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In this article, we study a restricted notion of subgraph epimorphism, corresponding to the application of node delete and merge operations in a reaction graph, in order to relate a source graph to a target graph through a model reduction relation.
The formal relations only guarantee, but do not define, the reduction relation.
His reduction relation is composed of two simpler intertheoretic relations called "restriction" and "embedding".
The authors consider an exact reduction relation as a certain relation between potential models of the respective theories.
Scheibe concedes that there are instances of incommensurability which make it difficult to find a reduction relation in certain cases.
His supplement builds the possibility of multiple realizability (including the strong type) directly into the definition of the reduction relation.
The relation between incommensurability and the Sneedean reduction relation is to some extent discussed in Balzer et al. (1987, chapter VI.7).
Bickle explicates the nature of the reduction relation in a specific case using a semi-formal account of 'intertheoretic approximation' inspired by structuralist results.
When does a theory T′ reduce to a theory T? How is one to understand the nature of this reduction relation?
These set-theoretical structures are then used to define a reduction relation in terms of mapping functions from one structure to another.
Schaffner (1974 , 1993 acknowledges that reductionism in his sense has been peripheral to the practice of molecular biology, but maintains that his formal model of reduction captures the reduction relation between theories.
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