How to convert this sentence into a first order logic well formed formula?

I am trying to convert the following sentence to a well formed formula using first-order logic(Predicate logic).

All towers are of the same color.

I have defined the following predicates:

Tower(x) :: x is a tower.

Color(x, y) :: x is of color y

I am not able to convert the aforementioned sentence into a well formed formula using the above predicates. Is it possible to convert it using the above predicates or some new predicate should be required. Please advise.

EDIT: Forgot to add a detail. There are only three available colours in the world (red, green, blue). Can this detail be used. Does that make any difference to the solution?

Upvotes: 2

Answers (3)

stressed_geek

Reputation: 2176

After posting this on StackOverflow, I realized that the problem is more suitable for Math. So I had reposted the problem there.

Although, Dave's solution is perfectly correct, the solution posted there seems more intuitive, so I am linking it here for reference of other users.

Upvotes: 0

Jeffrey L Whitledge

Reputation: 59443

Let's not assume that any towers or colors exist.

tower(x) ∧ tower(y) ∧ color(x,z) → color(y,z)

Upvotes: 2

David Thornley

Reputation: 57036

There exists a Y1 such that for all X Tower(X) implies Color(X, Y1)

Upvotes: 5

How to convert this sentence into a first order logic well formed formula?

Answers (3)

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