模式识别科学发展与现状(2.模式识别四种方法)

2 Four Approaches to Pattern Recognition

2 模式识别四种方法

 

In science, new knowledge is phrased in terms of existing knowledge. The starting point of this process is set by generally accepted evident views, or observations and facts that cannot be explained further. These foundations,however, are not the same for all researchers. Different types of approaches may be distinguished originating from different starting positions. It is almost a type of taste from which perspective a particular researcher begins. As a consequence, different ‘schools’ may arise. The point of view, however, determines what we see. In other words, staying within a particular framework of thought we cannot achieve more than what is derived as a consequence of the corresponding assumptions and constraints. To create more complete and objective methods, we may try to integrate scientific results originating from different approaches into a single pattern recognition model. It is possible that confusion arises on how these results may be combined and where they essentially differ. But the combination of results of different approaches may also appear to be fruitful, not only for some applications, but also for the scientific understanding of the researcher that broadens the horizon of allowable starting points. This step towards a unified or integrated view is very important in science as only then a more complete understanding is gained or a whole theory is built.

对于科学，新的知识是从已有的知识发展出来的。这个过程的起始点是来源于一般可让人接受的、显而易见的观点，或无法被进一步解释的观察结果和因素。然而这些创建过程不同的研究者有不同的过程。从最初的观点可以区别出各种不同的方法类型，这几乎成了发现某个研究者的研究起点的方法。这样便导致了不同派别的产生。然而，不同的看问题的角度决定了我们对问题的理解，换句话说，在某个思想的框架下，我们只能从相应的假设和约束去推理。如果要建立更全面和客观的方法，我们可以尝试把来源于不同方法的科学成果集成到一个模式识别模型中，不过，在集成方法和区别方法上有可能会产生混淆。但是综合应用各种方法也有可能看上去是很有用的，不仅是对于一些应用，对于研究者的科学理解也是很有益处的，帮助他们从更宽的角度来研究问题，这个方法便是统一或集成的观点，这种观点在科学研究中非常重要，可以让你得到更全面的理解或建立一个完整的理论。

 

Below we will describe four approaches to pattern recognition which arise from two different dichotomies of the starting points. Next, we will present some examples illustrating the difficulties of their possible interactions. This discussion is based on earlier publications [16, 17].

下面我们将描述从两种不同出发点而区分出来的四种模式识别方法。后面我们还将举些例子说明这四个方法要相互交互应用的困难。

 

2.1 Platonic and Aristotelian Viewpoints

2.1 柏拉图和亚里士多德观点

 

Two principally different approaches to almost any scientific field rely on the　so-called Platonic and Aristotelian viewpoints. In a first attempt they may　be understood as top-down and bottom-up ways of building knowledge. They　are also related to deductive (or holistic) and inductive (or reductionistic)　principles. These aspects will be discussed in Section 4.

几乎所有的科学领域主要都是通过这两个途径来进行研究的：柏拉图和亚里士多德观点。首先可以分别把它们理解成从顶到下和从底到上的建立知识的方法。它们又分别一个跟演译推理（或从整体上研究）有关，另一个跟归纳推理（或从重现的角度）有关。这些问题将在第四小节会有介绍。

 

The Platonic approach starts from generally accepted concepts and global　ideas of the world. They constitute a coherent picture in which many details　are undefined. The primary task of the Platonic researcher is to recognize in　his observations the underlying concepts and ideas that are already accepted　by him. Many theories of the creation of the universe or the world rely on　this scenario. An example is the drifts of the continents or the extinction of　the mammoths. These theories do not result from a reasoning based on observations,　but merely from a more or less convincing global theory (depending　on the listener!) that seems to extrapolate far beyond the hard facts. For　the Platonic researcher, however, it is not an extrapolation, but an adaptation　of previous formulations of the theory to new facts. That is the way this　approach works: existing ideas that have been used for a long time are gradually　adapted to new incoming observations. The change does not rely on an　essential paradigm shift in the concept, but on finding better, more appropriate　relations with the observed world in definitions and explanations. The　essence of the theory has been constant for a long time. So, in practise the Platonic researcher starts from a theory which can be stratified into to a number of hypotheses that can be tested. Observations are collected to test these hypotheses and, finally, if the results are positive, the theory is confirmed.

柏拉图方法以普遍可以被人接受的概念和公理为出发点，建立一个许多未被定义的具有逻辑连贯性的科学描述。柏拉图式科学研究者的主要工作是基于可以被接受的概念和方法来认识所观察到的事物。许多宇宙或世界的理论建立都是依赖于这个途径。这样的例子有大陆漂移说和孔龙灭绝说，这些理论不是通过观察来证明的，只是根据一个或多或少让人信服（依赖于不同人的理解）的理论，这个理论似乎是远超脱于那些不变的客观因素的推断。然而，对于柏拉图式研究者，这不是一个总结归纳过程，而是一个针对新因素做理论上公式形式的演译。这个方法的过程是这样的：依据已存在的理论，这些理论且并被应用很长时间了，在不断新的观察中这些理论逐渐被做适应性的修改，这种变化不是概念上的本质转换，而是在定义和解释的角度上，寻找与所观察到的世界更好更适合的关联。理论的基础已经在很长的时间内是稳定不变了，所以，在实践中柏拉图式研究者开始于这样的一个理论：这个理论可进行层次化，形成一些可以被检验的假设。收集观察到的事物，对假设进行检验，最后，如果得到的结果是正面的，则这个理论被确认了下来。

 

The observations are of primary interest in the Aristotelian approach. Scientific　reasoning stays as closely as possible to them. It is avoided to speculate　on large, global theories that go beyond the facts. The observations are always　the foundation on which the researcher builds his knowledge. Based on them,patterns and regularities are detected or discovered, which are used to formulate　some tentative hypotheses. These are further explored in order to arrive　at general conclusions or theories. As such, the theories are not global, nor　do they constitute high level descriptions. A famous guideline here is the socalled　Occam’s razor principle that urges one to avoid theories that are more　complex than strictly needed for explaining the observations. Arguments may　arise, however, since the definition of complexity depends, e.g. on the mathematical　formalism that is used.

观察在亚里士多德方法中起了主要作用。科学理论尽可能地与观察紧密相联系。这个方法躲避产生大的全局性的超脱于观察依据的理论。观察总是研究者建立他的理论的基础。根据观察，模式和规律被检测或发现出来，并且被用于证明一些试探性的假设。更进一步地，便可以达到一般性结论或理论。这样，得到的理论既不是全局性的，也不能用于建立高层次的表达。这里有一个著名的Occam剃刀原理：尽力避免产生超出解释观察所严格需要的更为复杂的理论。然而，对此可能会产生争议，因为对于复杂理论的定义是需要的，例如需要依赖于应用精确的形式描述。

 

The choice for a particular approach may be a matter of preference or determined by non-scientific grounds, such as upbringing. Nobody can judge what the basic truth is for somebody else. Against the Aristotelians may be held that they do not see the overall picture. The Platonic researchers, on the other hand, may be blamed for building castles in the air. Discussions between followers of these two approaches can be painful as well as fruitful.They may not see that their ground truths are different, leading to pointless debates. What is more important is the fact that they may become inspired by each other’s views. One may finally see real world examples of his concepts,while the other may embrace a concept that summarizes, or constitutes an abstraction of his observations.

对于一个特定途径的选择可能是一个优先选择的问题，或取决于非科学因素，如教育背景。没有人能够判断对于其他人来说什么是基本真理。相反地，亚里士多德式研究出来的理论可能无法说明事物的全局性的问题，另一方面，柏拉图式研究者可能被埋怨在建立空中楼阁。在二者之间进行有效地评判是件痛苦的事。他们可能会不明白二者的基本出发点是不同的，这样会导致没有结果的争论。重要的是二者之间可以互相启发。其中一方可能最终发现他的理论的实证，而另一方可能包含了这个理论，这个理论是对他所观察事物的总结或抽象。

 

2.2 Internal and the External Observations

2.2　内在的和外在的观察

 

In the contemporary view science is ‘the observation, identification, description,experimental investigation, and theoretical explanation of phenomena’or ‘any system of knowledge that is concerned with the physical world and its　phenomena and that entails unbiased observations and systematic experimentation.　So, the aspect of observation that leads to a possible formation of a concept or theory is very important. Consequently, the research topic of the　science of pattern recognition, which aims at the generalization from observations for knowledge building, is indeed scientific. Science is in the end a brief explanation summarizing the observations achieved through abstraction and their generalization.

根据现代的观点，科学就是“观察，鉴定，描述，试验性研究和对现象的理论上解释”，或者是“跟物理世界及物理世界的现象有关系的任何知识体系，且其必须是源于无偏见的观察和系统性的试验。”所以，可能引导一个概念或理论形成的观察是非常重要的。因此，以从观察中得到一般性法则来构建科学知识为目标，这样的模式识别科学研究方法才具有真正的科学性。科学最终目标是为了概括性地简要地解释所观察到的现象，这是通过抽象和一般性推广来达到的。

 

Such an explanation may primarily be observed by the researcher in his own thinking. Pattern recognition research can thereby be performed by introspection. The researcher inspects himself how he generalizes from observations. The basis of this generalization is constituted by the primary observations. This may be an entire object (‘I just see that it is an apple’)or its attributes (‘it is an apple because of its color and shape’). We can also observe pattern recognition in action by observing other human beings(or animals) while they perform a pattern recognition task, e.g. when they recognize an apple. Now the researcher tries to find out by experiments and measurements how the subject decides for an apple on the basis of the stimuli presented to the senses. He thereby builds a model of the subject, from senses to decision making.

科学解释可能可以主要通过研究者自己的思维被观察到。由此模式识别可以通过自省的方式来进行研究。研究者反省自己怎样通过观察来得到理论的推广。建立推广的基础是源于对事物的观察。这可能是一个事物的整体（“我只明白它是一个苹果”）或是它的属性（“它是一个苹果，是因为它的颜色和形状象苹果”）。当其他人（或动物）在做诸如模式识别行为时，例如当他们在辨认一个苹果时，我也可以通过观察他们的行为来研究模式识别。这时研究者通过试验和数据试图发现是通过感观刺激怎样来决定它是一个苹果。于是他建立了跟这个目的有关的模型，即从感知到下决定的识别模型。

 

Both approaches result into a model. In the external approach, however,the senses may be included in the model. In the internal approach, this is either　not possible or just very partially. We are usually not aware of what happens　in our senses. Introspection thereby starts by what they offer to our thinking(and reasoning). As a consequence, models based on the internal approach　have to be externally equipped with (artificial) senses, i.e. with sensors.

外在和内在的两种途径最后都是建立一个模型。在外在的途径中，无论如何感知是可能被包含在模型中。在内在的途径中，这不仅不可能而且也是十分局限性的。我们通常无法通过我们的感观来感知到事物的变化。从而通过内省发现哪些是有助于我们作判断的。由此，基于内在的途径来建立的模型必须配上外在的（人工）感知，例如感知器。

 

2.3 The Four Approaches

2．3　四种模式识别方法

 

The following four approaches can be distinguished by combining the two

dichotomies presented above:

下面四种方法可以通过上面所提到的柏拉图和亚里士多德观点把它们合并成两类来区别出来：

(1) Introspection by a Platonic viewpoint: object modeling.

(2) Introspection by an Aristotelian viewpoint: generalization.

(3) Extrospection by an Aristotelian viewpoint: system modeling.

(4) Extrospection by a Platonic viewpoint: concept modeling.

 

（1）柏拉图式内省：对象建模。

（2）亚里士多德式内省：推广。

（3）亚里士多德式外省：系统建模。

（4）柏拉图式外省：概念建模。

 

These four approaches will now be discussed separately. We will identify some

known procedures and techniques that may be related to these. See also Fig. 2.

现在来分别讨论这四种方法。我们将列出跟这四个方法有关的大家所熟知的过程和技术。如图2所示。

Object modeling. This is based on introspection from a Platonic viewpoint.The researcher thereby starts from global ideas on how pattern recognition systems may work and tries to verify them in his own thinking and reasoning.He thereby may find, for instance, that particular color and shape descriptions of an object are sufficient for him to classify it as an apple. More generally, he may discover that he uses particular reasoning rules operating on a fixed set of possible observations. The so-called syntactic and structural approaches to pattern recognition [26] thereby belong to this area, as well as the case-based reasoning [3]. There are two important problems in this domain: how to constitute the general concept of a class from individual object descriptions and how to connect particular human qualitative observations such as ‘sharp edge’or ‘egg shaped’ with physical sensor measurements.

对象建模：这是基于柏拉图观点的内省形式。研究者从能使模式识别系统工作起来的全局思路出发，设法检验他自己的思路和理论哪些是有用的。比如，他可能会发现用颜色和形状判断苹果就已经足够了。更一般地，他可能发现他可以用特定的规则对鉴别一组固定的观察到的事物。所谓的句法规则和结构模式识别就是属于这样的类型，即基于用例推理。在这方面有两个重要的问题：一个是怎么从个体对象描述中建立一个具有一般性意义的一个种类的概念，另一个是怎么把人对事物的感观认识（如“锐利边缘”或“蛋形状”）和物理感应器的度量联系起来。

 

Generalization. Let us leave the Platonic viewpoint and consider a researcher who starts from observations, but still relies on introspection. He wonders what he should do with just a set of observations without any framework.An important point is the nature of observations. Qualitative observations such as ‘round’, ‘egg-shaped’ or ‘gold colored’ can be judged as recognitions in themselves based on low-level outcomes of senses. It is difficult to neglect them and to access the outcomes of senses directly. One possibility for him is to use artificial senses, i.e. of sensors, which will produce quantitative descriptions. The next problem, however, is how to generalize from such numerical outcomes. The physiological process is internally unaccessible. A researcher who wonders how he himself generalizes from low level observations given by numbers may rely on statistics. This approach thereby includes the area of statistical pattern recognition.If we consider low-level inputs that are not numerical, but expressed in attributed observations as ‘red, egg-shaped’, then the generalization may be based on logical or grammatical inference. As soon, however, as the structure of objects or attributes is not generated from the observations, but derived (postulated) from a formal global description of the application knowledge,e.g. by using graph matching, the approach is effectively top-down and thereby　starts from object or concept modeling.

推广：让我们先不考虑柏拉图模式，来看一个以观察为研究出发点但仍以依靠内省形式的研究者。在没有任何框架下，他对所得到的一组观察无从下手。一个重要点是观察的角度。可度量观察，诸如“圆形”、“蛋形”或“金黄色”，这些都是可以在低层次上的感知直接判断到。对于他来说，一个可能的办法是通过使用人工感知设备，如感应器，它可以得到可度量的描述。生理上的处理过程是内在的，令人难以明白的。研究者不明白为什么自己可以从几个低层次的观察中就可得到推广，他可能要依赖统计的方法，这个方法包括统计模式识别领域。如果我们考虑低层次的非数据输入，只表达成如“红，蛋形”这样的观察结果，于是这种推广可能是要基于逻辑和语法推广。然而对象或属性的结构一旦不是从观察中得到，而（假定）是从应用知识的全局描述中继承出来，例如运用图像匹配方法，那么这种方法实际上是自顶向下的方法，属于对象或概念建模类型。

 

System modeling. We now leave the internal platform and concentrate on research that is based on the external study of the pattern recognition abilities of humans and animals or their brains and senses. If this is done in a bottom-up way, the Aristotelian approach, then we are in the area of low level modeling of senses, nerves and possibly brains. These models are based on the physical and physiological knowledge of cells and the proteins and minerals that constitute them. Senses themselves usually do not directly generalize from observations. They may be constructed, however, in such a way that this process is strongly favored on a higher level. For instance, the way the eye (and the retina, in particular) is constructed, is advantageous for the detection of edges and movements as well as for finding interesting details in a global, overall picture. The area of vision thereby profits from this approach. It is studied how nerves process the signals they receive from the senses on a level close to the brain. Somehow this is combined towards a generalization of what is observed by the senses. Models of systems of multiple nerves are called neural networks. They appeared to have a good generalization ability and are thereby also used in technical pattern recognition applications in which the physiological origin is not relevant [4, 62].

系统建模:我们现在走出内在的体系方法，集中研究人和动物或他们头脑和感官产生模式识别能力的外在学习方法。如果采用自底向上的方法，即亚里士多德方法，我们便是在感官、神经和头脑这样低层次上建模的领域里。这些模型是基于细胞和蛋白质和组成它们的矿物质的物理和生理知识。感官本身通常不能直接从观察中得到结果，可能要进行构建，然而这种处理过程总是在高层次进行。例如，眼睛（确切地说是视网膜）辨认事物方法是通过边缘和运动检测，从全局（整个画面）来发现感兴趣的细节信息。视觉领域的研究便是得益于这种方法，通过研究神经如何处理从感应器官收到的信号，接近于对人脑的研究。多个神经的系统建模称为神经网络，他们有很好的推广能力，也被用在了与生理学无关的模式识别应用技术中[4,62]。

 

Concept modeling. In the external platform, the observations in the starting point are replaced by ideas and concepts. Here one still tries to externally model the given pattern recognition systems, but now in a top-down manner.

概念建模:属于外在的体系方法，以理论和概念为出发点，而不是所观察到的事物。这里仍然以外在建模方式来建立模式识别系统，但是这里是从顶向下的方法。

 

An example is the field of expert systems: by interviewing experts in a particular pattern recognition task, it is attempted to investigate what rules they use and in what way they are using observations. Also belief networks and probabilistic networks belong to this area as far as they are defined by experts and not learned from observations. This approach can be distinguished from the above system modeling by the fact that it is in no way attempted to model a physical or physiological system in a realistic way. The building blocks are the ideas, concepts and rules, as they live in the mind of the researcher. They are adapted to the application by external inspection of an expert, e.g. by interviewing him. If this is done by the researcher internally by introspection,we have closed the circle and are back to what we have called object modeling,as the individual observations are our internal starting point. We admit that the difference between the two Platonic approaches is minor here (in contrast to the physiological level) as we can also try to interview ourselves to create an objective (!) model of our own concept definitions.

专家系统是这方面的例子：通过在特定的模式识别任务中研究专家的方法，研究他们所用的规则，研究他们怎么运用观察到的事物。信心网络和概率网络被专家设定，而不是从观察事物中得到，它们也属于概念建模方法。概念建模和系统建模的区别在于概念建模不会模仿现实事物而去建立物理或生理模型系统。概念建模建立在研究者头脑中的方法、概念和原则。通过外在地考察某个专家（如跟专家交谈）来建立应用系统。如果内在的自省式研究者用了这个方法，则我们接近形成了一个循环，回到前面所讲的对象建模，即以个体的观察事物为建模出发点。我们承认两个柏拉图方法的区别在这里区别是很小的（相对于生理学的层次），即我们也可以尝试通过内省来建立我们自己定义的概念的一个对象模型。

 

2.4 Examples of Interaction

2.4 四种方法交叉运用的例子

The four presented approaches are four ways to study the science of pattern recognition. Resulting knowledge is valid for those who share the same starting point. If the results are used for building artificial pattern recognition devices, then there is, of course, no reason to restrict oneself to a particular approach. Any model that works well may be considered. There are, however,certain difficulties in combining different approaches. These may be caused by differences in culture, assumptions or targets. We will present two examples,one for each of the two dichotomies.

上面介绍的四种方法是研究模式识别科学的四种途径。根据不同的出发点区别出了这四种方法。如果要建立一个人工模式识别设备，是不一定限制一定要用某一种方法的，任何方法模型都可能可以被用上。然而，困难的是怎么去综合运用这些方法，可能是因为不同的情况、假设或目标需要这样地去做。对这四种方法的两个大类我们将举两个例子来说明。

 

Artificial neural networks constitute an alternative technique to be used for generalization within the area of statistical pattern recognition. It has taken, however, almost ten years since their introduction around 1985 before neural networks were fully acknowledged in this field. In that period, the neural network community suffered from lack of knowledge on the competing classification procedures. One of the basic misunderstandings in the pattern recognition field was caused by its dominating paradigm stating that learning systems should never be larger than strictly necessary, following the Occam’s razor principle. It could have not been understood how largely oversized systems such as neural networks would have ever been able to generalize without adapting to peculiarities in the data (the so-called overtraining). At the same time, it was evident in the neural network community that the larger neural network the larger its flexibility, following the analogy that a brain with many neurons would perform better in learning than a brain with a few ones. When this contradiction was finally solved (an example of Kuhn’s paradigm shifts [48]), the area of statistical pattern recognition was enriched with a new set of tools. Moreover, some principles were formulated towards understanding of pattern recognition that otherwise would have only been found with great difficulties.

人工神经网络技术在统计模式识别领域中的推广能力上成为了一个替代技术。然而这个技术从1985年被介绍出来到被完全接受已花了十年时间。在这十年里，研究神经网络的人因缺少竞争分类方法知识而受挫折。在模式识别领域中有一个让引起误解的主流观点：学习系统不要比限定的需求更复杂，需遵从奥克母剃刀原则。这个原则让人无法明白系统要做到多大才能不用去适配数据的特殊点（所谓过学习）就能具有推广能力，如神经网络系统的大小。与此同时，在神经网络中可以被证明的是神经网络越大则适应性越强，这是依据这样的推理：具有较多神经的脑子比具有较少神经的脑子学习能力要更好。当这个矛盾最后被解决后（这是一个库恩范式转移的例子），统计模式识别领域才被广泛应用了起来。此外，已有一些原理可以被用来形式化地理解模式识别，其它的原理则很难被理解。

 

In general, it may be expected that the internal approach profits from the results in the external world. It is possible that thinking, the way we generalize from observations, changes after it is established how this works in nature.For instance, once we have learned how a specific expert solves his problems,this may be used more generally and thereby becomes a rule in structural pattern recognition. The external platform may thereby be used to enrich the internal one.

通常情况下,可能会被认为内在的方法是得益于对外部世界的推理结论。可能会这样认为：我们从观察中推广得到的方法在实际运用时会发生改变。例如，一旦我们知道一个专家怎么去解决他的问题，于是可以把他的方法更一般化，结果形成结构模式识别中的一条规则。外在的方法可以被用于完善内在方法。

 

A direct formal fertilization between the Platonic and Aristotelian approaches is more difficult to achieve. Individual researchers may build some understanding from studying each other’s insights, and thereby become mutually inspired. The Platonist may become aware of realizations of his ideas and concepts. The Aristotelian may see some possible generalizations of the observations he collected. It is, however, still one of the major challenges in science to formalize this process.

把柏拉图和亚里士多德方法从形式上直接联系起来是很难达到的，但是研究者个人可以从互相交流中得到一些理解，并互相得到启发。柏拉图派的人可能知道他的理论和概念的实现方法。亚里士多德派的人可能从他收集到的观察中得到推广理论，然而，在科学上形式化这个过程还是一个主要的挑战性工作。

 

How should existing knowledge be formulated such that it can be enriched by new observations? Everybody who tries to do this directly encounters the problem that observations may be used to reduce uncertainty (e.g. by the parameter estimation in a model), but that it is very difficult to formalize uncertainty in existing knowledge. Here we encounter a fundamental ‘paradox’for a researcher summarizing his findings after years of observations and studies: he has found some answers, but almost always he has also generated more new questions. Growing knowledge comes with more questions. In any formal system, however, in which we manage to incorporate uncertainty(which is already very difficult), this uncertainty will be reduced after having incorporating some observations.We need an automatic hypothesis generation in order to generate new questions. How should the most likely ones be determined? We need to look from different perspectives in order to stimulate the creative process and bring sufficient inspiration and novelty to hypothesis generation. This is necessary in order to make a step towards building a complete theory. This, however, results in the computational complexity mentioned in the literature [60] when the Platonic structural approach to pattern recognition has to be integrated with the Aristotelian statistical approach.

怎么把现有的知识形式化，这样可以通过新观察的到数据来加以完善？每位想直接这样做的人都碰到这样的问题：通过观察数据可能可以减少不可靠性（例如在建模中的参数估计方法），但是在现有的知识体系中进行形式化非确定性问题是非常困难的。这里我们碰到一个研究者在总结他多年观察和研究得到的一个基本“缪论”：他找到了一些答案，但是几乎同时他又总是碰到新问题，得到的知识越多，产生的疑问也越多。然而,在任何正式系统中,我们可以设法引入不可靠性(但这是非常困难的),这个不可靠性在加入一些观察数据后会得到减少。我们需要一个自动化的假设产生方法来发现新问题。怎么去决定哪个最好呢？我需要从不同的角度看问题，以此来模拟这样的创造性处理过程并产生富有灵感和新奇的假设。这对于逐步建立一个完整的理论是需要的。然而，在附录[60]所引文章中提到：当柏拉图式的结构模式识别方法要集成亚里士多德统计模式识别方法时要考虑到计算复杂度问题。

 

The same problem may also be phrased differently: how can we express the uncertainty in higher level knowledge in such a way that it may be changed (upgraded) by low level observations? Knowledge is very often structural and has thereby a qualitative nature. On the lowest level, however, observations are often treated as quantities, certainly in automatic systems equipped with physical sensors. And here the Platonic – Aristotelian polarity meets the internal– external polarity: by crossing the border between concepts and observations we also encounter the border between qualitative symbolic descriptions and quantitative measurements.

同样的问题也可以以这样的不同方式来表示:怎样用更高层次的知识来表示不确定性并且可以通过低层次的观察来改变(或升级)?知识通常是具有结构的形式和对自然界定性的描述。然而，在最低层次配备了物理感应器的自动化系统中，观察数据通常是被量化了的数据。这里柏拉图---亚里士多德方法两个极端对应内在---外在两个极端：从概念方法到观察数据方法之间进行转变也相应会碰到从定性符号描述到定量测定的转变