#81# P.Wang. From Inheritance Relation to NonAxiomatic Logic. Technical report, Center for Research on Concepts and Cognition, Indiana University, Bloomington, Indiana,, 1993. #82# S.M. Weiss, C.A. Kulikowski, andS.Amarel. A Model-Based Method for Computer-Aided Medical Decision-Making. Arti#cial Intelligence, 11,  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Our approach has the potential to be slower, but the explicit representation of all alternatives permits allows for global assessment criteria (e.g. our validation procedure described above) 6. 3 Other Abductive Research Descriptions of abduction date back to the fourthfigure of Aristotle [80]. In the modern era, abduction was described by Charles Sanders Pierce in the last century as follows: The surprising fact C is observed. But if A were true, C would be a matter of course. Hence, there is reason to suspect that A is true [56, introduction] Pople noted the connection between ....

....assumption set AB . However, we have argued in this article that not all BEST explanations are minimal. Rather, a comprehensive knowledge level modeling framework can be developed assuming customisable world assessment. Abduction is an interesting framework in which to explore non standard logics [47, 62, 80]. Many of the criticisms against AI (e.g. 2] are really criticisms of standard deductive logics where the conclusions reached are context independent. We view abduction as a more plausible model of human reasoning since the conclusions made are contextdependent on the T ASK at hand. Various ....

P. Wang. From Inheritance Relation to NonAxiomatic Logic. Technical report, Center for Research on Concepts and Cognition, Indiana University, Bloomington, Indiana,, 1993.

....uncertainty is measured I can say that my belief on a sentence is as strong as I have tested the sentence w times, and the tests succeeded w times, but failed w times , even though I did not really test the sentence in this way. For how to apply this measurement to a formal language, see [25, 26]. Because all the operations in the system are based on available evidence, w and w contain all the information about the uncertainty of the sentence. However, when represented in this way, the information is inconvenient for certain purposes. When comparing competing options and deriving new ....

....represent the uncertainty of a statement: by two of the three amounts of evidence (w , w , and w) by the two ratios (frequency and con dence) or by the lower upper frequency interval. From the above definitions, it is not dicult to get the one to one mappings among the three representations [25, 26]. No matter which form is used, we need two numbers to represent the uncertainty of a statement. Is this kind of information available to the system Even Bayesian network and fuzzy logic, which require the users to assign a single number to each statement, have diculty in getting the numbers. ....

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P. Wang. From inheritance relation to nonaxiomatic logic. International Journal of Approximate Reasoning, 11(4):281-319, November 1994.

....In the study of artificial intelligence, many researchers reach the conclusion that the currently dominating logic system, First Order Predicate Logic (FOPL) is not a proper model of intelligent reasoning, and various alternative logic systems have been proposed. Non Axiomatic Logic (NAL) [Wang, 1994; Wang, 1995; Wang, 2000] is one of them. What distinguishes NAL from other logic systems is its assumption of insufficient knowledge and resources. When the logic is used to answer questions according to given knowledge, the knowledge may be uncertain and incomplete (with respect to the ....

....Higher Order Non Axiomatic Logic (HONAL) is formally specified for the first time. Finally, NAL is compared with the other approaches, specially in its treatment of abduction. 2 First Order Non Axiomatic Logic This section provides an updated summary of FONAL, based on the previous publications [Wang, 1994; Wang, 1995; Wang, 2000] 2.1 Language and semantics Under the assumption of insufficient knowledge and resources, a statement in NAL cannot be either completely true or completely false. Instead, its truth value must be a matter of degree. Since the only available information about the world ....

P. Wang, From Inheritance Relation to Nonaxiomatic Logic. International Journal of Approximate Reasoning, Vol. 11, pages 281--319, 1994.

....in time. ffl A model of L is represented in another language ML, and it is not necessarily accessible to the system that use L, but experience is represented in L itself, and it is accessible to the system. 4 The Semantics of NARS In the following, we take Non Axiomatic Reasoning System (NARS) [19, 21, 22] as an example, to show how to apply experience ground semantics to a formal language used by a computerized reasoning system. As a general purpose intelligent reasoning system, NARS is designed to be adaptive with insufficient knowledge and resources [22] As discussed above, in such a system the ....

....their own truth values it seems to be a circular definition or infinite regression. The solution used in NARS is bootstrapping taking a subset of L to define the truth value of sentences and meaning of terms in L. In the following, we only discuss the core language of NARS, defined in [19], and ignore its extensions. NARS uses a term oriented language, in which each sentence consists of a subject term and a predicate term, related by a copula. Let us first define a copula for an ideal inheritance relation. The copula is written as , and the relation is defined to be a ....

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P. Wang. From inheritance relation to non-axiomatic logic. International Journal of Approximate Reasoning. Accepted in June 1994.

....f must be reevaluated. If we only know its previous value, we cannot determine how much it should be changed the absolute amount of evidence is absent in f . Though it is possible, in theory, to directly use w and w as measurements of uncertainty, it is often unnatural and inconvenient [17]. Can we capture this kind of information without recording w and w directly Yes, we can. From the viewpoint of evidence combination, the influence of w appears in the stability of a frequence evaluation based on it. Let us compare two situations: in the first w = 1000 and w = 600, and ....

....to situations in which the weights of evidence are not necessarily integers. In general, the interval bounds the frequence until the weight of new evidence reaches a constant unit. For the current purpose, the 1 that appears in the definitions of l and u can be substituted by any positive number [17]. 1 is used here to simplify the discussion. As bounds of frequency, l and u share intuitions with Dempster s P and P , as well as Shafer s Bel and P l. However, they have some properties that distance them from the functions of D S theory and other similar ideas like lower and upper bounds of ....

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P. Wang. From inheritance relation to nonaxiomatic logic. International Journal of Approximate Reasoning, 11(4):281--319, November 1994.

....NARS is an intelligent reasoning system, whose interaction with its environment can be described as a stream of input sentences in a formally defined language and a stream of output sentences in the same language. These two streams are called the system s experience and responses , respectively [Wang, 1994, Wang, 1995a, Wang, 1995b] Detailed description of the system can be found from the author s homepage. Each sentence in the language represents an inheritance relation between two terms. By definition, a sentence S ae P indicates that the subject term S is in the extension of the ....

Pei Wang. From inheritance relation to nonaxiomatic logic. International Journal of Approximate Reasoning, 11(4):281--319, November 1994.

....are the target. 2 Induction and Abduction in NARS NARS is an intelligent reasoning system I developed. In this position paper, I only introduce the part of it that is directly relevant to the Workshop on Abduction and Induction in AI of IJCAI 97. For detailed descriptions of the system, see [ Wang, 1994; Wang, 1995 ] which are also available via the Web at http: www.cogsci.indiana.edu farg peiwang papers.html. 2.1 Syntax and Semantics NARS is designed to be adaptive, and to work with insufficient knowledge and resources. The system answers questions in real time according to available ....

....is, the function values when the premises are complete inheritance relations. Second, these boundary conditions are extended into general situations according to some principles, such as the continuity of the function, the independence of the premises, and so on. For detailed discussion, see [ Wang, 1994; Wang, 1995 ] Intuitively, deduction extends the transitivity of complete inheritance relation into (incomplete) inheritance relation in general; induction establishes inheritance relations based on shared extension; abduction establishes inheritance relations based on shared intension. ....

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Wang, P. (1994). From inheritance relation to nonaxiomatic logic. International Journal of Approximate Reasoning, 11(4):281--319.

....by the above answers, this paper is an attempt to discuss the issue of reference class in more detail. 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 company, and you need to predict whether John Smith can live to 40. You have John s personal ....

....or typicality difference which favors the more general concept, the specificity priority can be more or less cancelled out. This conclusion from above analysis is consistent with the result of the thought experiment in the previous section. 4 Another approach Non Axiomatic Reasoning System (NARS) [16, 17, 18] is an intelligent system which works and adapts to its environment under the assumption of insufficient knowledge and resources. As a result of the assumption, it also meets the reference class problem. For our current purpose, let s say that each statement in NARS has the form of S ae P or S 2 P ....

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P. Wang. From inheritance relation to non-axiomatic logic. Technical Report 84, Center for Research on Concepts and Cognition, Indiana University, Bloomington, Indiana, 1993.

....NARS assumes the insufficiency of knowledge and resources, and attempts to coordinate the extension and intension of each term, it uses a truth value both extensionally and intensionally. As a result, some fallacies (according to extensional theories) become valid modes of reasoning in NARS (Wang, 1996a) 3. Language 40 Examples of this phenomenon will be discussed in Chapter 6. To represent a truth value by a frequency value is not enough for NARS: in addition, we (as well as a computer system) need to know the value of w in order to figure out how to revise frequency in response to new evidence (Wang, 1993a) ....

Wang, P. (1994c). From inheritance relation to nonaxiomatic logic. International Journal of Approximate Reasoning, 11(4):281--319.

....measure is not sufficient for uncertainty management in IRS since some operations are sensitive to the source of uncertainty. To solve such problems, some other method can be used as a supplement, rather than a replacement, of the numerical approach. For example, such a mechanism is described in [30] for detecting correlated evidence in revision. Though non numerical approach is unsuitable in IRS, their motivations need to be respected, that is, the numerical measurement should have a natural interpretation, so that the numbers can make sense to human beings. On the other hand, verbal ....

....intelligent reasoning system (IRS) Here, I ll concentrate on its representation and interpretation of uncertainty, and leave the other components (such as inference rules, memory structure, and control mechanism) to other papers. For more detailed and complete descriptions for NARS, see [32] and [30]. 3.1 The cardinal form As mentioned previously, NARS need to measure the weights of (positive and negative) evidence of a proposition. Such a task can be divided into three subtasks: to represent a proposition, to distinguish positive and negative evidence of a proposition, and to determine ....

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P. Wang. From inheritance relation to non-axiomatic logic. Technical Report 84, Center for Research on Concepts and Cognition, Indiana University, Bloomington, Indiana, 1993.

....and dynamically adjusts its bias according to new results. 2 NARS: Working under Insufficient Resources In this section, a new approach for working under insufficient resources is developed and discussed. This approach is used for resource management in the Non Axiomatic Reasoning System (NARS) (Wang, 1994; Wang, 1995) 2.1 The problem As a general purpose reasoning system, NARS accepts knowledge provided by the user in a formal language, and answers questions according to available knowledge and a set of inference rules. The user can assign two types of information processing tasks to the ....

....has to work in this situation, what is the best way (the Type II rationality ) for it to manage its resources In the remaining part of the paper, the resource management mechanism of NARS is discussed. For other components of NARS (such as knowledge representation and inference rules) see (Wang, 1994; Wang, 1995) 2.2 Controlled concurrency As discussed previously, in NARS to carry out a task means to interact the task, which may be a piece of knowledge or a question, with available knowledge. Such a process consists of a sequence of inference steps, in each of which a piece of knowledge ....

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Wang, P. (1994). From inheritance relation to nonaxiomatic logic. International Journal of Approximate Reasoning, 11(4):281--319.

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Wang, P. (1994a). From inheritance relation to nonaxiomatic logic. International Journal of Approximate Reasoning, 11(4):281--319.

....and membership: both are real numbers in [0; 1] and both are indicating the ratio of positive evidence among all relevant evidence, that is, w w . 2 Based on such an interpretation, I m building an intelligent reasoning system, Non Axiomatic reasoning System, or NARS for short ([27, 26]) where fuzziness and randomness are uniformly processed as (part of) a judgment s truth value, and referred as the frequency of the judgment. However, this doesn t mean that fuzziness and randomness cannot be distinguished. For a proposition S is P , randomness always comes from the variety ....

....and the uncertainty is randomness; when P has many properties (or intended meaning ) and some of them are possessed by S, while the others are not, S is P is also a matter of degree, but the uncertainty is fuzziness. In NARS, fuzziness and randomness are processed in a symmetrical way (see [26] for detail) and they are different in how the evidence is collected. If these two types of uncertainty are different, why bother to treat them in an uniform way The basic reason is: in many practical problems, they are involved with each other. Smets stressed the importance of this issue, and ....

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P. Wang. From inheritance relation to non-axiomatic logic. Technical Report 84, Center for Research on Concepts and Cognition, Indiana University, Bloomington, Indiana, 1993.

....suggested, by the definition, and how they differ from the components of an axiomatic system. Because this paper is concentrated in the philosophical and methodological foundation of the NARS project, formal descriptions and detailed discussions for the components are left to other papers (such as [40, 42]) 3.1 Experience grounded semantics The traditional model theoretic semantics is no longer applicable to NARS. Due to AIKR, no knowledge in NARS is true in the sense that it corresponds to state of affairs in the real world. Knowledge comes, directly or indirectly, from the experience of the ....

....makes the term different from other terms to the system, is determined by its relationships to other terms, according to the experience, rather than by an interpretation that mapping it into an object in a model. The new semantics is discussed in more detail, and applied to a formal language, in [40]. The basic differences between experience grounded semantics and model theoretic semantics are: 1. As descriptions of an environment, the former is partial, developing in time, and not conflict free, whereas the latter is complete, static, and consistent. 2. The former is accessible to the system ....

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P. Wang. From inheritance relation to non-axiomatic logic. Technical Report 84, Center for Research on Concepts and Cognition, Indiana University, Bloomington, Indiana, 1993. Available via WWW at http://www.cogsci.indiana.edu/farg/pwang papers.html. A revised version is going to appear in the International Journal of Approximate Reasoning.

....in a computer system for the purpose of artificial intelligence. 2. Extended Syllogism in NARS NARS is an intelligent reasoning system. In this chapter, I only introduce the part of it that is directly relevant to the theme of this book. For more comprehensive descriptions of the system, see (Wang, 1994; Wang, 1995) 2.1. Syntax and Semantics NARS is designed to be adaptive to its environment, and to work with insufficient knowledge and resources. The system answers questions in real time according to available knowledge, which may be incomplete (with respect to the questions to be answered) ....

....is, the function values when the premises are complete inheritance relations. Second, these boundary conditions are extended into general situations according to certain principles, such as the continuity of the function, the independence of the premises, and so on. For detailed discussions, see (Wang, 1994; Wang, 1995) From a semantic point of view, the truth value of an inheritance relation is determined in different ways in different inference types: deduction extends the transitivity of complete inheritance relation into (incomplete) inheritance relation in general; abduction establishes ....

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Wang, P. (1994). From inheritance relation to nonaxiomatic logic. International Journal of Approximate Reasoning, 11(4):281--319.

.... way to express one s uncertainty about some events or propositions, it does not contain the information about the amount of evidence that supports the probability distribution [13] This type of information is referred to by various authors as ignorance , confidence , reliability , and so on [16, 21]. Some people argue that this information can be derived from a probability distribution [15, 17] but this argument is invalid, because it is actually based on a confusion between the background knowledge that supports a probability assignment and the proposition that appears within a conditional ....

....Non Axiomatic Reasoning System (NARS) is an intelligent reasoning system which adapts to its environment under insufficient knowledge and resources. A formal and complete description about the system s logical kernel has been published, also in the International Journal of Approximate Reasoning [21]. It is assumed that the readers of the current paper have access to that paper, therefore in the following we only introduce the aspects of the system that are most closely related to our current issue. 3.1. Theoretical assumption NARS is designed under the assumption that the knowledge and ....

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P. Wang. From inheritance relation to non-axiomatic logic. International Journal of Approximate Reasoning, 11(4):281--319, November 1994.

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#81# P.Wang. From Inheritance Relation to NonAxiomatic Logic. Technical report, Center for Research on Concepts and Cognition, Indiana University, Bloomington, Indiana,, 1993. #82# S.M. Weiss, C.A. Kulikowski, andS.Amarel. A Model-Based Method for Computer-Aided Medical Decision-Making. Arti#cial Intelligence, 11,

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