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## Inverse Entailment for Full Clausal Theories (2001)

Venue: | In: LICS-2001 Workshop on Logic and Learning |

Citations: | 6 - 0 self |

### Citations

714 | Inverse entailment and progol
- Muggleton
- 1995
(Show Context)
Citation Context ...1 = f8x(human(x) oe mortal(x))g satisfies (1). In fact, B 1s:E 1 = fhuman(s); :mortal(s)g j= 9x(human(x)s:mortal(x)) = :H 1 : 1 The equation (2) can be seen in literature, e.g., [8] for abduction and =-=[13]-=- for induction. While the equation (2) is useful for computing abductive explanations of observations in abduction, it is more difficult to apply it to compute inductive hypotheses. In abduction, with... |

103 |
Linear resolution for consequence finding
- Inoue
- 1992
(Show Context)
Citation Context ... E 1 = fmortal(s)g, H 1 = f8x(human(x) oe mortal(x))g satisfies (1). In fact, B 1s:E 1 = fhuman(s); :mortal(s)g j= 9x(human(x)s:mortal(x)) = :H 1 : 1 The equation (2) can be seen in literature, e.g., =-=[8]-=- for abduction and [13] for induction. While the equation (2) is useful for computing abductive explanations of observations in abduction, it is more difficult to apply it to compute inductive hypothe... |

80 |
Causes of Events: Their Computation and Application
- Cox, Pietrzykowski
(Show Context)
Citation Context ...is the use of a generalizer (see [19], for example) which constructs a clausal theory H such that every clause in F is entailed by some clause in H. 1 In some case, reverse Skolemization in abduction =-=[1]-=- also works as a generalizer, but there exist other techniques to generalize clauses such as anti-instantiation (i.e., replacement of terms with variables), addition of clauses, dropping literals from... |

44 |
A Completeness Theorem and a Computer Program for Finding Theorems Derivable from Given Axioms
- Lee
- 1967
(Show Context)
Citation Context ...sequence-Finding For a clausal theory 6, a consequence of 6 is a clause entailed by 6. We denote by Th(6) the set of all consequences of 6. The consequence-finding problem is firstly addressed by Lee =-=[11]-=- in the context of resolution principle. Lee proved that, for any consequence D of 6, the resolution principle can derive a clause C from 6 such that C entails D. In this sense, the resolution princip... |

42 |
Induction as nonmonotonic inference
- Helft
- 1989
(Show Context)
Citation Context .... That is, given a background theory B and observations (or positive examples) E, the task of induction and abduction is common in finding hypotheses H such that BsH j= E; (1) where BsH is consistent =-=[7, 3, 6, 10]-=-. While the logic is in common, they differ in the usage in applications. According to Peirce, abduction infers a cause of an observation, and can infer something quite different from what is observed... |

34 |
Consequence finding algorithms
- Marquis
- 2000
(Show Context)
Citation Context ...nerality, E is written in a ground atom, and each H is usually assumed to be a conjunction of literals. These conditions make abductive computation relatively easy, and consequence-finding algorithms =-=[8, 2, 12]-=- can be directly applied. In induction, however, E can be clauses and H is usually a general rule. Universally quantified rules for H cannot be easily obtained from the negation of consequences of Bs:... |

26 | Which hypotheses can be found with inverse entailment
- Yamamoto
- 1997
(Show Context)
Citation Context ..., it is incomplete for finding hypotheses satisfying (1). Then, several improvements have been reported to make inverse entailment complete [14, 5, 19] or to characterize inverse entailment precisely =-=[17, 18, 15]-=-. However, such improved inductive procedures are not very simple when compared with abductive computation. More seriously, some improved procedures are unsound even though they are complete. Another ... |

24 | A new method for consequence finding and compilation in restricted language
- Val, A
- 1999
(Show Context)
Citation Context ...nerality, E is written in a ground atom, and each H is usually assumed to be a conjunction of literals. These conditions make abductive computation relatively easy, and consequence-finding algorithms =-=[8, 2, 12]-=- can be directly applied. In induction, however, E can be clauses and H is usually a general rule. Universally quantified rules for H cannot be easily obtained from the negation of consequences of Bs:... |

19 |
Abduction and inductive learning
- Dimopoulos, Kakas
- 1996
(Show Context)
Citation Context .... That is, given a background theory B and observations (or positive examples) E, the task of induction and abduction is common in finding hypotheses H such that BsH j= E; (1) where BsH is consistent =-=[7, 3, 6, 10]-=-. While the logic is in common, they differ in the usage in applications. According to Peirce, abduction infers a cause of an observation, and can infer something quite different from what is observed... |

15 | Inverse Entailment and - Muggleton - 1995 |

8 | Satoh: Completeness of pruning methods for consequence finding procedure SOL
- Iwanuma, Inoue, et al.
- 2000
(Show Context)
Citation Context ...focuses on deriving only those consequences belonging to the production field P. Various pruning methods are also introduced to enhance the efficiency of SOL resolution in a connection-tableau format =-=[9]-=-. Instead of ME, SFK resolution [2] is a variant of ordered resolution, which is enhanced with the Skip rule for finding characteristic clauses. An extensive survey of consequence-finding algorithms i... |

7 | Abduction and induction from a non-monotonic reasoning perspective. In: Abduction and Induction:
- Lachiche
- 2000
(Show Context)
Citation Context .... That is, given a background theory B and observations (or positive examples) E, the task of induction and abduction is common in finding hypotheses H such that BsH j= E; (1) where BsH is consistent =-=[7, 3, 6, 10]-=-. While the logic is in common, they differ in the usage in applications. According to Peirce, abduction infers a cause of an observation, and can infer something quite different from what is observed... |

4 |
Using abduction for induction based on bottom generalization
- Yamamoto
- 2000
(Show Context)
Citation Context ..., it is incomplete for finding hypotheses satisfying (1). Then, several improvements have been reported to make inverse entailment complete [14, 5, 19] or to characterize inverse entailment precisely =-=[17, 18, 15]-=-. However, such improved inductive procedures are not very simple when compared with abductive computation. More seriously, some improved procedures are unsound even though they are complete. Another ... |

4 |
Hypothesis Finding via Residue Hypotheses with the Resolution Principle
- Yamamoto, FronhÃ¶fer
- 2000
(Show Context)
Citation Context ...), i.e., H j= ?(E;B): While this method is adopted in Progol, it is incomplete for finding hypotheses satisfying (1). Then, several improvements have been reported to make inverse entailment complete =-=[14, 5, 19]-=- or to characterize inverse entailment precisely [17, 18, 15]. However, such improved inductive procedures are not very simple when compared with abductive computation. More seriously, some improved p... |

2 |
On the completion of the most specific hypothesis computation in inverse entailment for mutual recursion
- Furukawa
- 1998
(Show Context)
Citation Context ...), i.e., H j= ?(E;B): While this method is adopted in Progol, it is incomplete for finding hypotheses satisfying (1). Then, several improvements have been reported to make inverse entailment complete =-=[14, 5, 19]-=- or to characterize inverse entailment precisely [17, 18, 15]. However, such improved inductive procedures are not very simple when compared with abductive computation. More seriously, some improved p... |

1 |
Theory completion and inverse
- Muggleton, Bryant
- 2000
(Show Context)
Citation Context ..., it is incomplete for finding hypotheses satisfying (1). Then, several improvements have been reported to make inverse entailment complete [14, 5, 19] or to characterize inverse entailment precisely =-=[17, 18, 15]-=-. However, such improved inductive procedures are not very simple when compared with abductive computation. More seriously, some improved procedures are unsound even though they are complete. Another ... |