Predicate Logic and Popular Culture (Part 85): Three Dog Night

Let p be the proposition “Jeremiah was a bullfrog,” let q be the proposition “Jeremiah was a good friend of mine,” let W(x) be the proposition “x is a word,” let S(x,t) be the proposition “Jeremiah said x at time t,” let U(x,t) be the proposition “I understood x at time t,” let r be the proposition “I helped Jeremiah drink his wine,” let W(x) be the proposition “x is mighty fine wine,” and let J(x,t) be the proposition “Jeremiah had x at time t.” Translate the logical statement

p \land q \land \forall x \forall t<0(W(x) \land S(x,t) \Rightarrow \lnot U(x,t)) \land r \land \forall t<0 \exists x(W(x) \land J(x,t)),

where time 0 is now.

Of course, this matches the opening verse of one of the classics of the 1970s.

green line

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.

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