Handling Long Lists of Conditional Rules

[lsathelpwanted]

Hello!

I am on chapter 5 of the LG bible. pg 340 is the solution to a great exampl that I am currently on, but this question isn't about it specifically.

This example has 6 separate conditional rules. My troubles, are not with the logic, but my organization on how I go about comparing conditionals to find the hidden links. I will consistently get lost in all of the letters and arrows and forget what rule I was even using as my basis for comparison. And this is sucking up some time!

Previously, I would notate all of the rules, and underneath them notate their contrapositives. And then my problem had grown twice the size with a longer list of 12. So then I tried a new order.

I started notating the rule, and then its contrapositive to the right side to make two lists of six. This was immediately more manageable for me.

As I get more experience with this test, contrapositives are beginning to really stick out. I certainly don't have to diagram them to understand them. David does't always notate them. But I can't trust myself not to forget considering all of them under a timed clock. For me, I think it's best that I bite the bullet and just notate them; it really doesn't take long. I don't think the advantage of the 30 seconds I save from not notating them is worth the risk of potentially missing hidden inferences.

Below if my current process for inference making in these long lists of conditional rules. I'm not trying to micromanage it, but I need a process so I don't forget to check a rule and possibly miss an inference link.

My Steps:

Notate Rule on the left
Notate ContraP's on the right
Go to rules on the left, start at the top of the list. I take that first rule's sufficient condition, and go down the list to find any other rules with the same sufficient conditions. If there is a link, I notate it in the middle between the left and right lists (this was a nice touch on the organization too) Once I reach the bottom, I go back to the top to the second rule and do the same with its sufficient condition. On through the list I go, and then over to the contrapositive list and do it all again.

Question: I would be correct in saying that when I go through the list #2, the contrapositive list, after going through the original notations of list #1, I am basically just double checking for any missed inferences that I didn't see in the original notations? I really hope that's correct or I may have a drastic misunderstanding of these fundamental. But I think I am correct! Please tell me I'm correct....

I'm not sure how I feel about this. It seems like a lot when I am describing the process, and it makes me wonder if I could be more efficient, but it can seem to go very quickly too. Your thoughts? I mean, this is really really close to what David does in the book. My variation is far more rigid and doesn't offer much flexibility. There are so many moving parts, I feel like this helps ensure I don't look over a rule when looking for links.

Thank you for any and all help!

[Jeremy Press]

Hi lsathelp,

What you're describing is extremely close to the way I would proceed when I first started out with Undefined Grouping Games (or Grouping Games with mostly conditional rules). I agree with you that it's best to be comprehensive, but also to depict rules and contrapositives in a way that seems visually attractive and manageable to you. So I'm totally on board with your organization method as long as that works for you.

What you're describing about your inference-making process sounds fine, but I just want to make sure I understand you correctly. When you're trying to find "links" between conditional rules, you're looking for a variable that appears in a sufficient condition in one rule, and then in a necessary condition in another rule--to make the link, it must be the same variable, same "orientation" (whether negative or positive). Those are the rules that can be connected directly. So for example, let's say I have the following rules: A B, and B C. I can make a direct connection, because B is a necessary condition in the first rule, and a sufficient condition in the second rule. As long as that's what you're looking for in order to link conditional rules together, you're on the right track!

As far as looking for links in contrapositives or in original rules, it's true that sometimes it's easier to see the link based on one form of the rule rather than another. So as long as you found a link to a rule initially, looking at the contrapositive of that same rule will only show you the "contrapositive" side of that link (nothing new). But it's of course helpful to check just to make sure you didn't miss anything.

Let me know if I've answered all your questions here, and keep up the great work!

[lsathelpwanted]

Hi lsathelp,

What you're describing is extremely close to the way I would proceed when I first started out with Undefined Grouping Games (or Grouping Games with mostly conditional rules). I agree with you that it's best to be comprehensive, but also to depict rules and contrapositives in a way that seems visually attractive and manageable to you. So I'm totally on board with your organization method as long as that works for you.

What you're describing about your inference-making process sounds fine, but I just want to make sure I understand you correctly. When you're trying to find "links" between conditional rules, you're looking for a variable that appears in a sufficient condition in one rule, and then in a necessary condition in another rule--to make the link, it must be the same variable, same "orientation" (whether negative or positive). Those are the rules that can be connected directly. So for example, let's say I have the following rules: A B, and B C. I can make a direct connection, because B is a necessary condition in the first rule, and a sufficient condition in the second rule. As long as that's what you're looking for in order to link conditional rules together, you're on the right track!

As far as looking for links in contrapositives or in original rules, it's true that sometimes it's easier to see the link based on one form of the rule rather than another. So as long as you found a link to a rule initially, looking at the contrapositive of that same rule will only show you the "contrapositive" side of that link (nothing new). But it's of course helpful to check just to make sure you didn't miss anything.

Let me know if I've answered all your questions here, and keep up the great work!

Hi Jeremy thank you for the response.

My apologies, what I wrote did not convey the complete intention of what I meant! (says the dude studying to go to law school...) That was supposed to be TWO steps in the linking process. What I described, is searching for a sufficient with multiple necessaries. Like A>B and, hidden down my list I find A>C that I could have missed before. That would form:
--> B
A
--> C
THEN I would do the linking process in your description. As in if there was a C-->D, I could deduce A-->D. I assume that more difficult grouping games can have more complicated "trees" like this?

***I also feel I might be confusing this with sequencing diagrams. In the above diagram, I added the two "-->" specifically to show conditionality and NOT two "/" branching from the A that we use to imply order (A is before both B and C). So, if we had a C-->D, I could add -->D to the diagram to the right of C.


--> B
A
--> C --> D

That would show that A and/or C get me a D. But a B does not get me a D. With my power inference of A --> D I fear that I might forget that B is a dead end.

Ok, I think that is correct, but I haven't really seen it yet. I should probably finish this book before I post anymore. I have a feeling this is going to be on the next page or something.

Thank you again!

[Jeremy Press]

Hi lsathelp,

Your first step makes sense, and I see now what you're trying to describe. That's totally fine! Keep up the great work, and continue to be thorough in your chain-making process. It sometimes leads to a long list of rules/inferences. But as you've noticed, the more accustomed to the process you become, the faster it goes. And it will ensure you don't miss anything as you're going through the questions.

Let us know if other questions about this arise!

[lsathelpwanted]

Hi lsathelp,

Your first step makes sense, and I see now what you're trying to describe. That's totally fine! Keep up the great work, and continue to be thorough in your chain-making process. It sometimes leads to a long list of rules/inferences. But as you've noticed, the more accustomed to the process you become, the faster it goes. And it will ensure you don't miss anything as you're going through the questions.

Let us know if other questions about this arise!

Gracias! I will definitely be coming back to this chapter for a while; the amount of inferences is a lot to juggle. Thank you again for helping me wrap my head around this process.

[sdb606]

I just finished this chapter and I'm wondering if I really need to do all these inferences when it comes to a long list of conditionals. The list already took a while to write out including the contrapositives. Scanning the list and writing out every single chain inference with separate entries for intermediate chains (e.g. A B C D includes AB, AC, AD, BC, BD, CD plus all the contrapositives) which is a lot of extra work. Can't I just skip the inferences and simply follow the causal pathways with each question since I'd have to do that anyway except now the list is shorter? Even though there are 8 rules in Game 3, if a question triggers a rule, I can ignore its contrapositive on my way through the rest of the causal chain which saves time.

Am I being naive or is there room for personal preference here?

[Jeremy Press]

Hi sdb,

I'm not sure if I've understood you correctly, but I think what you're asking is whether you can just create a long conditional chain from a set of conditional rules, without writing out each separate link in that chain (and without writing out all the inferences and contrapositives contained within the chain). If that's your question, then the answer is that, yes, you can absolutely do that!

I was just corresponding with another student here about this, and I'll repeat what I wrote there: we don't ordinarily recommend the "long-chain" approach at first, because there's a tendency among students either to (a) "misread" (i.e. to try to go in reverse or try to jump between two conditions when there are either/or, or both/and, relationships in a condition) or (b) "miscreate" (i.e. put the chain together inaccurately). Some students also end up feeling like something was left out if they don't reproduce the contrapositive form of the long chain they create, or if they don't learn to read the contrapositives accurately off of that long chain.

But this really does come down to personal preference, as well as your level of comfort with conditional chains and contrapositives of those chains. Assuming you're comfortable, you can create one "master chain" and stick to it when evaluating questions.

I hope this helps!

[sdb606]

No, that is not what I meant. My apologies for the confusion. Looking at page 380 (2020 ed), for example, we see 6 original rules. You're missing 3 contrapositives so let's make that 9 rules if we write it all out. Then we see 14 inferences, counting each link in the chains separately. The inferences are missing 5 contrapositives so let's make that 19 inferences total. That's a lot. The book's method would have me drawing out 20 rules not including contrapositives (28 if including), and some of the inferences I may not even use. The book even says on page 381 that there are so many inferences that at some point you should just move to the questions. How do you know when it's time to move on? How do you know how hard a game will be before looking at the questions?

My feeling is to just write out the 9 original rules including contrapositives instead of the 28 rules including inferences and contrapositives. When a question activates a single rule, that rule will activate another rule, and another, etc. I simply follow the chain until no more rules get activated. Doing it this way means I don't spend time drawing inferences I'll never use and doesn't require me to guess how many inferences are enough. It doesn't take long to scan a list of 9 rules for a specific sufficient condition.

In other words, I think it would take longer for me to search for inferences and combinations of inferences than it would to simply write out the original rules and follow the causal pathways as appropriate.

Is this a reasonable strategy?

[Jeremy Press]

Hi sdb,

Yes, that works, again, assuming you're diagramming each relationship correctly originally and assuming you can see how you can keep following certain pathways (the kinds of things that inferences would reveal). Remember that the overarching approach to games like this often comes down to personal preference. When you're practicing, you should try it a few different ways to see what's most effective for you. That's ultimately what it's all about in more complex scenarios. It's not necessarily a one-size-fits-all!

Hope this helps!