Theoretical Underpinnings of Version Spaces
نویسنده
چکیده
Mitchell's version-space approach to inductive concept learning has been highly influential in machine learning, as it formalizes inductive concept learning as a search problem—to identify some concept definition out of a space of possible definitions. This paper lays out some theoretical underpinnings of version spaces. It presents the conditions under which an arbitrary set of concept definitions in a concept description language can be represented by boundary sets, which is a necessary condition for a set of concept definitions to be a version space. Furthermore, although version spaces can be intersected and unioned (version spaces are simply sets, albeit with special structure), the result need not be a version space; this paper also presents the conditions under which such intersection and union of two version spaces yields a version space (i.e., representable by boundary sets). Finally, the paper shows how the resulting boundary sets after intersections and unions can be computed from the in i tial boundary sets, and proves the algorithms correct.
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