Make individuals distinct

Question

I am trying to construct an ALCQ knowledge base (KB) for some sentences. Here is what I have:

Abox (Yiannis is a person and he drinks only one kind of a coffee, frappe):

• Person(YIANNIS)
• $\forall$ drinksCoffee.frappe(YIANNIS)

Tbox (A Greek person is a person who drinks only one kind of a coffee, frappe):

• Greek $\equiv$ Person $\sqcap$ $\forall$drinksCoffee.frappe

Now I want to augment my KB with the following sentence:

Yiannis has three distinct pets: Tsipras, Varoufakis and Podemos.

I would add to my Abox these:

• hasPet(YIANNIS, TSIPRAS) // maybe I need $\exists$ symbol in its start?
• hasPet(YIANNIS, VAROUFAKIS)
• hasPet(YIANNIS, PODEMOS)

but how to make these pets distinct?

Answer 1

ALCQ is an extension of the Description Language ALC described in the slides at http://cgi.di.uoa.gr/~pms509/lectures/dl-intro.pdf. Slide 41 states the Unique Names Assumption:

Unique Names Assumption (UNA): We will assume that if $a$ and $b$ are distinct individuals then $a^{\mathcal{I}} \ne b^{\mathcal{I}}$.

Thus, you don't have to do anything to ensure that the three distinctly named pets are interpreted as distinct individuals: the UNA states that in every interpretation they are guaranteed to denote distinct individuals. You get it "for free".