Polysillogism

[Fredo Corleone]

Finally completed writing the algo for polysillogism.

I need you guys for some testing:

1. No A is B

Some A is C

Some C is not B

Some C is E

All E is B

2. No B is A

All A is C

Some C is not B

All C is E

Some E is not B

3. All B is A

Some C is not A

Some C is not B

All C is E

Some E is not B


4. Some A is not B

All A is C

Some C is not B

All C is E

Some E is not B

Some F is E

Some F is B

5. Some A is B

All A is C

Some C is B

All C is E

Some E is B

Some F is not E

Some F is not B

6. No B is A

All C is A

No C is B

Some E is C

Some E is not B

All E is F

Some F is not B


7. No B is A

All C is A

No C is B

All E is C

No E is B

All E is F

Some F is not B

All F is G

Some G is not B

8. No A is B

Some C is A

Some C is not B

All C is E

Some E is not B

All E is F

Some F is not B

All F is G

Some G is not B

9. All B is A

No C is A

Some C is not B

All C is E

Some E is not B

All E is F

Some F is not B

All F is G

Some G is not B

If you intend to participate please answer to all 9 syllogism.
If something is not working it should be evident, I'm pretty tired and I couldn't confirm at the moment.

Let me know.
Thanks

[itrn...@gmail.com]

Where are the questions? Or do we check for the consistency of the statements?

[itrn...@gmail.com]

Also, how did you structure the data? Very curious because it was a super laborious process for me to structure data and have each unique type of statement manipulate the data differently, and how I did it used so much RAM that it couldn't make more than 8 statements(and 8 sets total) without crashing.

[Fredo Corleone]

I didn't really structure any data, I'm just making polysillogism by the definition of them "a sequence of syllogisms such that the conclusion of each syllogism, together with the next proposition, is a premise for the next, and so on".

There are certain rules, one is that for the polysillogism to make any sense the major premise of the next one has to be of the same quantifier of the conclusion of the previous one.

To make things more interesting I have to complete the algo with the fact that the probability of picking an incorrect syllogism in any point of the chain is distributed exponentially over the length of the syllogism. This is because there are A LOT more invalid syllogisms than valid ones and to pick invalid ones with even probability at any step of the chain would make extremely difficult to pick polysillogisms that do not die (in meaning) prematurely.

All BLOW is KEN

All BLOW is NIGHT

Some NIGHT is KEN

All NIGHT is FRAME

Some FRAME is KEN

All FRAME is ROPE

Some ROPE is KEN

All ROPE is AMEN

Some AMEN is KEN

All AMEN is LINE

Some LINE is KEN

All LINE is SHAME

Some SHAME is KEN

All SHAME is CORE

Some CORE is KEN

All CORE is LIGHT

Some LIGHT is KEN

All LIGHT is SLAP

Some SLAP is KEN

All SLAP is BYTE

Some BYTE is KEN

All BYTE is WINE

Some WINE is KEN

All WINE is SIGN

Some SIGN is KEN

All SIGN is KITE

Some KITE is KEN

All KITE is HOPE

Some HOPE is KEN

All HOPE is SLOPE

Some SLOPE is KEN

All SLOPE is SOAP

Some SOAP is KEN

All SOAP is FLOOR

Some FLOOR is KEN

All FLOOR is PINE

Some PINE is KEN

All PINE is BLAME

Some BLAME is KEN

All BLAME is BOW

Some BOW is KEN

All BOW is MEN

Some MEN is KEN

All MEN is CRAP

Some CRAP is KEN

All CRAP is DOOR

Some DOOR is KEN

You see that KEN is alway there at the end. The thing is that you either use the subject or the predicate of the conclusion before as the middle-term or predicate of the major premise that follows.
At the moment for easy of comprehension I'm always working with predicates, but I could substitute the middle-term and that trail of KENs would disappear.

[Fredo Corleone]

I've set up this playground here for you to test the polysillogism algorithm.

https://codepen.io/eternalsunshineofspotlessmind/full/powbjdZ

Please tell me if there's anything wrong!

[Aldona Odojewska]

Fredo, I think there'a mistake in your games, both that and previous (skinskywalker). I'm now talking about 2-premise syllogisms.

1. AaB & AaC does not imply BiC.

2. CeA & AaB does not imply BoC.

Premises can be true while conclusion false. I suppose but I could be wrong that it's because the program assumes that if X is a subset of Y, then X must not be empty.

--
You received this message because you are subscribed to the Google Groups "Dual N-Back, Brain Training & Intelligence" group.
To unsubscribe from this group and stop receiving emails from it, send an email to brain-trainin...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/brain-training/664d782f-419a-4ebc-8305-63a277420482n%40googlegroups.com.

[Leonardo]

I see some cool cursor tracking on that board ;)

Thank you, I will let you know my experience in the next few days. 

[Fredo Corleone]

aldona could you please report the exact syllogism? :)

By the way aai1 (Modus Barbari), aai3 (Modus Darapti) and aai4 (Modus Bamalip) are valid and eao (Modus Celaront, Modus Cesaro, Modus Felapton, Modus Fesapo) is valid for all figures.

[Leonardo]

For the moment, I have been getting just green halos. 

[Aldona Odojewska]

Sorry, maybe that's just convention of syllogistics that terms are not empty. E.g. Barbara is fine, but Barbari is enthymematic, it presumes non-emptiness. The sentence "Every A is B" should not be interpreted as "A is a subset of B", because in the latter A can be empty. But such an interpretation of "Every A is B" may not be proper for mathematical/logical thinking where what isn't explicitly said, can't be just added if it changes the scope of conclusions.

To view this discussion on the web visit https://groups.google.com/d/msgid/brain-training/b1827269-5f30-4e02-8bb2-8c17c52c9ec3n%40googlegroups.com.

[Fredo Corleone]

aldona to me All A is B simply means A is smaller than or equal to B, changing perspective I would say that B is at least A in size.

[Fredo Corleone]

aldona I get your view, but by the way I see syllogisms those are valid. If you feel like you can change the logic the way you want in the source code and simply invalidate those syllogisms you don't think are valid and keep training with your own version of the software :) I can teach you how to do it...

[Leonardo]

The real issue is that you only need to read the last 3 ones. No matter how long do you set the polysyllogism to be. 

After:

All A is C Some B is A Some B is C All C is F Some F is B All F is G Some G is B All G is H Some H is B All H is I Some I is B All I is J Some J is B All B is K Some K is J All K is L Some L is J All J is M Some M is L All L is N Some N is M All N is O Some O is M All M is P Some P is O All O is Q Some Q is P All P is R Some R is Q All R is S Some S is Q All S is T Some T is Q All T is U Some U is Q All U is V Some V is Q All Q is W Some W is V All V is X Some X is W All W is Y 

You just need to read:

Some Y is X 

All Y is Z 

Some Z is X

To know that the answer is True. 

[Fredo Corleone]

Nope, the chain can break at any point. But it's exponentialy more likely to break at the end.

[Leonardo]

Yes? I have not found any counterexample yet, but it could be just a matter of luck. 

[Fredo Corleone]

Because it's exponentially more likely to find it at the end, it means that most of them will fail close to the end, sum it with the fact that 50% are right and you have much more chances of it breaking later than earlier. But I'll fix this at one point xD