### Citations

734 |
A truth maintenance system
- Doyle
- 1985
(Show Context)
Citation Context ...n. RE(/L )-answer sets are in oneto -one correspondence with the generalized stable models of [11] , and hence, they provide the dependency-directed backtracking mechanism of justification-based TMSs =-=[6]-=- with a logical characterization. Theorem 3.13 Let P be a normal logic program with constraints. There is a one to one correspondence between consistent RE (/L )-answer sets of P and generalized stabl... |

369 |
Logic programs with classical negation.
- Gelfond, Lifschitz
- 1990
(Show Context)
Citation Context ...y, and let L denote the literal complementary to L . A default literal is a formula notL where L is an objective literal. We assume the reader to be familiar with extended logic programs (ELP's); see =-=[10]-=- for the definition of their syntax and semantics. Notation: the unique answer set of monotonic programs will be denoted by ANS(P ); the Gelfond-Lifschitz transformation of P w.r.t. S ` LIT will be de... |

240 | Automated Theorem Proving: A Logical Basis - Loveland - 1978 |

192 |
Nonmonotonic Logic: Context-Dependent Reasoning. 70 Robotic Soccer
- Marek, Truszczynski
- 1993
(Show Context)
Citation Context ...gation and various forms of implication 2.2 Default and Autoepistemic Logic We assume the reader to be familiar with default logic (DL) and autoepistemic logic (AEL) . For an extensive treatment, see =-=[12, 13]-=- . A few variants of DL and AEL are briefly recalled in this section. Baral and Subrahmanian [3] generalized default extensions by introducing the notion of extension class, that is a family of sets F... |

130 | Well founded semantics for logic programs with explicit negation.
- Pereira, Alferes
- 1992
(Show Context)
Citation Context ...re, Incomplete Information 1 Introduction Research on extended logic programs (ELP's) has been focussed on the semantics of default negation, not , and on its interplay with explicit negation, : (cf. =-=[16]-=-) . While several semantics have been proposed for not , there is little variety of meanings for the not -free fragment of the language, hereafter called monotonic. In [4] , the semantics of monotonic... |

120 | On stratified autoepistemic theories. - Gelfond - 1987 |

108 |
Seventy-five problems for testing automatic theorem provers
- Pelletier
- 1986
(Show Context)
Citation Context ...trary, contraposition makes it possible to solve in a natural and efficient way many difficult benchmark problems for automatic theorem provers. About 60% of the benchmarks without equality listed in =-=[15]-=- --- including some of the most difficult ones, according to Pelletier's rating---can be solved through / Lukasiewicz's semantics, and contraposition proves to be essential (cf. [4]) . This is an asto... |

93 | Dualities between alternative semantics for logic programming and nonmonotonic reasoning (extended abstract
- Baral, Subrahmanian
- 1991
(Show Context)
Citation Context ... = f S 1 ; S 2 g , where S 1 ` S 2 , F TR;/ P (S 1 ) = S 2 and F TR;/ P (S 2 ) = S 1 , then we say that F is an alternating TR(/)-answer set of P , and denote F by (S 1 ; S 2 ) . The major results of =-=[2]-=- can be immediately extended to our framework. First of all, F TR;/ P is anti-monotonic when TR is GL or the transformation RE which will be introduced in Sec. 3.2. Secondly, when F TR;/ P is anti-mon... |

57 |
Stable semantics for logic programs and default reasoning.
- Marek, Truszczyrlski
- 1989
(Show Context)
Citation Context ...eaning of monotonic ELP's. This result can easily be extended to unrestricted ELP's. Actually, we shall prove a more general result, relating ELP's with default logic. By following the terminology in =-=[14]-=-, given a program P , we will denote by tr 1 (P ) the default theory h ;; D i where D is the set of defaults L 1s: : :sLm : :Lm+1 ; : : : ; :L n = L 0 , such that L 0 / L 1 ; : : : ; Lm ; notLm+1 ; : ... |

54 |
Stable and extension class theory for logic programs and default logics
- Baral, Subrahmanian
- 1992
(Show Context)
Citation Context ...e familiar with default logic (DL) and autoepistemic logic (AEL) . For an extensive treatment, see [12, 13] . A few variants of DL and AEL are briefly recalled in this section. Baral and Subrahmanian =-=[3]-=- generalized default extensions by introducing the notion of extension class, that is a family of sets F such that F = f \Gamma \Delta (E) j E 2 F g , where \Gamma \Delta is Reiter's operator. This ap... |

51 | Natural 3-valued logics : characterization and proof theory.
- Avron
- 1991
(Show Context)
Citation Context ...ls are recalled in Fig. 1 where /K is Kleene's implication, /L is the one proposed by / Lukasiewicz, and ( is a less famous but important implication which has been considered by several authors (cf. =-=[1]-=-) and has been applied to non-monotonic reasoning [5] . The classical equivalence AsB j A /K :B holds for Kleene's implication but not for /L . The latter corresponds to a disjunction, usually denoted... |

22 |
Autoepistemic logic of knowledge
- Schwarz
- 1991
(Show Context)
Citation Context ...F such that F = f \Gamma \Delta (E) j E 2 F g , where \Gamma \Delta is Reiter's operator. This approach is more robust than DL ; in fact, every finite closed default theory has an extension class. In =-=[17]-=- , Schwartz introduced a variant of AEL based on the notion of reflexive expansions, which are the solutions of E = f / j T [ (LE j E) [ :LE ` / g ; (1) where LE j E is an abbreviation for f L/ $ / j ... |

18 | Autoepistemic logics as a unifying framework for the semantics of logic programs - Bonatti - 1995 |

14 |
AlberioMarttelli; Generalized Stable Models, Truth Maintenance and Conflict Resolution
- GIORDANO
- 1990
(Show Context)
Citation Context ...paper, we generalize this approach to unrestricted ELPs. We obtain a unifying view of many formalisms, including the answer set semantics, the well-founded semantics, generalized stable models (as in =-=[11]-=-), default logic, autoepistemic logic (AEL) and some of its variants (three-valued AEL and Schwartz's reflexive AEL) . Our framework highlights surprising similarities between previously unrelated for... |

13 |
Skeptical reason maintenance and belief revision
- Witteveen, Brewka
- 1993
(Show Context)
Citation Context ...ncy. Moreover, a well-founded version of / Lukasiewicz's semantics constitutes a natural semantics for Reason Maintenance, more powerful and more efficient than the skeptical belief revision model of =-=[18]-=- . 2 Preliminaries 2.1 Three-Valued Logic Three-valued interpretations are mappings from the set of ground atoms into the set f F; U; T g . As usual, three-valued interpretations will be represented a... |

3 |
Non-Monotonic Reasoning
- Lukasiewicz
- 1990
(Show Context)
Citation Context ...gation and various forms of implication 2.2 Default and Autoepistemic Logic We assume the reader to be familiar with default logic (DL) and autoepistemic logic (AEL) . For an extensive treatment, see =-=[12, 13]-=- . A few variants of DL and AEL are briefly recalled in this section. Baral and Subrahmanian [3] generalized default extensions by introducing the notion of extension class, that is a family of sets F... |

1 |
On the monotonic fragment of extended logic programs
- Bonatti
(Show Context)
Citation Context ...ms Piero A. Bonatti and Laura Giordano Dipartimento di Informatica, Universit`a di Torino Corso Svizzera 185, I-10149 Torino, Italy email: fbonatti,laurag@di.unito.it tel: +39-11-7429 111 Abstract In =-=[4]-=- , the semantics of monotonic (i.e. not -free) extended logic programs (ELPs) has been rephrased in three-valued logic for two purposes: achieving tractable reasoning with incomplete information and u... |

1 | Handbook of philosophical logic, Vol. III: Alternatives to classical logic - Gabbay, Guenthner - 1986 |

1 | Solving the Steamroller and other puzzles with extended disjunctive logic programs
- Wagner
- 1994
(Show Context)
Citation Context ...e problems that can be successfully solved include Schubert's Steamroller---one of the two most difficult problems of [15] ---and the Dreadsbury Mansion Mistery. Both have been recently considered in =-=[19]-=- , where a nonmonotonic version of the Steamroller is introduced and proposed as a benchmark. In the following example, we show how the non-monotonic Steamroller can be solved through / Lukasiewicz's ... |