What is the difference between "someValuesFrom" and "allValuesFrom"?

Question

In description logic, what is the difference between "someValuesFrom" and "allValuesFrom"? In other words, the difference between (limited existential quantification) and (value restriction).

For example, consider this:

∆ = {a, b, c, d, e}
ext(B) = {<c,d>}
ext(R) = {<a,b>, <a,c>, <d,c>, <c,e>}

So what is the difference between the following?

ext(∃R. B) = ?
ext(∀R. B) = ?

Is there any way to simplify the concept of somevaluefrom and allvaluesfrom?

Answer 1

First, allValuesFrom and someValuesFrom sound like OWL, and they are explained with examples in the specification.

In the context of OWL (which is a DL language) they respresent restrictions on properties, especially on the class of the property values, meaning e.g. that you want to state that a Car, which has a manufactured_by property, this property is restricted to members of the Class Manufacturer.

allValuesFrom and someValuesFrom differ in the sense, that the first requires all values of the property values, the latter at least one to be of a certain class.