### Citations

8903 |
Probabilistic reasoning in intelligent systems: networks of plausible inference
- Pearl
- 1988
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Citation Context ...3, 17] is often applied in AI the form of non-monotonic logic [4] or description logic [2]. Probability theory and statistics have also been used in AI as a model of reasoning, as in Bayesian Network =-=[6]-=-. Though both theories have achieved great successes in many fields, neither of them was designed to capture all major aspects of human reasoning. Mathematical logic was created to provide a theoretic... |

5444 |
Artio/cial Intelligence - A Modern Approach
- Russell, Norvig
- 1995
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Citation Context ...s domains, without changing the design.2 Pei Wang and Seemal Awan This idea is not new to AI. The first wave of practical applications that made AI an industry was the knowledge-based expert systems =-=[8]-=-. However, though such expert systems have been successfully built for certain domains, the techniques have not grown to other domains as expected. Among the issues raised, robustness and scalability ... |

576 |
An Analysis of TimeDependent Planning.
- Dean, Boddy
- 1988
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Citation Context ...efs are there, in what order they are considered, how much resource the problem has obtained in the competition with co-existent problems and activities, etc. Therefore, NAL makes “anytime” responses =-=[1]-=-. – The system is scalable to large amounts of knowledge and complicated problems, not because these factors do not make the system’s algorithm intractable, but because NAL does not exhaustively searc... |

235 |
Collected Papers of Charles Sanders Peirce.
- Peirce
- 1931
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Citation Context ...90〉” and “{John} → [sick] 〈1, 0.90〉,” the rule derives “{John} → patient 〈1, 0.45〉” (“John may be a patient”). Therefore, induction and abduction can be seen as “inverse deduction,” in different ways =-=[7]-=-, while inductive and abductive conclusions usually have lower confidence values than deductive conclusions, given the same truth-values of the premises.Reasoning in Non-Axiomatic Logic: A Case Study... |

234 | Reasoning in Description Logics. In:
- Donini, Lenzerini, et al.
- 1996
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Citation Context ...ent time, the two major theories on reasoning are mathematical logic and probability theory. Mathematical logic [3, 17] is often applied in AI the form of non-monotonic logic [4] or description logic =-=[2]-=-. Probability theory and statistics have also been used in AI as a model of reasoning, as in Bayesian Network [6]. Though both theories have achieved great successes in many fields, neither of them wa... |

200 |
A theory of approximate reasoning
- Zadeh
- 1979
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Citation Context ... A Case Study in Medical Diagnosis 7 then the conclusion is (25) {John-Doe} → flu-patient 〈0.73, 0.67〉 Here the frequency value is more similar to a “degree of membership” as discussed in fuzzy logic =-=[18, 11]-=- than a probability value in the usual sense — John Doe is still judged to be a flu patient, though not a typical one. Case 5. Even if there are lot of statistical data, a direct application of probab... |

132 |
Principia Mathematica.
- Russell, Whitehead
- 1927
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Citation Context ...of this failure may be found in the theoretical foundation of these systems. At the current time, the two major theories on reasoning are mathematical logic and probability theory. Mathematical logic =-=[3, 17]-=- is often applied in AI the form of non-monotonic logic [4] or description logic [2]. Probability theory and statistics have also been used in AI as a model of reasoning, as in Bayesian Network [6]. T... |

45 |
The reference class
- Kyburg
- 1983
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Citation Context ...ot of statistical data, a direct application of probability theory can still be difficult. For example, a patient may belong to two categories A and B, and they have different risks to have disease D =-=[5]-=-. In nonmonotonic logic, a similar “multiple inheritance” problem is called the “Nixon Diamond” [8]. In NARS, the two competing conclusions can be merged by the revision rule [10]. When the two conclu... |

40 | Non-Axiomatic Reasoning System --- Exploring the essence of intelligence
- Wang
- 1995
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Citation Context ...be a logic system that can be used when a system has insufficient knowledge and resources, that is, the perfect solution to a problem is beyond the knowledge scope and resource capacity of the system =-=[9, 13]-=-. In such a situation, a rational solution is the one that is best supported by the available evidence that the system can find with the available resources. Since this logic has been described in pre... |

39 |
Rigid Flexibility: The Logic of Intelligence
- Wang
- 2006
(Show Context)
Citation Context ...be a logic system that can be used when a system has insufficient knowledge and resources, that is, the perfect solution to a problem is beyond the knowledge scope and resource capacity of the system =-=[9, 13]-=-. In such a situation, a rational solution is the one that is best supported by the available evidence that the system can find with the available resources. Since this logic has been described in pre... |

37 |
Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought
- Frege
- 1967
(Show Context)
Citation Context ...of this failure may be found in the theoretical foundation of these systems. At the current time, the two major theories on reasoning are mathematical logic and probability theory. Mathematical logic =-=[3, 17]-=- is often applied in AI the form of non-monotonic logic [4] or description logic [2]. Probability theory and statistics have also been used in AI as a model of reasoning, as in Bayesian Network [6]. T... |

12 | Confidence as higher-order uncertainty.
- Wang
- 2001
(Show Context)
Citation Context ...earns and creates new statements, but also how it learns and creates new terms and concepts. 4 Comparison and Discussion Since NAL has been compared to mathematical logic [10, 15], probability theory =-=[12, 15]-=-, fuzzy logic [11], etc., in the theoretical assumptions and properties, in this paper we only compare the approaches from a practical point of view. NAL works with insufficient knowledge, which has t... |

8 | Formalization of evidence: A comparative study
- Wang
(Show Context)
Citation Context ...ly specifies how the system learns and creates new statements, but also how it learns and creates new terms and concepts. 4 Comparison and Discussion Since NAL has been compared to mathematical logic =-=[10, 15]-=-, probability theory [12, 15], fuzzy logic [11], etc., in the theoretical assumptions and properties, in this paper we only compare the approaches from a practical point of view. NAL works with insuff... |

7 | Reference classes and multiple inheritances
- Wang
- 1995
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Citation Context ...sks to have disease D [5]. In nonmonotonic logic, a similar “multiple inheritance” problem is called the “Nixon Diamond” [8]. In NARS, the two competing conclusions can be merged by the revision rule =-=[10]-=-. When the two conclusions are equally strong, the conclusion does not favor either of the two. For example, from the following given knowledge, (26) {John-Doe} → [runny-nose] (27) {John-Doe} → [chest... |

4 | Case-by-case problem solving
- Wang
(Show Context)
Citation Context ...number of inference steps. However, since a problem usually can be solved in many different ways, in NAL the process does not follow a predetermined algorithm, but is handled in a case-by-case manner =-=[14]-=-.Reasoning in Non-Axiomatic Logic: A Case Study in Medical Diagnosis 9 – The resource cost for a given problem is not a constant, but depends on the current context, that is, what relevant beliefs ar... |

1 | The evaluation of AGI systems
- Wang
- 2010
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Citation Context ...e model of reasoning, its design decisions cannot be directly evaluated and justified by comparing them with human psychological data, but by checking against the fundamental assumptions of the model =-=[16]-=-. Even so, it still makes sense to test such a system in a practical situation, to verify the applicability of its assumptions and the correctness of the implementation. Especially, in this project we... |