Some modeling tools are commercially available products, while others may be created or customized to provide unique modeling solutions. Modeling tools are often used as part of a broader set of engineering tools which constitute the systems development environment.
There is increased emphasis on tool support for standard modeling languages that enable models and modeling information to be interchanged among different tools. This contrasts with the traditional document-centric approach to systems engineering, where text-based documentation and specifications are managed and controlled. Leveraging a model-based approach to systems engineering is intended to result in significant improvements in system specification and design quality quality , lower risk risk and cost cost of system development by surfacing issues early in the design process, enhanced productivity through reuse of system artifacts, and improved communications among the system development and implementation teams.
In addition to creating models, the MBSE approach typically includes methods for model management model management , which aim to ensure that models are properly controlled, and methods for model validation model validation , which aim to ensure that models accurately represent the systems being modeled.
Many system modeling methods and associated modeling languages have been developed and deployed to support various aspects of system analysis, design, and implementation. Other behavioral modeling techniques include the classical state transition diagram, statecharts Harel , and process flow diagrams.
Structural modeling techniques include data structure diagrams Jackson , entity relationship diagrams Chen , and object modeling techniques Rumbaugh et al. The modeling standards section refers to some of the standard system modeling languages and other modeling standards that support MBSE.
Since Estefan's report, a number of surveys have been conducted to understand the acceptance and barriers to model-based systems engineering Bone and Cloutier , ; Cloutier Bellinger, G.
Bone, M. Accessed May 26, Cloutier, R. Chen, P. Dori, D. Estefan, J. Friedenthal, S. Moore, R. Steiner, and M. Guizzardi, G. Harel, D. Menzel, C. Bernus, K. Mertins, and G. Schmidt, Eds. Handbook on Architectures for Information Systems. Berlin, Germany: Springer-Verlag, pp. MDA Foundation Model. Rumbaugh, J. Not a MyNAP member yet? Register for a free account to start saving and receiving special member only perks.
Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. The kinds of models that scientists construct vary widely, both within and across disciplines.
Nevertheless, in building and testing theories, the practice of science is governed by efforts to invent, revise, and contest models. Using models is another important way that scientists make their thinking visible. Representation is a predecessor to full-fledged modeling. Even very young children can use one object to stand in for, or represent, another. But they typi- cally do not recognize or account for the relationships and separations between the real world and models: the features of a phenomenon that a representation accounts for or fails to account for.
The use of all forms of symbolic representa- tion, such as graphs, tables, mathematical expressions, and diagrams, can be developed in young children and lead to more sophisticated modeling in later years. They depicted Air Puppies as dots in some scenarios and as numbers in others see Figures and Modeling involves the construction and testing of representations that are analogous to systems in the real world.
These representa- FIGURE tions can take many forms, including physical Taylor explaining the movement of the wall-on-wheels with Air Puppies models, computer programs, diagrams, math- represented as dots. The Models allow scientists to summa- rize and depict the known features of a physical system and predict out- comes using these depictions. Thus, they are often important tools in the development of scientific theories.
Instead, they are deliberate simplifications of more complex systems. This means that no model is completely accurate. For example, in modeling air molecules with Air Puppies, certain characteristics of molecules are represented, such as the fact that they move constantly without intention, and other characteristics are not, such as their being composed of hydrogen and oxygen atoms.
Students need guidance in recognizing what characteristics are included in a model and how this helps fur- ther their understanding of how a system works. Do they sleep? Do they die? Mathematics For the past years, science has moved toward increasing quantification, visu- alization, and precision.
Mathematics provides scientists with another system for sharing, communicating, and understanding science concepts. Often, expressing an idea mathematically results in the discovery of new patterns or relationships that otherwise might not be seen. In the grade-level representation activities that follow, third-grade children investigating the growth of plants wondered whether the shoots the part of the plant growing above the ground and the roots grow at the same rate.
However, one student pointed out that the curves for both the roots and the shoots showed the same S-shape. This S-shape appeared again on graphs describ- ing the growth of tobacco hornworms and populations of bacteria on a plate. Students came to recognize this shape as a standard graph pattern that indicated growth.
This similarity in patterns would not have been noticeable without the mathematical representation afforded by the graph. Given the importance of mathematics in understanding science, elementary school mathematics needs to go beyond arithmetic to include ideas regarding space and geometry, measurement, and data and uncertainty. Measurement, for example, is a ubiquitous part of the scientific enterprise, although its subtleties are almost always overlooked. Students are usually taught procedures for mea- suring but are rarely taught a theory of measure.
As a result, students may fail to understand that measurement entails the use of repeated constant units and that these units can be partitioned. Even upper elementary students who seem proficient at measuring lengths with rulers may believe that measuring merely entails counting the units between boundar- ies. If these students are given unconnected units say, tiles of a constant length and asked to demonstrate how to measure a length, some of them almost always place the units against the object being measured in such a way that the first and last tiles are lined up flush with the end of the object measured, leaving spaces among the units in between.
Data Data modeling is central to a variety of scientific enterprises, including engi- neering, medicine, and natural science. Scientists build models with an acute awareness of the data that are required, and data are structured and recorded as a way of making progress in articulating a scientific model or deciding among rival models. Students are better able to understand data if as much attention is devoted to how they are generated as to their analysis.
First and foremost, students need to understand that data are constructed to answer questions, not provided in a Making Thinking Visible Questions are what determine the types of informa- tion that will be gathered, and many aspects of data coding and structuring also depend on the questions asked.
Data are inherently abstract, as they are observations that stand for con- crete events. Data may take many forms: a linear distance may be represented by a number of standard units, a video recording can stand in for an observation of human interaction, or a reading on a thermometer may represent a sensation of heat.
Collection of data often requires the use of tools, and students often have a fragile grasp of the relationship between an event of interest and the operation or output of a tool used to capture data about the event. Whether that tool is a microscope, a pan balance, or a simple ruler, students often need help understand- ing the purpose of the tool and of measurement.
Data do not come with an inherent structure. Rather, a structure must be imposed on data. Scientists and students impose structure by selecting categories with which to describe and organize the data. However, young learners often fail to grasp this as evidenced in their tendency to believe that new questions can be addressed only with new data.
They rarely think of querying existing data sets to explore questions that were not initially conceived when the data were collected. For example, earlier we described a biodiversity unit in which children cataloged a number of species in a woodlot adjacent to their school.
The data generated in this activity could later be queried to determine the spread of a given population or which species of plants and animals tend to cluster together in certain areas of the woodlot. Finally, data are represented in various ways to see, understand, or com- municate different aspects of the phenomenon being studied.
There are many different kinds of repre- sentational displays, including tables, graphs of various kinds, and distributions.
Not only should students understand the procedures for generating and reading displays, but they should also be able to critique them and to grasp the advantages and disadvantages of different displays for a given purpose.
Interpreting data often entails finding and confirming relationships in the data, and these relationships can have varying levels of complexity. Simple linear relationships are easier to spot than inverse relationships or interactions. Students may often fail to consider that more than one type of relationship may be present. For example, children investigating the health of a population of finches may wish to examine the weight of birds in the population.
The weight of adult finches is likely to be a nonlinear relationship. That is, as both low weight and high weight are disadvantageous to survival, one would expect to find a number of weights in the middle, with fewer on both ends of the distribution. The desire to interpret data may lead to the use of various statistical mea- sures. These measures are a further step of abstraction beyond the objects and events originally observed. For example, understanding the mean requires an understanding of ratio.
However, with good instruction, middle and upper elementary students can learn to simultaneously consider the center and the spread of the data.
Students also can generate various mathematical descriptions of error. This is particularly true in the case of measurement: they can readily grasp the relation- ships between their own participation in the act of measuring and the resulting variation in measures.
Scale Models, Diagrams, and Maps Scale models, diagrams, and maps are additional examples of modeling. Scale models, such as a model of the solar system, are widely used in science education so that students can visualize objects or processes that they cannot perceive or handle directly. The ease with which students understand these models depends on the com- plexity of the relationship being communicated.
Even preschoolers can under- stand scale models used to depict location in a room. This approach faces underdetermination issues in that the same target can instantiate different structures.
A more radical version simply identifies targets with structures Tegmark This approach is highly revisionary in particular when considering target systems like populations of breeding rabbits or economies.
So the question remains for any structuralist account of scientific representation: where are the required target-end structures to be found? The core idea of the inferential conception is to analyse scientific representation in terms of the inferential function of scientific models. The accounts discussed in this section reverse this order and explain scientific representation directly in terms of surrogative reasoning.
The last step is necessary because demonstrations establish results about the model itself, and in interpreting these results the model user draws inferences about the target from the model Unfortunately Hughes has little to say about what it means to interpret a result of a demonstration on a model in terms of its target system, and so one has to retreat to an intuitive and unanalysed notion of drawing inferences about the target based on the model.
Hughes is explicit that he is not attempting to answer the ER-problem, and that he does not offer denotation, demonstration, and interpretation as individually necessary and jointly sufficient conditions for scientific representation. He prefers the more. This is unsatisfactory because it ultimately remains unclear what allows scientists to use a model to draw inferences about the target, and it raises the question of what would have to be added to the DDI conditions to turn them into a full-fledged response to the ER-problem.
If, alternatively, the conditions were taken to be necessary and sufficient, then the account would require further elaboration on what establishes the conditions. Two different notions of deflationism are in operation in his account. The first is to abandon the aim of seeking necessary and sufficient conditions; necessary conditions will be good enough On might worry that explaining representation in terms of representational force sheds little light on the matter as long as no analysis of representational force is offered.
The second condition is in fact just the Surrogative Reasoning Condition, now taken as a necessary condition on scientific representation. Contessa 61 points out that it remains mysterious how these inferences are generated. So the tenability of Inferentialism in effect depends on the tenability of deflationism about scientific representation.
In as far as one accepts representational force as a cogent concept, targetless models are dealt with successfully because representational force unlike denotation does not require the existence of a target Inferentialism repudiates the Representational Demarcation Problem and aims to offer an account of representation that also works in other domains such as painting The account is ontologically non-committal because anything that has an internal structure that allows an agent to draw inferences can be a representation.
Relatedly, since the account is supposed to apply to a wide variety of entities including equations and mathematical structures, the account implies that mathematics is successfully applied in the sciences, but in keeping with the spirit of deflationism no explanation is offered about how this is possible. The account does not directly address the Problem of Style. Contessa introduces the notion of an interpretation of a model, in terms of its target system, as a necessary and sufficient condition on epistemic representation see also Ducheyne for a related account :.
The leading idea of an interpretation is that the model user first identifies sets of relevant objects in the model and the target, and then pins down sets of properties and relations these objects instantiate both in the model and the target.
Interpretation offers a neat answer to the ER-problem. The account also explains the directionality of representation: interpreting a model in terms of a target does not entail interpreting a target in terms of a model. Contessa does not comment on the applicability of mathematics but since his account shares with the structuralist account an emphasis on relations and one-to-one model-target correspondence, Contessa can appeal to the same account of the applicability of mathematics as the structuralist.
But it remains unclear how Interpretation addresses the Problem of Style. As we have seen earlier, in particular visual representations fall into different categories and there is a question about how these can be classified within the interpretational framework.
With respect to the Question of Ontology, Interpretation itself places few constraints on what scientific models are.
All it requires is that they consist of objects, properties, relations, and functions but see Contessa for further discussion of what he takes models to be, ontologically speaking. A recent family of approaches analyses models by drawing an analogy between models and literary fiction. This analogy can be used in two ways, yielding two different version of the fiction view. The first is primarily motivated by ontological considerations rather than the question of scientific representation per se.
Scientific discourse is rife with passages that appear to be descriptions of systems in a particular discipline, and the pages of textbooks and journals are filled with discussions of the properties and the behaviour of those systems. In mechanics, for instance, the dynamical properties of a system consisting of three spinning spheres with homogenous mass distributions are the focus of attention; in biology infinite populations are investigated; and in economics perfectly rational agents with access to perfect information exchange goods.
Their surface structure notwithstanding, no one would mistake descriptions of such systems as descriptions of an actual system: we know very well that there are no such systems. The face-value practice raises a number of questions. What account should be given of these descriptions and what sort of objects, if any, do they describe? Are we putting forward truth-evaluable claims when putting forward descriptions of missing systems?
The fiction view of models provides an answer: models are akin to places and characters in literary fiction and claims about them are true or false in the same way in which claims about these places and characters are true or false. Such a position has been recently defended explicitly by some authors Frigg a,b; Frigg and Nguyen ; Godfrey-Smith ; Salis , but not without opposition Giere ; Magnani It does bear noting that the analogy has been around for a while Cartwright ; McCloskey ; Vaihinger [].
This leaves the thorny issue of how to analyse fictional places and characters. Here philosophers of science can draw on discussions from aesthetics to fill in the details about these questions Friend and Salis provide useful reviews. The second version of the fiction view explicitly focuses on representation. Most theories of representation we have encountered so far posit that there are model systems and construe scientific representation as a relation between two entities, the model system and the target system.
Toon calls this the indirect view of representation Indeed, Weisberg views this indirectness as the defining feature of modelling see also Knuuttila and Loettgers This view contrasts with what Toon 43 and Levy call a direct view of representation. This view does not recognise model systems instead aims to explain representation as a form of direct description.
At the heart of this theory is the notion of a game of make-believe see the SEP entry on imagination for further discussion. We play such a game if, for instance, when walking through a forest we imagine that stumps are bears and if we spot a stump we imagine that we spot a bear. Together a prop and principle of generation prescribe what is to be imagined.
Walton considers a vast variety of different props, including statues and works of literary fiction. Toon focuses on the particular kind of game in which we are prescribed to imagine something of a real world object. A statue showing Napoleon on horseback Toon 37 is a prop mandating us to imagine, for instance, that Napoleon has a certain physiognomy and certain facial expressions. The crucial move is to say that models are props in games of make believe.
Specifically, material models are like the statue of Napoleon and theoretical models are like the text of The War of the Worlds : both prescribe, in their own way, to imagine something about a real object.
A ball-and-stick model of a methane molecule prescribes us to imagine particular things about methane, and a model description describing a point mass bob bouncing on a perfectly elastic spring represents the real ball and spring system by prescribing imaginings about the real system.
This provides the following answer to the ER-problem Toon 62 :. This account solves some of the problems posed in Section 1 : Direct Representation is asymmetrical, makes room for misrepresentation, and, given its roots in aesthetics, it renounces the Demarcation Problem. The view absolves the Problem of Ontology since models are either physical objects or descriptions, neither or which are problematic in this context.
Toon remains silent on both the Problem of Style, and the applicability of mathematics. Important questions remain. According to Direct Representation models prescribe us to imagine certain things about their target system.
The account remains silent, however, on the relationship between what a model prescribes us to imagine and what a model user should actually infer about the target system, and so it offers no answer to the ER-problem. A further worry is how Direct Representation deals with targetless models. If there is no target system, then what does the model prescribe imaginings about?
Toon is well aware of such models and suggests the following solution: if a model has no target it prescribes imaginings about a fictional character This solution, however, comes with ontological costs, and one of the declared aims of the direct view was to avoid such costs by removing model systems from the picture. Levy aims to salvage ontological parsimony and proposes a radical move: there are no targetless models. If a purported model has no target then it is not a model.
There remains a question, however, how this view can be squared with scientific practice where targetless models are not only common but also clearly acknowledged as such. Elgin further developed this account and, crucially, suggested that it also applies to scientific representations.
Caricatures are paradigmatic examples: Churchill is represented as a bulldog and Thatcher is represented as a boxer. The leading idea of the views discussed in this section is that scientific representation works in much the same way.
A model of the solar system represents it as consisting of perfect spheres; the logistic model of growth represents the population as reproducing at fixed intervals of time; and so on.
In each instance, models can be used to attempt to learn about their targets by determining what the former represent the latter as being. The question then is what establishes this sort of representational relationship. The answer requires introducing some of the concepts Goodman and Elgin use to develop their account of representation-as. A painting of a unicorn is a unicorn-representation because it shows a unicorn, but it is not a representation of a unicorn because there are no unicorns.
Being a representation of something is established by denotation; it is a binary relation that holds between a symbol and the object which it denotes. The two can, but need not, coincide. Some dog-representations are representations of dogs, but not all are e.
In the current context properties are to be understood in the widest possible sense. An item can exemplify one-place properties, multi-place properties i. Paradigmatic examples of this are samples. Notice that instantiation is necessary but insufficient for exemplification: the sample card does not exemplify being rectangular for example. When a object exemplifies a property it provides us with epistemic access to that property.
Elgin This provides the following account of epistemic representation:. Applying this in the scientific context, i. Representation-As also answers the other problems introduced in Section 1 : it repudiates the demarcation problem and it explains the directionality of representation. It accounts for surrogative reasoning in terms of the properties imputed to the target. However, at least as stated, the account remains silent on the problem of ontology and the applicability of mathematics.
We discuss below how to account for targetless models. Representation-As raises a number of questions when applied in the scientific context. While it has intuitive appeal in the case of pictures, it is less clear how it works in the context of science. Phillips and Newlyn constructed an elaborate system of pipes and tanks, now know as the Phillips-Newlyn machine, to model an economy see Morgan and Boumans and Barr for useful discussions.
So the machine is an economy-representation. But what turns a system of pipes and tanks into an economy-representation? This notion of a model explicitly does not presuppose a target system and hence makes room for targetless models.
The next issue is that exemplified properties are rarely exactly imputed onto target systems. Frigg and Nguyen , building on Frigg a: — , prefer to be explicit about the relationship between the exemplified properties and the ones to be imputed onto the target. For example, in the case of a London Tube map, the key associates particular colours with particular tube lines, and in the case of idealisations the key associates de-idealised properties with model-properties.
Gathering the various pieces together leads to the following account of representation Frigg and Nguyen :. However, it adds to the latter in at least three ways. Secondly, it makes explicit that the properties exemplified by the model need not be imputed exactly onto the target, and highlights the need to investigate keys specifying the relationship between properties in models and the properties that models actually impute onto their targets.
Finally, it makes explicit how to account for targetless models. A model of a bridge that is never built is still a bridge-representation, which exemplifies properties related to bridges stability and so on , despite the fact that it is not a representation of anything. However, as in the case of Representation-As questions remain with respect to the problem of ontology and the applicability of mathematics.
Goodman, Nelson: aesthetics imagination mathematics, philosophy of mathematics, philosophy of: nominalism measurement: in science models in science Platonism: in the philosophy of mathematics reference scientific realism scientific theories: structure of theoretical terms in science truth: deflationary theory of.
Problems Concerning Scientific Representation 2. General Griceanism and Stipulative Fiat 3. The Similarity Conception 3. The Structuralist Conception 4. The Inferential Conception 5. The Fiction View of Models 7.
Representation-As 7. Problems Concerning Scientific Representation In most general terms, any representation that is the product of a scientific endeavour is a scientific representation. In sum, a theory of scientific representation has to respond to the following issues: Address the Representational Demarcation Problem the question how scientific representations differ from other kinds of representations. Respond to the Problem of Style what styles are there and how can they be characterised?
Formulate Standards of Accuracy how do we identify what constitutes an accurate representation? Address the Problem of Ontology what are the kind of objects that serve as representations? Any satisfactory answer to these five issues will have to meet the following five conditions of adequacy: Surrogative Reasoning scientific representations allow us to generate hypotheses about their target systems.
Targetless Models what are we to make of scientific representations that lack targets? Requirement of Directionality scientific representations are about their targets, but targets are not about their representations. Applicability of Mathematics how does the mathematical apparatus used in some scientific representations latch onto the physical world. General Griceanism and Stipulative Fiat Callender and Cohen give a radical answer to the demarcation problem: there is no difference between scientific representations and other kinds of representations, not even between scientific and artistic representation.
GG then comes with a practical prescription about how to proceed with the analysis of a representation: the General Gricean view consists of two stages. Callender and Cohen do admit some representations are more useful than others, but claim that the questions about the utility of these representational vehicles are questions about the pragmatics of things that are representational vehicles, not questions about their representational status per se.
The Structuralist Conception The structuralist conception of model-representation originated in the so-called semantic view of theories that came to prominence in the second half of the 20 th century see the SEP entry on the structure of scientific theories for further details.
The Inferential Conception The core idea of the inferential conception is to analyse scientific representation in terms of the inferential function of scientific models.
He prefers the more modest suggestion that, if we examine a theoretical model with these three activities in mind, we shall achieve some insight into the kind of representation that it provides. The Fiction View of Models A recent family of approaches analyses models by drawing an analogy between models and literary fiction.
Anscombe, G. Aronson, Jerrold L. Bailer-Jones, Daniela M. Brandom, Robert B. Knowles and J. Skorupski eds. Oxford: Blackwell.
0コメント