A Classic Datalog Problem to Solve

In the Alpine Club all members are skiers or (mountain) climbers. All climbers do not like rain. All skiers like snow. Tony, Mike, and John are members of the Alpine Club. Mike likes what Tony dislikes and Mike dislikes what Tony likes. Tony likes both rain and snow.

Who among the members are climbers?

ChatGPT-4

Given the information:

All climbers do not like rain.
All skiers like snow.
Tony likes both rain and snow.
Mike likes what Tony dislikes, and dislikes what Tony likes.

We can deduce the following:

Since Tony likes both rain and snow, he must be a skier because skiers like snow. However, because Tony also likes rain, he cannot be a climber since climbers do not like rain.

Now, we know that Mike likes what Tony dislikes and dislikes what Tony likes. Since Tony likes rain and snow, it means Mike dislikes both rain and snow. Therefore, Mike cannot be a skier since he dislikes snow. However, Mike can be a climber, as climbers do not like rain, and he dislikes rain.

There is not enough information provided about John’s preferences, so we cannot determine whether he is a skier or a climber.

In conclusion, among the members, Mike is a climber. We cannot determine John’s status due to insufficient information.

Finn

So far so good. The answer is as expected. Then I asked it to write a program in the Datalog language that solve this problem.

ChatGPT4

Here is a program in the Datalog language that models the given problem and can be used to deduce the roles of the members:

% Define the roles
member(X) :- skier(X).
member(X) :- climber(X).

% Define the preferences
likes(X, snow) :- skier(X).
dislikes(X, rain) :- climber(X).

% Define the members' preferences
likes(tony, rain).
likes(tony, snow).

% Define the relationship between Tony and Mike
likes(mike, X) :- dislikes(tony, X).
dislikes(mike, X) :- likes(tony, X).

% Query for climbers in the Alpine Club
?- climber(X).

This Datalog program defines the roles and preferences of the members, as well as the relationship between Tony and Mike. Running this program with a Datalog interpreter will output the climbers in the Alpine Club. Since we haven’t mentioned John in the rules, the program doesn’t have enough information to determine whether he is a skier or climber.

Finn:

I am not sure this is accurate.

https://github.com/finnpedersenkazes/flix-examples/tree/master/example04

Here is the solution written in Flix.

/// Declare predicate symbols.
rel Member(x: String)
rel Like(x: String, y: String)
rel Dislike(x: String, y: String)
rel Climber(x: String)
 Skier(x: String)

/// Returns a collection of facts.
def getFacts(): #{ Member, Like, Dislike, Climber, Skier } = #{
    Member("Tony").
    Member("Mike").
    Member("John").
    Like("Tony","Rain").
    Like("Tony","Snow").
/// Returns a collection of rules.
def getRules(): #{ Member, Like, Dislike, Climber, Skier } = #{
    Climber(x) :- Member(x), Dislike(x, "Rain").
    Skier(x) :- Member(x), Like(x, "Snow").
    Like("Mike", x) :- Dislike("Tony", x).
    Dislike("Mike", x) :- Like("Tony", x).
/// Composes the facts and rules, and computes the result.
def main(_args: Array[String]): Int32 & Impure =
    query getFacts(), getRules()
        select (x) from Climber(x) |> println;
    0 // exit code