- #1

Knark

- 12

- 0

## Homework Statement

Formalize (in PL) the relations/predicates stated in (a)-(e) using just these relations/predicates:

1) Pxy: x is a parent of y

2) Fx: x is a female

3) Sxy: x is a sibling of y

(a) x is an uncle of y

(b) x is a great-aunt of y

(c) x is an aunt

(d) x is a great-uncle

(e) x is an uncle of a great-aunt of y

## Homework Equations

The above relations/predicates (1, 2 and 3) are the only ones we are allowed to use. Furthermore, in brackets the question has: A great-aunt/uncle is the sister/brother of a parent. You can assume that you're working within a universe of discourse consisting just of human beings.)

## The Attempt at a Solution

There are two aspects of this problem that I am unsure of which can be illustrated by what I have tried so far.

(a) ~Fx & (Pzy & Sxz)

(b) Fx & (Pwz & (Pzy & Swx)

(c) Fx & (Pzy & Sxz)

I haven't tried (d) and (e) since I ran into some confusion doing these first three. I'm wondering how I differentiate between (a) and (c). In my answers they are identical except for the ~Fx to show that an uncle is not a female. Yet I believe they should be distinct because (a) asks for "x is an uncle of y" but (c) asks only for "x is an aunt" and not "x is an aunt of y". How do I formalize the fact that they are different in this way.

Additionally, I'm wondering whether I am within the bounds of the question to include the predicates z and w. I just don't see any other way to formalize a relationship that includes an uncle or great-uncle without using a third and fourth predicate.