Let us have some Kelsey k. This we know about Kelsey: he is love. Formally, this may be expressed as: k≡L, for L as love.
Let us also have some David d. David, of course, is the opposite of Kelsey; he is the anti-Kelsey. We may express this as d≡~k.
At this point, the power of logic already - with such a small number of propositions - allows us to reach conclusions! The transitive property allows us to equate d as d≡~L; David is the antithesis of love! A valid conclusion, well supported by everyday evidence. What power this has!
Let's try another simple exercise. Let there be some Nikolas n. Now, a Nikolas is of course the opposite of David: n≡~d. Again using the transitive property, we may quickly determine that n≡~~L; or, using the double-negative property, n≡L. Like the Kelsey, the Nikolas is love! What a wonderful thing to discover!
Now let's try something more complex. Assume there is one room being describe. The presence of David in that room may be described as d, to continue our previous convention; the presence of Nikolas in the room is n, and the presence of a Kelsey will be called k. Ryan T. will be described by r, and attractive persons of a female persuasion as w.
Now, a Ryan is followed everywhere he goes by females; therefore, we may say that r→w, or that the presence of a Ryan in the room implies the presence of females also present. A David is terrified by females, and will go nowhere near them; we may thus continue by saying that d→~w, or the presence of a David in the room implies the absence of females. Using the transitive property, we may comment as an aside that r→~d, or d→~r; they cannot be in the same room, at least for long, a fact which (as a further aside) causes the illustrious d no end of jealousy.
Now, we may establish more facts. The Kelsey, as a Kelsey, follows the David wheresoever he may go; thus, d→k. The Nikolas is friends with Kelsey and David, and will be present when- and wheresoever the both of them are; k∧d→n. This last statement, the trained logician will note, is exactly equivalent to replacing the earlier d→k with d→k∧n.
We have learned many things from this! We have learned that wheresoever a David goes, so does a Kelsey and a Nikolas; we have learned that Davids cannot be found in the same room as Ryans. As we add more propositions, we may learn more; for instance, a simple addition of a Devin to the simulation (included in the appendix) immediately creates a sort of "Mormon Invasion" of any room; but even this simple model teaches us so much. Enjoy - the power of logic!
