On a Notion of Extensionality for Artifacts

The notion of extensionality means in plain sense that properties of complex things can be expressed by means of their simple components, in particular, that two things are identical if and only if certain of their components or features are identical; e.g., the Leibniz Identitas Indiscernibilium Principle: two things are identical if each applicable to them operator yields the same result on either; or, extensionality for sets, viz., two sets are identiccal if and only if they consist of identical elements. In mereology, this property is expressed by the statement that two things are identical if their parts are the same. However, building a thing from parts may proceed in various ways and this unexpectedly yields various extensionality principles. Also, building a thing, may lead to things identical with respect to parts but distinct with respect, e.g., to usage. We address the question of extensionality for artifacts, i.e., things produced in some assembling or creative process and we formulate the extensionality principle for artifacts which takes into account the assembling process and requires for identity of two artifacts that assembling graphs for the two be isomorphic in a specified sense.