Has anyone developed an efficient inference management syste

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longdaysjourney
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Has anyone developed an efficient inference management syste

Postby longdaysjourney » Mon May 10, 2010 11:48 am

Has anyone developed an *efficient* inference management system for grouping games?

To expand:

Say that the rules if a game give you the following.

If H not G.
If J then H.
If M then H.
If W the G.
If not J then S.

Obviously, there are a lot of inferences to be made. Is there a way to progress that guarantees that all of the possible inferences will be made? I have a basic system that I've come up with, but it is definitely hodge-podge and I am certain that someone has come up with a better system.

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Always Credited
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Re: Has anyone developed an efficient inference management syste

Postby Always Credited » Mon May 10, 2010 11:58 am

longdaysjourney wrote:Has anyone developed an *efficient* inference management system for grouping games?

To expand:

Say that the rules if a game give you the following.

If H not G.
If J then H.
If M then H.
If W the G.
If not J then S.

Obviously, there are a lot of inferences to be made. Is there a way to progress that guarantees that all of the possible inferences will be made? I have a basic system that I've come up with, but it is definitely hodge-podge and I am certain that someone has come up with a better system.



Form lodge brah

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suspicious android
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Re: Has anyone developed an efficient inference management syste

Postby suspicious android » Mon May 10, 2010 12:12 pm

longdaysjourney wrote:Has anyone developed an *efficient* inference management system for grouping games?

To expand:

Say that the rules if a game give you the following.

If H not G.
If J then H.
If M then H.
If W the G.
If not J then S.

Obviously, there are a lot of inferences to be made. Is there a way to progress that guarantees that all of the possible inferences will be made? I have a basic system that I've come up with, but it is definitely hodge-podge and I am certain that someone has come up with a better system.


For a pure conditional game like this, I don't see the point of making all 50 bajillion inferences. I don't write out contrapositives, and I don't link multiple statements together. When I'm given a certain variable, I just apply the rules that contain that variable, find what's in or out, apply the rules relevant to those. For the above rule set, you can figure out the consequence of any variable set either in or out within 10 seconds.

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longdaysjourney
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Re: Has anyone developed an efficient inference management syste

Postby longdaysjourney » Mon May 10, 2010 12:21 pm

Form lodge brah


I assume that this is what you are referring to? http://www.sacred-texts.com/mas/sof/sof15.htm

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malfurion
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Re: Has anyone developed an efficient inference management syste

Postby malfurion » Mon May 10, 2010 4:37 pm

longdaysjourney wrote:If H not G.
If J then H.
If M then H.
If W the G.
If not J then S.


For ones like this where there are a lot of interconnections, it helps me a lot to go ahead and write out chains with connected rules/contrapositives:

J
\
H --> not G --> not W
/
M

W --> G --> not H --> J and M

not J --> S


You can often blow through questions quickly when you see the whole path like that and don't have to keep looking at all the individual rules over and over.

Not sure if that's really what you were asking about though.

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LSAT Blog
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Re: Has anyone developed an efficient inference management syste

Postby LSAT Blog » Mon May 10, 2010 8:03 pm

The OP is referring to the Birds in the Forest game: PrepTest 33 (December 2000), Game 2 (p177 in Next 10).

I agree with malfurion's general approach as described (although that chain isn't 100% complete or accurate).

When diagramming with this style, the end product should be something more like this:

Image


We can connect the rules to form two long conditional chains (which are the contrapositives of each other). We do this by looking for cases where the necessary condition of one rule and the sufficient condition of another are identical. If they are the same, we can link them.


I know the above diagram may look a little intimidating, so I'll go into the step-by-step process that allows us to create it.


I start with the first rule:
H --> NOT G

and take the contrapositive, writing it immediately below the original:
G --> NOT H


I then connect the next rule because it mentions one of the same variables we've already been dealing with ("H"). I also connect the contrapositive of this new rule to "NOT H", giving us the following:

Image

I then connect the next rule (W->G) because I already have G on my diagram. I also connect the contrapositive of this rule to "NOT G" in my first conditional chain, giving us the following:

Image

Finally, we add the last rule, "NOT J -> S", as well as its contrapositive, "NOT S -> J" to both diagrams, giving us the final product:

Image


Now we have every rule connected in one big chain - in both the original form of each rule, and its contrapositive. I simply connected each new rule (and its contrapositive) with a previous rule (or its contrapositive) as I read it.

With this big conditional chain, we know that when W is in, both G and S are in, and H, J, and M are out.

When S is out, both J and H are in, and G and W are out. However, we don't know where M is.

On the chain, proximity/closeness doesn't matter.

Anytime we have a positive variable followed by a negative variable, at least one of those two variables is out. (Maybe both are out.) We don't care whether the negative is immediately after the positive or several variables later.

Anytime we have a negative variable followed by a positive variable, at least one of those two variables is in. (Maybe both are in.) We don't care whether the positive is immediately after the negative or several variables later.


One benefit of using this system for this particular type of Selection/In-Out is that it ensures you won't miss any inferences. It's also concise, and everything you write down for your initial diagram becomes part of the final setup. Contrast with the LGB setup on page 250 of the 2008 edition / page 134 of the 2003 edition.

Many alternative methods require writing out all the rules and then looking for connections. This leads to a moment of panic when you're not confident whether you've made all your inferences or not. You're never confident that you've done everything.

The method I've laid out above does not require any extra writing, which saves space and time. As long as you can do the contrapositive, you can do this. Just remember that you can only follow an arrow in the direction it points.

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malfurion
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Re: Has anyone developed an efficient inference management syste

Postby malfurion » Mon May 10, 2010 8:55 pm

Doh, I knew I should've double-checked that. Forgot a couple not's in there. Great explanation in the above post. I haven't done that particular game you mentioned, but I've done some similar ones and it definitely helps to make the chains. Often you can quickly figure out that there are only 2 or 3 possible templates, which you would never see if you were just looking at a big list of 2-element rules and their contrapositives.

barnum
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Re: Has anyone developed an efficient inference management syste

Postby barnum » Tue May 11, 2010 8:11 am

For an even more complete explanation of the bird game question by question using the chain, you should visit this website.

http://www.griffonprep.com/Birdgamesolution.html

Griffon Prep was one of the first companies to post this chain explanation.




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