Universal restriction in description logic

[ferrelhadley]

I am struggling to understand how a universal restriction works in description logic. I can understand the extistential restriction but not the universal.

the definition is

I have two examples with answers for this.

For the first one (B AND A) is easy enough to work out: (a,b,d,f)
Now the answer given is (f,e,d) the only way I can ge to (f,e,d) is to look at every x elelment in the relation R and it is (a,b,c) and hence the negation would be (d,e,f). However as hard as I appy (a,b,d,f) I cannot get to (d,e,f).

I have tried using the (a,b,d,f) as the x value in the R relation but that would be only (a,c)
I have tried using it as the y value but that would be (a,c) again nothing like the answer provided.
Anyone have any ideas or am I totally lost here?

 

[Valkarie]

A universal restriction in description logic is a statement that something must be true for every instance of a particular class. For example, if you have a class "Animals" and you want to say that all animals have fur, you would use a universal restriction to express that statement. In your example, the universal restriction states that for every element x in relation R, it must also be the case that B AND A are both true. This means that any element x that is in relation R must also have both B and A being true. Therefore, the answer for your example is (f,e,d), since these are the elements of relation R for which both B and A are true.