## Reference classes and multiple inheritances (1995)

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Venue: | International Journal of Uncertainty, Fuzziness and and Knowledge-based Systems |

Citations: | 7 - 7 self |

### BibTeX

@ARTICLE{Wang95referenceclasses,

author = {Pei Wang},

title = {Reference classes and multiple inheritances},

journal = {International Journal of Uncertainty, Fuzziness and and Knowledge-based Systems},

year = {1995},

pages = {79--91}

}

### Years of Citing Articles

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### Abstract

The reference class problem in probability theory and the multiple inheritances (extensions) problem in non-monotonic logics can be referred to as special cases of con icting beliefs. The current solution accepted in the two domains is the speci city priority principle. By analyzing an example, several factors (ignored by the principle) are found to be relevant to the priority of a reference class. A new approach, Non-Axiomatic Reasoning System (NARS), is discussed, where these factors are all taken into account. It is argued that the solution provided by NARS is better than the solutions provided by probability theory and non-monotonic logics. 1

### Citations

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Probabilistic Reasoning in Intelligent Systems
- Pearl
- 1988
(Show Context)
Citation Context ...o paradigms that use this type of inference: non-monotonic logics (for example, Touretzky's inheritance network in [15]), and probabilistic reasoning systems (for example, Pearl's Bayesian network in =-=[9]). In non-monotonic logics, if-=- the only relevant knowledge is "A is an instance of R" and "Normally, R's instances have the property Q", a defeasible conclusion is "A has the property Q". In probabili... |

3654 |
Fuzzy Sets
- Zadeh
- 1965
(Show Context)
Citation Context ...tely defined. Obviously it is a simplification. Though we can ignore the boundary cases for "male", the fuzziness in "white-collar worker" cannot be neglected so easily. As argued =-=by fuzzy set theory [19] and -=-prototype theory [13], whether an instance belongs to a concept is usually a matter of degree. This membership function is also related to the current issue: if John can be referred to as a "whit... |

304 |
Norm Theory: Comparing Reality to its Alternatives
- Kahneman, Miller
- 1986
(Show Context)
Citation Context ...eted in a pure frequentist way as "in most cases", we still have reason to argue that for many purposes, it is better to see them as closely related to empirical evidences, and have differen=-=t degrees [5, 13]-=-. Therefore, it makes sense, and often necessary, to measure the relations between the default rules and available evidence, which cannot be done in the framework of binary logic. In summary, though n... |

178 |
The mathematics of inheritance systems
- Touretzky
- 1986
(Show Context)
Citation Context ... from the class. In the field of reasoning under uncertainty, there are (at least) two paradigms that use this type of inference: non-monotonic logics (for example, Touretzky's inheritance network in =-=[15]), and probabil-=-istic reasoning systems (for example, Pearl's Bayesian network in [9]). In non-monotonic logics, if the only relevant knowledge is "A is an instance of R" and "Normally, R's instances h... |

175 |
On the internal structure of perceptual and semantic categories
- Rosch
- 1973
(Show Context)
Citation Context ... is a simplification. Though we can ignore the boundary cases for "male", the fuzziness in "white-collar worker" cannot be neglected so easily. As argued by fuzzy set theory [19] a=-=nd prototype theory [13], whether -=-an instance belongs to a concept is usually a matter of degree. This membership function is also related to the current issue: if John can be referred to as a "white-collar worker", but not ... |

109 |
On the Comparison of Theories: Preferring the Most Specific Explanation
- Poole
- 1985
(Show Context)
Citation Context ...ble) A has the property Q, what conclusion can we reach? In different context, the problem is referred to as "multiple inheritance problem", "multiple extension problem", or "=-=reference class problem" [3, 6, 7, 9, 10, 11, 15]-=-. Though the above theories treat the problem differently, they have something in common: None of them suggest a general solution to the problem, though they agree on a special case: if R 2 is a (prop... |

89 |
Nonmonotonic reasoning
- Reiter
- 1987
(Show Context)
Citation Context ...e often referred as "defeasible logic", but actually what is defeasible are only the conclusions derived from the default rules, rather than the rules themselves. The rules are treated as co=-=nventions [12], which ar-=-e immune from empirical revision. As long as "Birds fly" is a default rule, it remains to be valid no matter how many birds found later cannot fly. To treat default rules as convention is po... |

64 |
A class of fuzzy measures based on triangular norms
- Dubois, Prade
- 1982
(Show Context)
Citation Context ...gher confidence, and ignores the other. The deduction rule can infer S ae P !f 0 ; c 0 ? from M ae P !f 1 ; c 1 ? and S ae M !f 2 ; c 2 ?. The truth value function is derived from T-norm and T-conorm =-=[1, 2]-=-, and the derivation can be found in [17]. The resulting function is: f 0 = f 1 f 2 f 1 + f 2 \Gamma f 1 f 2 ; c 0 = (f 1 + f 2 \Gamma f 1 f 2 ) c 1 c 2 Now we are ready to see how NARS treats the ref... |

44 |
The reference class
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- 1983
(Show Context)
Citation Context ...ble) A has the property Q, what conclusion can we reach? In different context, the problem is referred to as "multiple inheritance problem", "multiple extension problem", or "=-=reference class problem" [3, 6, 7, 9, 10, 11, 15]-=-. Though the above theories treat the problem differently, they have something in common: None of them suggest a general solution to the problem, though they agree on a special case: if R 2 is a (prop... |

38 |
The early growth of logic
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(Show Context)
Citation Context ...stified? It can be derived from a more fundamental principle: the extension (instances) and intension (properties) of a concept is co-ordinated during the development of human classification behavior =-=[4]-=-. As a result, we can predict extensional relations from intensional relations (e.g., to determine whether a concept includes an instance by checking the properties of the concept), and to predict int... |

34 | Implicit Ordering of Defaults in Inheritance Systems
- Touretzky
- 1982
(Show Context)
Citation Context ...reference class is not ignored. In this situation, the reference class competing is solved not by choosing one of them, but by combining the two. Let us see how NARS treats the famous "Nixon Diam=-=ond" [14]. Putting into the previous framework, i-=-n this problem we have "Nixon" as A, "Quaker" as R 1 , "Republican" as R 2 , and "Pacifist" as Q. It is also given that J 1 , J 2 , and J 3 are positive, but J ... |

33 | From inheritance relation to non-axiomatic logic
- Wang
- 1994
(Show Context)
Citation Context ...il. An example, with its variations, will be discussed as a starting point, then, after analyzing the factors that influence the result, the solution provided by Non-Axiomatic Reasoning System (NARS) =-=[16, 17, 18]-=- is discussed and compared with the specificity priority principle. 2 A thought experiment Let us reconstruct Kyburg's example in the following way: Imaging that you are working for a life insurance c... |

25 |
Summarizing and propagating uncertain information with triangular norms
- Bonissone
- 1987
(Show Context)
Citation Context ... definition of evidence and its weight, see [17]. In NARS, the truth value of a statement, indicating how the statement is supported by available evidence, is represented by a pair of real numbers in =-=[0, 1]-=-, ! f; c ?, where f is w + w , the relative frequency of positive evidence, and c is the confidence. Confidence is defined in NARS as w w+k , a monotonic increasing function of total weight, indicatin... |

24 |
Defaults and Probabilities: Extensions and Coherence
- Neufeld
- 1989
(Show Context)
Citation Context ...ble) A has the property Q, what conclusion can we reach? In different context, the problem is referred to as "multiple inheritance problem", "multiple extension problem", or "=-=reference class problem" [3, 6, 7, 9, 10, 11, 15]-=-. Though the above theories treat the problem differently, they have something in common: None of them suggest a general solution to the problem, though they agree on a special case: if R 2 is a (prop... |

21 | Typicality in logically defined categories: Exemplar-similarity versus rule instantiation
- Nosofsky
- 1991
(Show Context)
Citation Context ...ine the membership function for a concept like "white-collar worker"? Psychologists suggest that it can be determined by the degree of similarity of the instance to a prototype [13] or an ex=-=emplifier [8]-=- of the concept. A common way to determine the similarity between two concepts is to compare their properties. Like the situation of probability prediction, similarity evaluation is also influenced by... |

21 | Belief revision in probability theory
- Wang
- 1993
(Show Context)
Citation Context ...il. An example, with its variations, will be discussed as a starting point, then, after analyzing the factors that influence the result, the solution provided by Non-Axiomatic Reasoning System (NARS) =-=[16, 17, 18]-=- is discussed and compared with the specificity priority principle. 2 A thought experiment Let us reconstruct Kyburg's example in the following way: Imaging that you are working for a life insurance c... |

13 | Non-axiomatic reasoning system (version 2.2 - Wang - 1993 |

12 |
Nonmonotonic reasoning. Annual Review of Computer Science 2:147–186
- Reiter
- 1987
(Show Context)
Citation Context ...e often referred as \defeasible logic", but actually what is defeasible are only the conclusions derived from the default rules, rather than the rules themselves. The rules are treated as conventions =-=[12]-=-, which are immune from empirical revision. As long as \Birds y" is a default rule, it remains to be valid no matter how manybirds found later cannot y. To treat default rules as convention is possibl... |

3 |
The Theory of Probability. University of California
- Reichenbach
- 1949
(Show Context)
Citation Context |

3 |
Typicality in logically de ned categories: exemplar-similarity versus rule instantiation
- Nosofsky
- 1991
(Show Context)
Citation Context ...ermine the membership function for a concept like \white-collar worker"? Psychologists suggest that it can be determined by the degree of similarity of the instance to a prototype [13] oranexempli er =-=[8]-=- of the concept. A common way to determine the similarity between two concepts is to compare their properties. Like the situation of probability prediction, similarity evaluation is also in uenced by ... |

1 |
Defeasible reasoning and uncertainty: comments
- Grosof
- 1990
(Show Context)
Citation Context |

1 |
The Early Growth of LogicintheChild
- Inhelder, Piaget
- 1969
(Show Context)
Citation Context ... justi ed? It can be derived from a more fundamental principle: the extension (instances) and intension (properties) of a concept is co-ordinated during the development ofhuman classi cation behavior =-=[4]-=-. As a result, we can predict extensional relations from intensional relations (e.g., to determine whether a concept includes an instance by checking the properties of the concept), and to predict int... |