8]-=-) for checking the consistency of the defaults' justifications, and for deriving negative autoepistemic literals (disbeliefs). In the present paper, we proceed along the line of research initiated in ... |

9 |
Completeness proofs for the intuitionistic sentential calculus
- Scott
- 1957
(Show Context)
Citation Context ...l entailment [32] , and Bonatti's sequent calculi for credulous reasoning in default logic and normal autoepistemic logic [6] . A novel feature of [6] is the use of an axiomatic rejection method (cf. =-=[21, 37, 38, 10, 11, 40, 41, 39, 8]-=-) for checking the consistency of the defaults' justifications, and for deriving negative autoepistemic literals (disbeliefs). In the present paper, we proceed along the line of research initiated in ... |

8 | A proof theoretical approach to default reasoning I: Tableaux for default logic
- Amati, Aiello, et al.
- 1996
(Show Context)
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8 |
A Formal System for the Non-Theorems of the Propositional Calculus
- Caicedo
- 1978
(Show Context)
Citation Context |

8 |
The method of axiomatic rejection for the intuitionistic propositional logic
- Dutkiewicz
- 1989
(Show Context)
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7 |
A Gentzen system for non-theorems
- Bonatti
- 1993
(Show Context)
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5 |
On the relation between default and modal consequence relations
- Bochman
- 1994
(Show Context)
Citation Context ...non-monotonic inference, rather than on specific formalisms. In particular, they do not axiomatize any form of non-monotonic assumption making. A similar consideration holds for the papers by Bochman =-=[5]-=- and Nait Abdallah [28]. The only complete axiomatizations are Levesque's Hilbert-style system for skeptical reasoning in a generalized autoepistemic logic [20], 2 Olivetti's sequent calculus for mini... |

5 | Complementary logics for classical propositional languages”, Kriterion. Zeitschrift für Philosophie
- Varzi
- 1992
(Show Context)
Citation Context |

4 | Autoepistemic logic programming - Bonatti - 1994 |

3 | An extended framework for default reasoning
- Abdallah
- 1989
(Show Context)
Citation Context ...e, rather than on specific formalisms. In particular, they do not axiomatize any form of non-monotonic assumption making. A similar consideration holds for the papers by Bochman [5] and Nait Abdallah =-=[28]-=-. The only complete axiomatizations are Levesque's Hilbert-style system for skeptical reasoning in a generalized autoepistemic logic [20], 2 Olivetti's sequent calculus for minimal entailment [32] , a... |

3 |
Complementary sentential logics
- Varzi
- 1990
(Show Context)
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2 |
calculi for default and autoepistemic logics
- Sequent
- 1996
(Show Context)
Citation Context ...generalized autoepistemic logic [20], 2 Olivetti's sequent calculus for minimal entailment [32] , and Bonatti's sequent calculi for credulous reasoning in default logic and normal autoepistemic logic =-=[6]-=- . A novel feature of [6] is the use of an axiomatic rejection method (cf. [21, 37, 38, 10, 11, 40, 41, 39, 8]) for checking the consistency of the defaults' justifications, and for deriving negative ... |

2 |
A first step towards autoepistemic logic programming
- Jiang
- 1992
(Show Context)
Citation Context ...g. 1 We mention the semantics of negation in logic programming, inheritance in object oriented languages, and the structured operational semantics of process algebras. 2 From Levesque's system, Jiang =-=[16]-=- derived a resolution principle for clausal autoepistemic theories. -- It constitutes an intermediate step toward a general framework, where different proof strategies and heuristics can be explored a... |

2 |
Non-Monotonic Reasoning
- Lukasziewicz
- 1990
(Show Context)
Citation Context |

2 |
Trusczy'nski (eds). Logic Programming and Nonmonotonic Reasoning
- Marek, Nerode, et al.
- 1995
(Show Context)
Citation Context |

2 |
Nerode (eds.). Logic Programming and Non-monotonic Reasoning
- Pereira, A
(Show Context)
Citation Context |

2 |
Theory of rejected propositions. Studia Logica
- Slupecki, Bryll, et al.
- 1971
(Show Context)
Citation Context |

1 |
A new methodology for query answering in default logics via structureoriented theorem proving
- Schaub
- 1995
(Show Context)
Citation Context |