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## From inheritance relation to nonaxiomatic logic (1994)

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### Other Repositories/Bibliography

Venue: | International Journal of Approximate Reasoning |

Citations: | 33 - 25 self |

### Citations

8903 |
Probabilistic reasoning in intelligent systems: networks of plausible inference
- Pearl
- 1988
(Show Context)
Citation Context ... the estimation is. Actually, several approaches are working along this line [14, 15, 27]. However, there are problems in how to interpret the second value, and how it helps in the related operations =-=[23, 29]. At least unde-=-r the assumption of insufficient knowledge, it make little sense to talk about the "probability" that "the frequency is an accurate estimation of an `objective first-order probability' ... |

3134 |
A Mathematical Theory of Evidence
- Shafer
- 1976
(Show Context)
Citation Context ... calculate the weight of evidence is to simply count such terms. In this way, weight of evidence take its values in [0; 1], and is additive when combining two pieces of evidence from distinct sources =-=[32, 41]-=-. If the experience of the system is represented by a string of propositions in IL, then, by using the string as premises set K, we can determine extension and intension for each term. For each judgme... |

2584 |
Judgment under uncertainty: heuristics and biases.
- Tversky, Kahneman
- 1974
(Show Context)
Citation Context ...nsion) of the subject (as Aristotle did) or predicate (as Bentham and Hamilton did, see [4]). The propositions represented in this way are closely related to "typicalness " [31], "repre=-=sentativeness" [36], "normality&qu-=-ot; [20], and "fuzziness" [45]. All these concepts are proposed, from different standing points, to capture the phenomenon that an instance does (or doesn't) possess all (or some) properties... |

785 |
Family resemblances: Studies in the internal structure of categories.
- Rosch, Mervis
- 1975
(Show Context)
Citation Context ...than to the instances (extension) of the subject (as Aristotle did) or predicate (as Bentham and Hamilton did, see [4]). The propositions represented in this way are closely related to "typicalne=-=ss " [31], "representativeness&quo-=-t; [36], "normality" [20], and "fuzziness" [45]. All these concepts are proposed, from different standing points, to capture the phenomenon that an instance does (or doesn't) posse... |

519 |
The Society of Mind. Simon
- Minsky
- 1988
(Show Context)
Citation Context ...ze information about evidence into truth values causes information loss, but it is absolutely necessary for the system, because qualitatively different evidence need to be treated in a unified manner =-=[26]. This wil-=-l lead to what I call "experience-grounded semantics", where the truth value of a judgment indicates the degree to which the judgment is supported by the system's experience. Defined in this... |

501 |
Norm theory: Comparing reality to its alternatives.
- Kahneman, Miller
- 1986
(Show Context)
Citation Context ...ect (as Aristotle did) or predicate (as Bentham and Hamilton did, see [4]). The propositions represented in this way are closely related to "typicalness " [31], "representativeness"=-=; [36], "normality" [20], and &quo-=-t;fuzziness" [45]. All these concepts are proposed, from different standing points, to capture the phenomenon that an instance does (or doesn't) possess all (or some) properties of a category. Th... |

360 |
Logical Foundations of Probability
- Carnap
- 1950
(Show Context)
Citation Context ...retely define the positive and negative evidence for a judgment, and 2. to define a measurement unit. These problems are hard for predicate logics (as revealed by the famous "Raven Paradox" =-=of Hempel [8]-=-), but in a term logic like NAL1, we can find a natural solution of them. In summary, the truth value of a judgment in NAL1 is a numerical representation indicating the weights of positive and negativ... |

235 |
Collected Papers of Charles Sanders Peirce.
- Peirce
- 1931
(Show Context)
Citation Context ...onclusions, corresponding to the four gures of Aristotle's syllogisms: 1. From \M P < f1� c1 >" and\S M < f2� c2 >" to get \S P <f� c>". This is Aristotle's rst gure, and what Peirce called deduction =-=[1, 30]-=-. Let us refer to the function that calculate f and c from f1, c1, f2, andc2 as F1. 2. From \P M < f1� c1 >" and\S M < f2� c2 >" to get \S P<f�c>". This is Aristotle's second gure, and what Peirce cal... |

195 |
The Mathematics of Inheritance Systems.
- Touretzky
- 1986
(Show Context)
Citation Context ...ely related to many well-known relations, for instance, "ISA" (in semantic network), "belongs to" (in Aristotle's syllogism), "subset" (in set theory), "inheritance =-=assertion" (in inheritance network [35]), as well as many relations studied in -=-psychology and philosophy, such as "type-token", "category-instance", "general-specific", and "superordinate-subordinate" [7]. What make it different from the o... |

138 |
What IS-A Is and Isn't: An Analysis of Taxonomic Links in Semantic Networks,"
- Brachman
- 1983
(Show Context)
Citation Context ...ssertion" (in inheritance network [35]), as well as many relations studied in psychology and philosophy, such as "type-token", "category-instance", "general-specific"=-=;, and "superordinate-subordinate" [7]-=-. What make it different from the others are: it is a relation between two terms, and the 4 relation is completely defined by the two properties: reflexivity and transitivity. 1 This logic (as well as... |

138 |
Collected Papers of Charles Sanders Peirce, Volume
- Peirce
- 1933
(Show Context)
Citation Context ...g to the four figures of Aristotle's syllogisms: 1. From "M ae P ! f 1 ; c 1 ?" and "S ae M ! f 2 ; c 2 ?" to get "S ae P ! f; c ?". This is Aristotle's first figure, and=-= what Peirce called deduction [1, 30]. Let us refer to the function-=- that calculate f and c from f 1 , c 1 , f 2 , and c 2 as F 1 . 2. From "P ae M ! f 1 ; c 1 ?" and "S ae M ! f 2 ; c 2 ?" to get "S ae P !f; c?". This is Aristotle's seco... |

137 | Confidence in judgment: Persistence in the illusion of validity.
- Einhorn, Hogarth
- 1978
(Show Context)
Citation Context ...nfidence, the harder the frequency can be changed by new evidence, but this does not mean that the judgment is "truer", or the more "accurate", as some psychologists means by the c=-=oncept "confidence" [12]-=-. It is easy to calculate w and w + from f and c, therefore the truth value of a judgment can also be represented as a pair of ratio !f; c? [38]. Amazingly, there is a third way to represent a truth v... |

135 |
A critique of pure reason
- McDermott
- 1987
(Show Context)
Citation Context ...tions from f 1 , c 1 , f 2 , c 2 to f and c, we have F 2 : f = f 2 c = f1c1c2 f1c1c2+k F 3 : f = f 1 c = f2c1c2 f2c1c2+k Defined as above, abduction and induction are no longer "inversed deductio=-=ns " [25, 30]-=-, and the difference between them and deduction is still there: deductive conclusions are usually much more confident (with 1 as upper bound) than abductive and inductive conclusions (with 1 1+k as up... |

129 |
The cognition of inductive methods.
- Carnap
- 1952
(Show Context)
Citation Context ...ed to Hardy's beta-form based continuum (with equally weighted positive evidence and negative evidence) [16], and Carnap's "- continuum" (with the logical factor, or the prior probability, t=-=o be 1/2) [9]-=-. Though interpreted differently, the three continua share the same formula, and make identical predictions. All the three continua have Laplace's low of succession as a special case (when k = 2), whe... |

101 | Perspectives on the theory and practice of belief functions.
- Shafer
- 1990
(Show Context)
Citation Context ... of "current relevant evidence" to the weight of "relevant evidence in the near future". It indicates how much the system knows about the inheritance relation, so is similar to Sha=-=fer's "reliability" [33] or Yager'-=-s "credibility" [44]. Since k is a constant, the more the system knows about the inheritance relation (represented by a bigger w), the more confident the system is about the frequency, since... |

97 |
The logical foundations of statistical Inference.
- Kyburg
- 1974
(Show Context)
Citation Context ...to probability and statistics, and often appears is our everyday life. However, it is still different from probability under the traditional interpretations (logical, frequentist, and subjective, see =-=[21]-=-) because it is determined by finite empirical evidence. Another basic difference between probability and frequency is: probability is traditionally interpreted as about extensions of sets. For exampl... |

92 | The Estimation of Probabilities.
- Good
- 1965
(Show Context)
Citation Context ...e system make predictions according to its (past) experience, it is natural to use f as e's "first-order approximation". However, such a maximum-likelihood estimate is not good enough when c=-= is small [16]. For-=- example, if a hypothesis has been tested only once, nobody will take an expectation as 1 (if the test is a success) or 0 (if the test leads is failure). Intuitively, e should be more "conservati... |

90 |
Bayesian and non-Bayesian evidential updating
- Kyburg
- 1987
(Show Context)
Citation Context ...ill be w + +k w+k ; in the "worst" case, when all evidence in the near future is negative, the new frequency will be w + w+k . This measurement shares similar intuition with other interval a=-=pproaches [5, 22, 43]. For exam-=-ple, "ignorance", i, can be represented by the width of the interval (here it happens to be 1 \Gamma c, so ignorance and confidence are complement to each other). However, in NAL1 the interv... |

69 |
A Class of Fuzzy Measures Based on Triangular Norms,"
- Dubois, Prade
- 1982
(Show Context)
Citation Context ...e function from [0; 1] \Theta [0; 1] to [0; 1] that are monotonic, commutative, associative, and with boundary conditions satisfying the truth tables of the logical operatorssAND and OR, respectively =-=[5, 6, 11]-=-. They also can be extended to take more than two arguments. The usage of T-norm and T-conorm in NAL1 is different from their usual usage [6, 11] in which they are used to determine the degree of cert... |

65 |
The Early Growth of Logic
- Inhelder, Piaget
- 1964
(Show Context)
Citation Context ...ly defined as an object, or a set of objects, which is in a "physical world", and denoted by the term; intension is usually defined as a concept, which is in a "Platonic world", an=-=d denoting the term [4, 19]-=-. In spite of the differences among the exact ways the two words are used by different authors, they indicate relations between a term in a language and something outside the language. However, in the... |

48 |
Foundations of cognitive science”,
- Simon, Kaplan
- 1993
(Show Context)
Citation Context ...ximate Reasoning 1994 7:1--74 c fl 1994 Elsevier Science Inc. 655 Avenue of the Americas, New York, NY 10010 0888-613X/94/$7.00s2 A reasoning system, in its general form, has the following components =-=[5, 34]-=-: 1. A domain-independent formal language by which the system can communicate with its environment, that is, to get knowledge and questions, and to provide answers according to its knowledge; 2. A sem... |

46 |
A History of Formal Logic.
- Bochenski
- 1970
(Show Context)
Citation Context ...unified manner. 2. THREE SIMPLE SYSTEMS 2.1. Inheritance Logic The four logics discussed in this paper are all term logics, which are different from predicate logics by having the following features: =-=[4, 13] 1. Each p-=-roposition consists of a subject term and a predicate term, which are related by a copula; 2. The copula is intuitively interpreted as "to be"; 3. The basic inference rules take two proposit... |

45 | A theory of higher order probabilities.
- Gaifman
- 1986
(Show Context)
Citation Context ...eferred to as an estimation of "the firstorder probability", and the second-order probability is used to represent how good the estimation is. Actually, several approaches are working along =-=this line [14, 15, 27]-=-. However, there are problems in how to interpret the second value, and how it helps in the related operations [23, 29]. At least under the assumption of insufficient knowledge, it make little sense t... |

44 |
Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic.
- Lukasiewicz
- 1951
(Show Context)
Citation Context ...oposition cannot be a "singular term", such as "Tweety" or "Socrates". On the other hand, as in Aristotle 's logic, "the same term may be used as a subject and as a =-=predicate without any restriction" [24]-=-. 5 questions are search problems either for the existence of a path from a given node to another given node (evaluation) or for a node in a path from (or to) a given node (selection). Up to now, we h... |

28 | On the validity of Dempster-Shafer theory - Dezert, Wang, et al. - 2012 |

25 |
Summarizing and propagating uncertain information with triangular norms
- Bonissone
- 1987
(Show Context)
Citation Context ...e function from [0; 1] \Theta [0; 1] to [0; 1] that are monotonic, commutative, associative, and with boundary conditions satisfying the truth tables of the logical operatorssAND and OR, respectively =-=[5, 6, 11]-=-. They also can be extended to take more than two arguments. The usage of T-norm and T-conorm in NAL1 is different from their usual usage [6, 11] in which they are used to determine the degree of cert... |

21 | Belief revision in probability theory
- Wang
- 1993
(Show Context)
Citation Context ...s and represent it in NARS. To represent a truth value by a frequency value is not enough for NARS: we still need the information about the absolute value of w to manage the revision of the frequency =-=[38]. Can we find a natu-=-ral way to represent this information in the form of a 15 "relative measurements", or specially, as a ratio? An attractive idea is to define it as the "second-order probability". T... |

21 |
A methodology for uncertainty in knowledgebased systems, volume 419
- Weichselberger, Pöhlmann
- 1990
(Show Context)
Citation Context ...ill be w + +k w+k ; in the "worst" case, when all evidence in the near future is negative, the new frequency will be w + w+k . This measurement shares similar intuition with other interval a=-=pproaches [5, 22, 43]. For exam-=-ple, "ignorance", i, can be represented by the width of the interval (here it happens to be 1 \Gamma c, so ignorance and confidence are complement to each other). However, in NAL1 the interv... |

15 | On the working definition of intelligence
- Wang
- 1994
(Show Context)
Citation Context ...As an intelligent system, NARS is designed to be an adaptive system under the constraints that its knowledge and resources are usually insufficient to answer the questions proposed by the environment =-=[40, 42]-=-. Concretely, it has the following features: Finite: The system works with respect to its constant information processing capacity; Real-time: New knowledge and questions can arrive at any time, and q... |

12 | Non-axiomatic reasoning system (version 2.2
- Wang
- 1993
(Show Context)
Citation Context ...semantics, measurements of uncertainty, revision, deduction, abduction, induction. 1. INTRODUCTION Non-Axiomatic Reasoning System (NARS) is proposed as a formal model of intelligent reasoning systems =-=[40]-=-. This work is supported by a research assistantship from Center for Research on Concepts and Cognition, Indiana University. Address correspondence to 510 North Fess, Bloomington, IN47408 pwang@cogsci... |

10 |
How Could a copycat Ever Be Creative
- Hofstadter
- 1994
(Show Context)
Citation Context ... is not always chosen as the answer, but is given a higher probability to be chosen. In this way, the decisions are more variable and indeterministic, so have some advantages in certain circumstances =-=[18]-=-. 4.4. Syllogisms The major inference rules in NAL1 are the (extended) syllogisms. When two judgments share a common term, they can be used as premises to infer the inheritance relations between the o... |

10 |
Higher order probabilities
- Kyburg
- 1987
(Show Context)
Citation Context ... the estimation is. Actually, several approaches are working along this line [14, 15, 27]. However, there are problems in how to interpret the second value, and how it helps in the related operations =-=[23, 29]. At least unde-=-r the assumption of insufficient knowledge, it make little sense to talk about the "probability" that "the frequency is an accurate estimation of an `objective first-order probability' ... |

9 |
Fuzzy sets. Information and Control, 8:338–353, 1965. Samenvatting Sir Francis Bacon zei ongeveer vier eeuwen geleden: “knowledge is power” (kennis is macht). Als we kijken naar de huidige maatschapij, dan zien we dat informatie steeds belangrijker wordt.
- Zadeh
(Show Context)
Citation Context ...) or predicate (as Bentham and Hamilton did, see [4]). The propositions represented in this way are closely related to \typicalness" [31], \representativeness" [36], \normality" [20], and \fuzziness" =-=[45]-=-. All these concepts are proposed, from di erent standing points, to capture the phenomenon that an instance does (or doesn't) possess all (or some) properties of a category. The related problems cann... |

8 |
Second order probabilities for uncertain and con icting evidence
- Paa
- 1991
(Show Context)
Citation Context ...eferred to as an estimation of "the firstorder probability", and the second-order probability is used to represent how good the estimation is. Actually, several approaches are working along =-=this line [14, 15, 27]-=-. However, there are problems in how to interpret the second value, and how it helps in the related operations [23, 29]. At least under the assumption of insufficient knowledge, it make little sense t... |

8 |
Aristotle’s Theory of the Syllogism
- Patzig
- 1968
(Show Context)
Citation Context ...\Gamma EP = ;) () (E S ` EP ), we have (S ! a P ) () (S ! P ). Though described differently, ETL turns out to be isomorphic with Aristotle 's syllogistic logic. For each property of Aristotle's logic =-=[1, 24, 28]-=-, there is a corresponding one in ETL, and vice versa. The square of opposition: The relations among the four types of extensional inheritance can be represented in Figure 1 [4], where there are four ... |

7 |
Credibility discounting in the theory of approximate reasoning
- Yager
- 1991
(Show Context)
Citation Context ..." to the weight of "relevant evidence in the near future". It indicates how much the system knows about the inheritance relation, so is similar to Shafer's "reliability" [33] =-=or Yager's "credibility" [44]-=-. Since k is a constant, the more the system knows about the inheritance relation (represented by a bigger w), the more confident the system is about the frequency, since the effect of evidence that c... |

6 |
Metaprobability and Dempster-Shafer in evidential reasoning
- Fung, Chong
- 1986
(Show Context)
Citation Context ...eferred to as an estimation of "the firstorder probability", and the second-order probability is used to represent how good the estimation is. Actually, several approaches are working along =-=this line [14, 15, 27]-=-. However, there are problems in how to interpret the second value, and how it helps in the related operations [23, 29]. At least under the assumption of insufficient knowledge, it make little sense t... |

5 |
Three Logicians. Van Gorcum
- Englebretsen
- 1981
(Show Context)
Citation Context ...unified manner. 2. THREE SIMPLE SYSTEMS 2.1. Inheritance Logic The four logics discussed in this paper are all term logics, which are different from predicate logics by having the following features: =-=[4, 13] 1. Each p-=-roposition consists of a subject term and a predicate term, which are related by a copula; 2. The copula is intuitively interpreted as "to be"; 3. The basic inference rules take two proposit... |

4 |
Selecting uncertain calculi and granularity
- Bonissone, Decker
- 1986
(Show Context)
Citation Context ...e function from [0; 1] \Theta [0; 1] to [0; 1] that are monotonic, commutative, associative, and with boundary conditions satisfying the truth tables of the logical operatorssAND and OR, respectively =-=[5, 6, 11]-=-. They also can be extended to take more than two arguments. The usage of T-norm and T-conorm in NAL1 is different from their usual usage [6, 11] in which they are used to determine the degree of cert... |

3 |
First Ladies and Fluid Logics
- Wang
- 1992
(Show Context)
Citation Context ... as well; 5. A control mechanism which chooses premises and rule(s) in each inference step to answer the questions. The first three components can be called a "logic", in the broad sense of =-=this term [37]-=-. As an intelligent system, NARS is designed to be an adaptive system under the constraints that its knowledge and resources are usually insufficient to answer the questions proposed by the environmen... |

3 |
Con dence in judgment: persistence of illusion of validity
- Einhorn, Hogarth
- 1978
(Show Context)
Citation Context ...con dence, the harder the frequency can be changed by new evidence, but this does not mean that the judgment is \truer", or the more \accurate", as some psychologists means by the concept \con dence" =-=[12]-=-. It is easy to calculate w and w + from f and c, therefore the truth value of a judgment can also be represented as a pair of ratio <f� c> [38]. Amazingly, there is a third way to represent a truth v... |

2 |
A mathematical theory for evidence combination. Unpublished manuscript
- Bai
- 1991
(Show Context)
Citation Context ... three forms of truth value, in Table 5. It is possible to find direct intuitive justifications for a function in a form that is different from the previously discussed ones (for example, Bai Shuo in =-=[2]-=- also reached the revision rule in the ratio form from a different starting point), but such justifications are not always obvious. 5. An Example Up to now, we have completely defined a non-axiomatic ... |

2 |
order probabilities for uncertain and con icting evidence
- Paa
- 1991
(Show Context)
Citation Context ... referred to as an estimation of \the rstorder probability", and the second-order probability is used to represent how good the estimation is. Actually, several approaches are working along this line =-=[14, 15, 27]-=-. However, there are problems in how tointerpret the second value, and how it helps in the related operations [23, 29]. Atleast under the assumption of insu cient knowledge, it make little sense to ta... |

2 |
First ladies and uid logics
- Wang
- 1992
(Show Context)
Citation Context ...ce as well� 5. A control mechanism which chooses premises and rule(s) in each inference step to answer the questions. The rst three components can be called a \logic", in the broad sense of this term =-=[37]-=-. As an intelligent system, NARS is designed to be an adaptive systemunder the constraints that its knowledge and resources are usually insu cient to answer the questions proposed by theenvironment [4... |

2 |
On the working de nition of intelligence
- Wang
- 1994
(Show Context)
Citation Context ...7]. As an intelligent system, NARS is designed to be an adaptive systemunder the constraints that its knowledge and resources are usually insu cient to answer the questions proposed by theenvironment =-=[40, 42]-=-. Concretely, it has the following features: Finite: The system works with respect to its constant information processing capacity� Real-time: New knowledge and questions can arrive atany time, and qu... |

1 |
Rigor mortis: a response to Nillsson's "logic and artificial intelligence
- Birnbaum
- 1991
(Show Context)
Citation Context ...atterns appearing in human reasoning [37]. By naming it a "Non-Axiomatic Logic", I am trying to show that, from the viewpoint of artificial intelligence, the problems of the traditional &quo=-=t;symbolic AI" [3, 25, 34] are not caused by the ideas like "formalization", &quo-=-t;symbolization", "logical inferences ", and so on, but by the ideas like "axiomatization", "computation", "binary logics", "consistent and complete s... |

1 |
Inheritance theory and path based reasoning: an introduction
- Carpenter, Richmond
- 1990
(Show Context)
Citation Context ...tions. If only the relations "S ! a P " and "S ! e P " are represented and processed, ETL will degenerate into a special case, which is identical with the 8 "Monotonic Inherit=-=ance Network" defined in [10]. 2.4. Intensional T-=-erm Logic Since extension and intension are defined as a "dual" in IL, we get an Intensional Term Logic (ITL) "for free", which is isomorphic with ETL. Definition 2.6. S ! a P if a... |

1 | From Euler to Ulam: discovery and dissection of a geometric gem - Hofstadter - 1993 |

1 |
fw + ; wg !f; c? [l; u] fw + ; wg w + = k fc 1\Gammac w + = k l u\Gammal w = k c 1\Gammac w = k 1\Gamma(u\Gammal) u\Gammal ! f; c ? f = w + w f = l 1\Gamma(u\Gammal) c = w w+k c = 1 \Gamma (u \Gamma l) [l; u] l = w + w+k l = fc u = w + +k w+k u = 1 \Gamma
- Information, Control
- 1965
(Show Context)
Citation Context ... or predicate (as Bentham and Hamilton did, see [4]). The propositions represented in this way are closely related to "typicalness " [31], "representativeness" [36], "normalit=-=y" [20], and "fuzziness" [45]-=-. All these concepts are proposed, from different standing points, to capture the phenomenon that an instance does (or doesn't) possess all (or some) properties of a category. The related problems can... |

1 |
Rigor mortis: a response to Nillsson's \logic and arti cial intelligence
- Birnbaum
- 1991
(Show Context)
Citation Context ...patterns appearing in human reasoning [37]. By naming it a \Non-Axiomatic Logic", I am trying to show that, from the viewpoint of arti cial intelligence, the problems of the traditional \symbolic AI" =-=[3, 25, 34]-=- arenot caused by the ideas like \formalization", \symbolization", \logical inferences", and so on, but by the ideas like \axiomatization", \computation", \binary logics", \consistent and complete sys... |