Difficulty with propositional logic in prolog

I need to convert the following propositions into prolog code and I have do not understand how the operators work. I usually use java.

"Jeans are only casual, dress pants are only formal, kakis are only semi-formal, belts are not casual, black socks are acceptable anytime. Casual = C, Semi-Formal = SF, Formal = F, Jeans = J, Dress pants = DP, Kakis = K, Belts = B, Black socks = BS. J -> C, DP -> F, K -> SF, B -> !C, BS -> (C v SF v F)"

Here is the code I already have:

casual(jeans).
formal(dress_pants, belt, black_socks).
semiFormal(khakis).
formal(belt).
semiFormal(belt).
casual(black_socks).
formal(black_socks).
semiFormal(black_socks).

Informally, a unary predicate p can be viewed as a set P and, consequently, a literal p(X) can be viewed as the set membership test X∈P. Therefore, a goal p(X) will be true or false (i.e., a proposition), depending on whether X belongs to the set P or not.

The sentences "Jeans are only casual, dress pants are only formal, kakis are only semi-formal, belts are not casual, black socks are acceptable anytime." can be represented as the sets:

• casual = {jeans, black_socks}.
• formal = {dress_pants, belt, black_socks}
• semi_formal = {khakis, belt, black_socks}

And these sets can be represented in Prolog by the facts:

casual(jeans).
casual(black_socks).

formal(dress_pants).
formal(belt).
formal(black_socks).

semi_formal(khakis).
semi_formal(belt).
semi_formal(black_socks).

Here are some Prolog queries about these facts:

?- casual(jeans).
true.

?- casual(belt).
false.

?- casual(X).
X = jeans ;
X = black_socks.

?- formal(X).
X = dress_pants ;
X = belt ;
X = black_socks.

?- semi_formal(X).
X = khakis ;
X = belt ;
X = black_socks.