By Abraham Ginzburg
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Additional info for Algebraic Theory of Automata
The a t t r i b u t e s clause in the definitions of model fragment classes defines the p a r a m e t e r functions that can be used on components being modeled by that model fragment class. The definition of the p a r a m e t e r function includes a : r a n g e specification, which is the class of the p a r a m e t e r returned by the function. For example, the R e s i s t o r model fragment class defines the r e s i s t a n c e p a r a m e t e r function, which returns an instance of R e s i s t a n c e - p a r a r a e t e r representing the resistance of components being modeled as R e s i s t o r s .
1 Hence, a set of model fragments is an implicit representation of an exponentially large set of models. Alternate representations of this large space of models, by explicitly representing each model, are unrealistic. To put it another way, explicitly representing the space of possible models restricts us to representing a much smaller set of models. Third, model fragments are reusable, not just in different models of the same device, but in different models of different devices. 1, but also in models of other devices that use wires.
Intuitively, the model fragment describing the tap water flow must say that the water flowing through the tap tends to increase the volume of water in the bathtub. Similarly, the model fragment describing the drain water flow m u s t say that the water flowing out of the drain tends to decrease the volume of water in the bathtub. We can express this using the I + and I - operators introduced by Forbus [Forbus, 1984]. I+(ql,q2) says that q2 is a positive influence on ql, while I - ( q l , q2) says that q2 is a negative influence on ql.