Why use blocks to represent adjacent variables?

[Nikki Siclunov]

We recently received the following question from a student:

In the book "Y is tutored during the hour immediately before Z is tutored ", is notated that this should be diagrammed using the block diagram method.

Why isn’t it diagrammed like this, Y Z using the variable placement method since the statement simply means Y is tutored before Z?

Please advise, I am working on Logic Games in my studies.

Thanks for your question!

The rule you're asking about is not a simple sequencing rule: there is more to it than what you seem to suggest Not only do we need to ensure that Y is tutored before Z, but we must also ensure that Y is tutored immediately before Z. The difference may seem trivial, but it is not. In the first instance, we'd have a simple sequencing rule (Y Z), allowing Y to be anywhere as long as it is earlier than Z. In the second instance—this is the actual rule we have—Y and Z are adjacent to each other, with a specified order. This is why we'd use a Block to represent their relationship.

Unfortunately, the rule in question does not allow us to determine specifically where, in our Linear diagram, to place Y and Z. This is why the variable placement method will not be suited to this particular rule. Remember: Variable placement rules specify where a variable must be placed, or cannot be placed. While the placement of the YZ block cannot be determined, we can use Not Laws (another type of Variable Placement rule) to represent the inference that Y cannot be the last student tutored, and Z cannot be the first.

Let us know if you have any other questions, and good luck with the Logic Games Bible!