Models and languages

The previous sections have described mainstream database models and languages, presenting facilities that are in widespread use today. This section introduces several extensions to the mainstream data models and languages with facilities that allow the database to capture certain application requirements more directly. 

This work has been partly supported by the Italian project PACO (Performability-Aware Computing Logics, Models, and Languages) funded by MIUR and by the UK EPSRC research grant EP/D076633/1 UbiVal (Fundamental Approaches to the Validation of Ubiqituous Systems). 

Predictive Model Markup Language (PMML) is far more than just another format of a data container flat file [7]. As is clear from the name, it is an XML-based markup language delivering all the power of XML. Readers are recommended to consult Section 2.4.5 and the website www.xml.org for more details on XML and its applications in chemistry. 

Collins, A., Gentner, D. (1987). How people construct mental models. In D. Holland N. Quinn (Eds.), Cultural models in language and thought (Vol. 1, pp. 243-265). New York University of Cambridge. 

Finally, reductionism is closely tied to the so-called syntactic approach to theories, an approach which treats theories as axiomatic systems expressed in natural or artificial languages. Indeed, closely tied may be an understatement, since deduction is a syntactic affair, and is a necessary component of reduction. Once philosophers of science began to take the semantic approach to theories seriously, the very possibility of reduction became moot. For the semantic approach treats theories as families of models, and models as implicit definitions, about which the only empirical question is whether they are applicable to phenomena. For reduction to be obtained among models semantically characterized requires an entirely different conception of reduction, and whether such a conception would capture anything of interest about inter-theoretical relations is questionable. 

We examine these models not only as mathematical entities but also as a means of determining what the mathematical properties of schemes tell us regarding programming problems and languages. In studying alternative models an important point to consider is their relative power. 

We regard as objects primitive concepts such as dates, numbers, and the two Boolean values. You can alter an attribute (such as maxSize) to refer to a different number, but the number itself does not change. Useful basic and immutable attributes of numbers include next and previous, so that, for example, 5. next = 6. (Many tools and languages like to separate primitives from objects in some fundamental way. The separation is useful for the practicalities of databases and the like, but for most modeling there is no point in this extra complication.)... 

In this fashion, we can build up a hierarchy of basic types and operators—not only the syntactic definitions but also their meanings And because the basics can be different for different modeling and programming languages—for example, not all have exactly the same idea of the passage of time—different packages can be supplied for users of different dialects and can be referenced as stereotypes. 

The notation here is not limited to complete documents delivered within a standard development process. Designers sketch these diagrams on whiteboards when they are discussing their designs with their colleagues. In short, this is a specialized language for communication models and designs. 

Kenneth J. Arrow, "On Mathematical Models in the Social Sciences," 1951, cited and discussed in Max Black, Models and Metaphors. Studies in Language and Philosophy (Ithaca Cornell University Press, 1962) 223225. 

The table uses a system of symbols for the elements and a system of conventions for atomic weights it employs a classification, or a visual array, that groups the symbols so that their relations and properties are immediately suggested to the viewer who knows the principles of classification and a few facts. Deductions can be made both to the facts that established the table and to the facts that were unknown when the table was first set out. Here is a scheme that is an explanatory and predictive model and an icon in both the semiotic and the popular senses of the word. But its power comes from visual display, from image, not the principles and facts that can be recorded in ordinary or conventional language. 

The lack of dynamic models and rigorous mathematics makes nineteenth-century chemistry a different science from physics, but it is no less methodologically sophisticated. Chemists employed varieties of signs, metaphors, and conventions with self-conscious examination and debates among themselves. Nineteenth-century chemists were neither militant empiricists nor naive realists. These chemists were relatively unified in their focus on problems and methods that provided a common core for the chemical discipline, and the language and imagery they used strongly demarcated mid-nineteenth-century chemistry from the field of mid-nineteenth-century physics and natural philosophy. 

Black, Max. Models and Metaphors Studies in Language and Philosophy. Ithaca Cornell University Press, 1962. 

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