P. Cheeseman. An inquiry into computer understanding. Computational Intelligence, 4:58--142, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....has been pursued. For many years researchers indulged in ideological slanging matches of almost religious fervour in which the formalism that they championed was compared with its competitors and found to exhibit superior performance. Examples of this behaviour abound, particularly notable are [10, 12, 42, 66, 88, 105]. It is only recently that a more moderate eclectic view has emerged, 13, 32, 48, 78] for example, which acknowledges that all formalisms are useful for the solution of different problems. A general realisation of the strength of this eclectic position has motivated research both into ways in ....

....issue, though all the theories that we shall consider assume allocation by an assignment function that distributes belief to possible events under consideration. Belief may be distributed on the basis of statistical information [81, 92] physical possibility [103] or purely subjective assessment [12] by an expert or otherwise. The belief assigned is a number between 0 and 1, with 0 being the belief assigned to a fact that is known to be false, and 1 the belief assigned to a fact known to be definitely true. The infinite number of degrees of belief between the limits represent various shades ....

P. Cheeseman. An inquiry into computer understanding. Computational Intelligence, 4:58--142, 1988.

....to statements represented by sentences in our language. To each of these facets we associate a specific measure. We associate fuzzy measures to vagueness [DP88, Rus90b, Zad88] probabilities on the domain to statistics [Bac90c, Hal90] and probabilities on possible worlds to degrees of belief [Che88, CdSB91, KJ87, Nil86, Pea88, Sha76]. The expected contribution of this work is the empirical confirmation that automated reasoning with multiple representations of uncertainty can be done in a practical sense. Nonetheless, the language which was constructed to provide this confirmation is expected to be useful as a tool to ....

P. Cheeseman. An Inquiry into Computer Understanding. Computational Intelligence, 4:58--66, 1988.

....Figure 1. DAG for the Sprinkler Problem 3. The Entropic Prior of a Discrete Probabilistic Network An understanding of Cox s [9] argument should be su#cient to impose the rules of probability to the treatment of uncertainty in AI. But it has taken, however, a long heated debate (see [10] and [11]) the invention of new e#cient methods of computation (e.g. the junction tree algorithm, see [12] and the publication of Pearl s text [13] to arrive at today s dominant view of a complete probabilistic approach. 3.1. DAGS The current recipe for the thinking machine consists of a fully ....

P. Cheeseman, "An inquiry into computer understanding," Computational Intelligence, 4, (1), pp. 58--66, 1988.

....in the form of how to train the AI# model. More practical aspects, like language or image processing have to be learned by AI# from scratch. Other theories, like fuzzy logic, possibility theory, Dempster Shafer theory, are partly outdated and partly reducible to Bayesian probability theory [Che85, Che88]. The interpretation and consequences of the evidence gap g: 1 #(yx k yx k ) 0 in # may be similar to those in Dempster Shafer theory. Boolean logical reasoning about the external world plays, at best, an emergent role in the AI# model. Other methods, which don t seem to be contained in the ....

P. Cheeseman. An inquiry into computer understanding. Computational Intelligence, 4(1):58--66, 1988.

....of the approach from a mathematical point of view even led to a world wide debate concerning the appropriateness of probability theory for handling uncertainty in a knowledge based context. Here, we will not enter into this debate; for a wide range of diverging opinions, the reader is referred to [Cheeseman, 1988] with its ensuing discussions. Although the above mentioned debate had not yet subdued, in the mid 1980s the belief network framework was introduced as a novel approach to applying probability theory for reasoning with uncertainty in knowledge based systems [Pearl, 1988] When compared to the ....

P. Cheeseman. An inquiry into computer understanding. Computational Intelligence, vol. 4, 1988, pp. 58 - 66.

....has been pursued. For many years researchers indulged in ideological slanging matches of almost religious fervour in which the formalism that they championed was compared with its competitors and found to exhibit superior performance. Examples of this behaviour abound, particularly notable are [10, 12, 42, 66, 88, 105]. It is only recently that a more moderate eclectic view has emerged, 13, 32, 48, 78] for example, which acknowledges that all formalisms are useful for the solution of di erent problems. A general realisation of the strength of this eclectic position has motivated research both into ways in ....

....issue, though all the theories that we shall consider assume allocation by an assignment function that distributes belief to possible events under consideration. Belief may be distributed on the basis of statistical information [81, 92] physical possibility [103] or purely subjective assessment [12] by an expert or otherwise. The belief assigned is a number between 0 and 1, with 0 being the belief assigned to a fact that is known to be false, and 1 the belief assigned to a fact known to be de nitely true. The in nite number of degrees of belief between the limits represent various shades of ....

P. Cheeseman. An inquiry into computer understanding. Computational Intelligence, 4:58-142, 1988.

....is the clarity property. This states that every proposition that is a subject of a probability assertion must be decidable as either true or false. Proponents of the subjective school of thought in probability theory say that they ve solved the problem of vagueness (or fuzziness) Cheeseman[7] proposed that the membership function can be viewed as a probability function. Let define a fuzzy set of tall men. Then say we are given a precise value of the height, u. Then (u) is simply the conditional probability P (ju; c) where c is the context within which the meaning of is derived. ....

P. C. Cheeseman. An inquiry into computer understanding. Computational Intelligence, (4):58--66, 1 1988.

.... is that we take as our starting point the following idea: Wrong Yet Useful (WYU) Principle In many situations, the subjective probabilities of an agent will be very useful (in that they 1 communicated to this author by several AI Researchers at several conferences; see also the discussion in (Cheeseman, 1988). Taking the Sting out of Subjective Probability 3 lead to good predictions or decisions concerning some aspects of the domain) yet by no means (universally) true or correct or optimal (in that they do not lead to good predictions concerning some other aspects of the domain and or another ....

....probabilities are routinely used. The examples will hopefully show (a) the usefulness of subjective probability and (b) the fact that people, at least in some cases, more or less know how to interpret subjective probabilities (both (a) and (b) seem to be disputed by some statisticians, cf. Cheeseman (1988)) Example 1 [the professional weather forecaster] Consider a weather forecaster who on each day i (i 2 f1; 2; 3; g) has to predict whether or not it will rain on day i 1. Let X i 2 f0; 1g indicate whether it rains (X i = 1) on day i or not (X i = 0) The forecaster s predictions are ....

Cheeseman, P. 1988. An inquiry into computer understanding. Computational Intelligence, 4(1):58--66,67--129. Discussion: pages 67--129.

....of the approach from a mathematical point of view even led to a world wide debate concerning the appropriateness of probability theory for handling uncertainty in a knowledge based context. Here, we will not enter into this debate; for a wide range of diverging opinions, the reader is referred to [Cheeseman, 1988] with its ensuing discussions. Although the above mentioned debate had not yet subdued, in the mid 1980s the belief network framework was introduced as a novel approach to applying probability theory for reasoning with uncertainty in knowledge based systems [Pearl, 1988] When compared to the ....

P. Cheeseman. An inquiry into computer understanding. Computational Intelligence, vol. 4, 1988, pp. 58 - 66.

....distributions associated with the relevant statistical hypotheses into the probabilistic considerations peculiar to a specific decision context. There is, however, a computational cost involved. For present purposes, we have chosen to stand aside from the Bayesian non Bayesian debate. See [ Cheeseman, 1988 ] and [ Kyburg, 1994 ] 6 Problems and Questions We are left with a number of important questions. 1. Assuming that acceptance is useful on some occasions, it remains to be seen whether purely probabilistic acceptance, as outlined here, is as useful as other forms of nonmonotonic acceptance. ....

Peter Cheeseman. Inquiry into computer understanding. Computational Intelligence, 4:58--66., 1988.

....arguments in the way suggested, it is to be understood as an abbreviation or shorthand for a more adequate view of induction, which should proceed strictly according to schema II. For Carnap there is no place for arguments conforming to schema II. This seems to be true of Cheeseman, as well [ Cheeseman, 1988 ] Nevertheless, there are some arguments in favor of schema II playing a role in uncertain inference. 7 ARGUMENTS IN FAVOR OF SCHEMA II First, as many writers agree, if the use of schema II is only a shorthand approximation for the use of schema II, it is nevertheless an approximation that ....

Peter Cheeseman. Inquiry into computer understanding. Computational Intelligence, 4:58--66, 1988.

....the incomplete knowledge; they will show non monotonic behaviour when the knowledge is increasing. Recently, probability theory has become more and more accepted as an appropriate tool for that purpose, especially in connection with the notion of entropy ( Paris Vencovska, 1989] Pearl, 1988] [Cheeseman, 1988]) Following [Cox, 1979] we consider probability 2 Non Monotonic reasoning on probability models theory as an adequate model for one dimensional belief of propositional expressions 1 . Following [Adams, 1975] we consider the conditional probability to be much more adequate compared to the ....

P. Cheeseman, "An Inquiry into Computer Understanding", Computational Intelligence, Vol. 4, pp. 58-66, 1988.

.... class (which is not always, according to him, the most specific one on which we have some information available) while Bayesian probability supporters emphasize the fact that a probability is always a conditional probability in order to take into account the current context (see Cheeseman [10] and Pearl [50] for instance) In this paper we develop preliminary works reported in [20] 22] 23] and mainly focus our attention on the possible relationship between the three valued calculus developed on conditional objects like q p and nonmonotonic reasoning systems based on the study of ....

Cheeseman P., An inquiry into computer understanding. Computational Intelligence, 4, 1988, 58-66.

.... aims are thus to: ffl Define what is meant by an argument, and how arguments are used ffl Model how previous cases can be used in conjunction with arguments to solve new problems ffl Avoid the use of numerical measures of probability or belief, deemed unintuitive and problematic by many (see [Cheeseman, 1988] and subsequent debate for an excellent discussion) This last aim is particularly important, as it distinguishes this work from other attempts to handle uncertainty with numerical approaches. To address this task we only deal with relative strengths of arguments, rather than any absolute measure ....

Peter Cheeseman. An inquiry into computer understanding. Computational Intelligence, 4(1), Feb 1988. (followed by 23 commentaries).

....belief of propositional expressions. For 14 propositional logic can be used to describe relations between properties of individuals, especially in connection with probability theory (for examples see later) discussions comparing non monotonic logics with probability theory see e.g. [Pea88, BGHK94, Che88]) So we inherit a formally and semantically very well known tool. It allows us to express incomplete knowledge as disjunction of models, possibly incomplete) ranking information by precise probabilities, and imprecise probabilities with probability intervals (here expressed by a disjunction of ....

P. Cheeseman. An Inquiry into Computer Understanding. Computational Intelligence, 4:58--66, 1988.

....not requiring precise probability measures to be supplied. A second problem is that many probabilistic representations are only proof functional (i.e. able to calculate a value for A B given A and B [1] by making assumptions of independence generally not justified in many domains. Cheeseman [2] and the subsequent debate provides an excellent discussion on the issue of Bayesian and other probabilistic representations for learning systems. This has led us to propose a representation of background knowledge based on the use of arguments for and against a hypothesis being true as a means ....

P. Cheeseman. An inquiry into computer understanding. Computational Intelligence, 4(1), Feb 1988. (followed by 23 commentaries).

....and semantics for the combination of both kinds of probability and defines a sound axiom system for reasoning with this logic. He also shows that, in general, no complete axiomatization can be found while the specified axiom system is complete in particular cases which are of interest in practice. [9] gives a full discussion on the issue of combining logic and probability theory. 4.2 Knowledge Based Model Construction (KBMC) Also research on reasoning systems has been done that actually perform inference in this setting, none of them uses a first order probabilistic calculus comparable to the ....

P. Cheeseman. An inquiry into computer understanding. Computational Intelligence, 4(1):58--66, February 1988.

....with a deductive reasoning system. The second approach uses fuzzy set theory [Zad83, Zad86a] The third approach is based on probabilistic methods. While the use of probabilistic methods is gaining acceptance, the appropriateness of these techniques has been hotly debated. An essay by Cheeseman [Che88] and the follow up discussion in a special issue of Computational Intelligence provides a good summary of the issues. Two main probabilistic approaches are in use. The first uses conventional probabilistic methods [Pea88, LS88, AOJJ89] and the second uses the DempsterShafer theory of evidence ....

Cheeseman, Peter. An inquiry into computer understanding. Computational Intelligence, 4:58--66, February 1988.

....inference C BK , E; therefore, tentatively, pending new information, C. 1 Both views are discussed in detail in Kyburg 1970, mainly from the point of view of the philosophy of statistics and philosophy of science. For example, see Carnap 1950, Dewey 1953, Peirce 1877. 2 See, for example, Peter Cheeseman 1988. 3 See AIJ 1980, or Ginsberg 1987. 4 Isaac Levi (Levi 1991) shows by example that it is possible to work directly with an algebra of full beliefs. While this is of philosophical importance, it is of questionable relevance to artificial intelligence. 5 The representation is due to Hemple 1961. 3 ....

....of hallucination. 25 For a discussion of the issue of observation, see Kyburg forthcoming. 26 A sentence made famous by Roderick Chisholm (Chisholm 1957) who is the twentieth century philosopher who has explored most thoroughly the problem of perceptual input. 27 In Carnap 1968. 28 For example, Cheeseman 1988. 29 In philosophy Braithwaite 1946, and Levi and Morgenbesser 1964 have argued along these lines: to accept a contingent statement is to act as if it is true in all circumstances. 22 What we take as practically certain we depend on in our deliberations; we use it as data for engineering design; ....

Cheeseman, Peter (Cheeseman 1988): "Inquiry into Computer Understanding," This Journal 4, 58-66.

....formalisms from probability and decision theory rather than developing new ones. This question, of course, has a long history in AI and I am not going to rehash it all here. The discussion is excellently summarized in two special issues of Computational Intelligence, with position papers by Cheeseman [1988] and Kyburg [1994] respectively. One way of looking at the defeasible rules employed in argumentation is as statements of qualitative conditional probability. This yields the interpretation of defaults like birds fly as most things that are birds are things that fly. However, another ....

Peter Cheeseman, "An inquiry into computer understanding," Computational Intelligence, 4(1):58--66, 1988.

....logically determined initial probability function, and the agent can change his degrees of belief by conditioning this prior probability with his new information. Alternately, on the Bayesian or subjective view (De Finetti [ 1964 ] Savage [ 1964 ] Lindley [ 1965a; 1965b ] Jeffrey [ 1983 ] Cheeseman [ 1988 ] there is no such thing as a logically determined prior probability, instead the agent has a personal prior probability distribution that can be anything the agent wishes. My aim here is not to argue about what interpretation of probabilities is better. Rather, I would claim that both ....

....these worlds. The simplest representation using universal quantification, then, fails to do the job. Another possibility, however, is to use conditional probabilities. We have probabilities attached to sentences hence with two sentences we can form conditional probabilities. It has been suggested (Cheeseman [ 1988 ] that meta level statements of the following form can be used to capture statistical statements, in particular for the statement about birds: 8x:pr[Fly(x)jBird(x) 0 :9 : The reason that this is a meta level quantification is that the universal quantifier is quantifying over a formula ....

Peter Cheeseman. An inquiry into computer understanding. Computational Intelligence, 4(1), February 1988.

....of learning that have developed within the computer science community; in other ways it is more primitive. I believe that it is instructive to include Bayesian inference in a study of machine learning in order to highlight these differences. Cheeseman has several interesting articles (e.g. [1, 2]) that make a good starting point for reviewing the issues. The journal containing [2] has many other articles discussing Bayesian approaches versus others. Bayesian inference handles the following issues reasonably well: 1. Prior knowledge of the learner; these are reflected in the learner s set ....

....it is more primitive. I believe that it is instructive to include Bayesian inference in a study of machine learning in order to highlight these differences. Cheeseman has several interesting articles (e.g. 1, 2] that make a good starting point for reviewing the issues. The journal containing [2] has many other articles discussing Bayesian approaches versus others. Bayesian inference handles the following issues reasonably well: 1. Prior knowledge of the learner; these are reflected in the learner s set of prior probabilities. 2. Evidence that does not eliminate hypotheses, but which ....

Peter C. Cheeseman. An inquiry into computer understanding. Computational Intelligence, 4(1):58--66, February 1988.

....of a given set. This difference is minor there are well known mappings from propositions to events, and vice versa. I use events here since they are more standard in the probability literature. c fl1999 AI Access Foundation and Morgan Kaufmann Publishers. All rights reserved. Halpern ffl Cheeseman (1988) has called it the strongest argument for use of standard (Bayesian) probability theory . Similar sentiments are expressed by Jaynes (1978, p. 24) indeed, Cox s Theorem is one of the cornerstones of Jaynes recent book (1996) ffl Horvitz, Heckerman, and Langlotz (1986) used it as a basis for ....

Cheeseman, P. (1988). An inquiry into computer understanding. Computational Intelligence, 4 (1), 58--66.

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Peter Cheeseman. An inquiry into computer understanding. Computational Intelligence, 4(1):58--66, February 1988.

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Peter Cheeseman. An inquiry into computer understanding. Computational Intelligence, 4(1):58--66, 1988.

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