Diagramming Drills

[SGD2021]

Hello, on page 85 of the Logic Games Bible (within the Linear Games Rule Diagramming Drill in the 2020-2021 edition), exercise 4 lists a rule that says "Either S or T must speak on the third day. Why is the rule diagram drawn this way: 3—> S/T? Isn’t “must” a word that introduces a necessary condition so the diagram would be S/T—>3? Are there many instances where the words indicated in the bible as those used to introduce a sufficient or necessary condition do not always apply? Also, is it necessary to use conditional diagraming for rules like this (or for a rule like “z is selected during one of the first two days")?

Finally, on page 79 of the Logic Games bible, for exercise 7, the following example appears: F sings immediately before K if G sings immediately after K. The diagram for this question is [KG]-->[FKG]. Should we always add the information from the sufficient condition to the necessary condition the way it is done here?

Thank you!

[Adam Tyson]

You're correct that "must" indicates a Necessary Condition, SGD2021, but you have to ask yourself here what the construction of that rule really means. If we just mechanically say "must is right before speaking on the 3rd day, so speaking 3rd is what's necessary," then we are missing the meaning of the rule. Interpreting it that way would mean that if S or T is in the game at all, then they must be 3rd and can never be in any other position.

What the rule actually means is that those are the only things that can be third; nothing else can be in that space. Think of the necessary condition as the answer to a question: what must occur? The thing that must occur is "S or T 3rd". So, if a variables is 3rd, then that variable is either S or else T; if not S and not T, then not 3rd.

And you're right to ask if we have to do a conditional diagram, because the answer is no, we don't have to do that. You can cut to the chase here and just put that S/T on the 3rd spot, guaranteeing that one of those two variables will be in that space and that nothing else can be. The conditional representation is true and accurate, but it may be unnecessary. That's up to you whether to include it in your diagram or not! Just be sure you include some visual representation of the rule, such as placing them on that 3rd space.

Regarding the rule on page 79, in this case I would say yes, you should absolutely include the sufficient condition in your diagram, because without it you might accidentally treat the FK block (or FKG block) as an absolute rule rather than a conditional one. That would mean you would be overlooking the possibility of solutions with no KG block and no FK block. The conditional aspect of this rule is crucial to understanding it and applying it, so diagram it accordingly.