Real-Time Systems. Design Principles for Distributed Embedded Applications. Herman Kopetz. Second Edition (811374), страница 15
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The notion of category is recursive: the elementsof a category can themselves be categories. We thus arrive at a hierarchy ofcategories, going from the concrete to the abstract. At the lowest level we findimmediate sensory experiences.A concept is a category that is augmented by a set of beliefs about its relations toother categories [Rei10, pp. 261–300].
The set of beliefs relates a new concept toalready existing concepts and provides for an implicit theory (a subjective mentalmodel). As a new domain is penetrated, new concepts are formed and linked to theconcepts that are already present in the conceptual landscape. A concept is a mentalconstruct of the generalizable aspects of a known entity. It has an intension (What is2.1 Cognition33the essence?) and an extension, answering the question as to which things andmental constructs are exemplars of the concept.
A concept can also be considered asa unit of thought [Vig62].2.1.3Cognitive ComplexityWhat do we mean when we say an observer understands a scenario? It meansthat the concepts and relationships that are employed in the representation ofthe scenario have been adequately linked with the conceptual landscape and themethods of reasoning of the observer. The tighter the links are, the better isthe understanding. Understanding (and therefore simplicity) is thus a relationbetween an observer and a scenario, not a property of the scenario.We take the view of Edmonds [Edm00] that complexity can only be assigned tomodels of physical systems, but not to the physical systems themselves, no matterwhether these physical systems are natural or man made.
A physical system has anearly infinite number of properties – every single transistor of a billion-transistorsystem-on-chip consists of a huge number of atoms that are placed at distinctpositions in space. We need to abstract, to build models that leave out the seeminglyirrelevant detail of the micro-level, in order to be able to reason about properties ofinterest to us at the macro-level.What then is a good measure for the cognitive complexity of a model? We arelooking for a quantity that measures the cognitive effort needed to understand themodel by a human observer. We consider the elapsed time needed to understand amodel by a given observer a reasonable measure for the cognitive effort and thusfor the complexity of a model relative to the observer. We assume that the givenobserver is representative for the intended user group of the model.According to the scientific tradition, it would be desirable to introduce anobjective notion of cognitive complexity without reference to the subjectivehuman experience.
However, this does not seem to be possible, since cognitivecomplexity refers to a relation between an objective external scenario and thesubjective internal conceptual landscape of the observer.The perceived complexity of a model depends on the relationship between theexisting subjective conceptual landscape and the problem solving capability ofthe observer versus the concepts deployed in the representation of the model, theinterrelations among these concepts and the notation used to represent these concepts. If the observer is an expert, such as the chess grandmaster in the previousexample, the experiential subsystem provides an understanding of the scenariowithin a short time and without any real effort.
According to our metric, thescenario will be judged as simple. An amateur has to go through a tedious causeand-effect analysis of every move employing the rational subsystem that takes timeand explicit cognitive effort. According to the above metric, the same chessscenario will be judged as complex.342 SimplicityThere are models of behavior and tasks that are intrinsically difficult tocomprehend under any kind of representation. The right column of Table 2.2 inSect. 2.5 lists some characteristics of intrinsically difficult tasks. It may take a longtime, even for an expert in the field, to gain an understanding of a model thatrequires the comprehension of the behavior of difficult tasks – if at all possible.According to the introduced metric, these models are classified as exceedinglycomplex.In order to gain an understanding of a large system we have to understand manymodels that describe the system from different viewpoints at different abstractionlevels (see also Sect.
2.3.1). The cognitive complexity of a large system depends onthe number and complexity of the different models that must be comprehended inorder to understand the complete system. The time it takes to understand all thesemodels can be considered as a measure for the cognitive complexity of a largesystem.Case studies about the understanding of the behavior of large systems haveshown that the perceptually available information plays an important role fordeveloping an understanding of a system [Hme04]. Invisible information flowsbetween identified subsystems pose a considerable barrier to understanding.If every embedded system is one of its kind and no relationships betweendifferent instances of systems can be established, then there is hardly a chancethat experience-based expert knowledge can be developed and the transition fromthe tedious and effortful rational subsystem to the effortless experiential subsystemcan take place.One route to simplification is thus the development of a generic model of anembedded system that can be successfully deployed in many different domains at aproper level of abstraction.
This model should contain few orthogonal mechanismsthat are used recursively. The model must support simplification strategies andmake public the internal information flow between identified subsystems, such thatthe process of gaining an understanding of the behavior is supported. By gettingintimately acquainted with this model and gaining experience by using this modelover and over again, the engineer can incorporate this model in the experientialsubsystem and become an expert.
It is one stated goal of this book to develop such ageneric cross-domain model of embedded systems.2.1.4Simplification StrategiesThe resources in the rational problem solving subsystem of humans, both in storageand processing capacity, are limited. The seminal work of Miller [Mil56] introduced a limit of five to seven chunks of information that can be stored in short-termmemory at a given instant. Processing limitations are established by the relationalcomplexity theory of Halford [Hal96].
Relational complexity is considered tocorrespond to the arity (number of arguments) of a relation. For example, binaryrelations have two arguments as in LARGER-THAN (elephant, mouse). The2.2 The Conceptual Landscape35relational complexity theory states that the upper limits of adult cognition seem tobe relations at the quaternary level.If a scenario requires cognitive resources that are beyond the given limits, thenhumans tend to apply simplification strategies to reduce the problem size andcomplexity in order that the problem can be tackled (possibly well, possibly inadequately) with the limited cognitive resources at hand.
We know of four strategies tosimplify a complex scenario in order that it can be processed by the limited cognitivecapabilities of humans: abstraction, partitioning, isolation, and segmentation:llllAbstraction refers to the formation of a higher-level concept that captures theessence of the problem-at-hand and reduces the complexity of the scenario byomitting irrelevant detail that is not needed, given the purpose of the abstraction.Abstraction is applied recursively.Partitioning (also known as separation of concerns) refers to the division of theproblem scenario into nearly independent parts that can be studied successfully inisolation.
Partitioning is at the core of reductionism, the preferred simplificationstrategy in the natural sciences over the past 300 years. Partitioning is not alwayspossible. It has its limits when emergent properties are at stake.Isolation refers to the suppression of seemingly irrelevant detail when trying tofind a primary cause. The primary cause forms the starting point of the causalchain that links a sequence of events between this primary cause and theobserved effect. There is a danger that the simplification strategy of isolationleads to a too simplistic model of reality (see the example on skidding of a car inSect. 2.1.1).Segmentation refers to the temporal decomposition of intricate behavior intosmaller parts that can be processed sequentially, one after the other.
Segmentation reduces the amount of information that must be processed in parallel at anyparticular instant. Segmentation is difficult or impossible if the behavior isformed by highly concurrent processes, depends on many interdependent variables and is strongly non-linear, caused by positive or negative feedback loops.2.2The Conceptual LandscapeThe notion of conceptual landscape, or the image [Bou61], refers to the personalknowledge base that is built up and maintained by an individual in the experientialand rational subsystem of the mind. The knowledge base in the experiential subsystem is implicit, while the knowledge base in the rational subsystem is explicit.
Theconceptual landscape can be thought of as a structured network of interrelatedconcepts that defines the world model, the personality, and the intentions of anindividual. It is built up over the lifetime of an individual, starting from pre-wiredstructures that are established during the development of the genotype to the phenotype, and continually augmented as the individual interacts with its environment byexchanging messages via the sensory systems.362 Simplicity2.2.1Concept FormationThe formation of concepts is governed by the following two principles [And01]:llThe principle of utility states that a new concept should encompass those properties of a scenario that are of utility in achieving a stated purpose.
The purpose isdetermined by the human desire to fulfill basic or advanced needs.The principle of parsimony (also called Occam’s razor) states that out of a set ofalternative conceptualizations that are of comparable utility the one that requiresthe least amount of mental effort is selected.There seems to be a natural level of categorization, neither too specific nor toogeneral, that is used in human communication and thinking about a domain. We callthe concepts at this natural level of categorization basic-level concepts [Rei01, p.
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