# Predicate Logic and Popular Culture (Part 12): Frozen

Let $H(x,t)$ be the proposition “$x$ happens at time $t$.” Translate the logical statement

$\exists t (H(\hbox{music},t) \land H(\hbox{light},t) \land H(\hbox{I dance through the night},t)) \land \forall s < t \lnot(H(\hbox{music},s) \lor H(\hbox{light},s) \lor H(\hbox{I dance through the night},s)))$

where the domain is all times.

This very complex statement reads, “There is a time when there will be music, there will be light, and I will dance through the night, and at all previous times, there is no music, there is no light, and I will not dance through the night.” More briefly, there is a time that will be the first time for music, light, and dancing through the night.

Of course, this sounds a whole lot better when Princess Anna sings it.

Context: This semester, I taught discrete mathematics for the first time. Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

While I’m marginally on the topic, here’s the best parody of “For the First Time in Forever” that I’ve seen:

And here’s the best parody of a Frozen song that I’ve seen.