[ivan.moony]

Here is Stanford Introduction to Logic, an online course on symbolic logic. I believe it covers the most interesting knowledge of logic in general. Enjoy

[LOCKSUIT]

FINALLY

All these professors and everyone talking about induction etc, now we got it right here. Of course, I read wiki, etc, and my own work.

I'll see if I get anything out of it.

[LOCKSUIT]

So far its gold 100%.

[LOCKSUIT]

Lol what made you find this ivan? Are you reading it yourself? Btw how much of a Logic expert are you?

What else goes with it? Any other material? Just as an example, does Chaos Theory go with this? LSTMs? Some more abstract form of this on some higher level? Sorta like its chocolate, hence, maybe you got vanilla, of which not only is good/related too but also tops it and makes it 260% better.

Lol it has the alice in wonderland infurl

[ivan.moony]

Lol what made you find this ivan?

I was designing my own logic and wanted to name it "relational logic". Then I googled it up to check if the name is taken. Then I stumbled upon Stanford material, realizing that they use name "relational logic" as a synonym for predicate logic. Still, I didn't see the same naming anywhere else, but I'm pretty sure they are describing what is widely accepted by the name predicate logic. But it's a Stanford, I guess they can allow themselves to push in their own naming standards.

Are you reading it yourself?

As for reading material, I was reading a book with a similar content some twenty years ago and I liked it very much. I was thrilled to see the Stanford edition with some additional content and I wanted to share it here. The edition is written in very readable language, which added some pluses for sharing it. What I like about the book is that it shows how to describe knowledge in a way that we can extract answers from it. Still, keep in mind that it shows only fragments (the most of books of this kind do) which you have to connect on your own. For example, it is not possible to read this material and then sit down and program something meaningful right away. Some glue connecting pieces is missing, but I believe it is a status of scientific logic research these days. Researchers mostly care about abstract scientific value, and less about the real world use.

Btw how much of a Logic expert are you?

You can say that I understand a bit of logic, propositional and predicate more thoroughly, and higher order in some lesser extent. So, if you don't understand something, don't hesitate to freely ask, maybe I can answer.

What else goes with it? Any other material? Just as an example, does Chaos Theory go with this? LSTMs? Some more abstract form of this on some higher level? Sorta like its chocolate, hence, maybe you got vanilla, of which not only is good/related too but also tops it and makes it 260% better.

What else goes with this edition? Well, It's subject is knowledge, so an answer would be anything that can be known. Theoretically, logic is supposed to be the starting point for anything else that takes a form of thought. In practice, it contains a certain level of abstraction, so you may find it necessary to drift it gently towards specific use. I propose (after reading the material) to google up your newly created ideas and questions, just to see where the world can get you.

[LOCKSUIT]

That's ok, I am a puzzle-putter-together-machine, digesting bits of info. Even 'if' it doesn't contain an overview of all Logic or all the details, it still is a good resource. I can see/realize the AGI overview, and fill the details.

Little confused on something, with the Sorority Girls case with many input sentences given. In one side of my mind I see it as sequence prediction after the input "Bess likes Cody. Cody doesn't like Abby. Etc. Etc." where the prediction has to satisfy all conditions....HAHAHAHAHAHA...........while on another side of my mind I see it as saying 'find a fact that is green, small, thin, and grown outside' in your 'DB'................while on another area of my brain it means the sum of their Truths satidfying everything enough.................while on another location in my brain tells me it is it suggest trying Induction more...............while on another planet of my brain says it says given those 4 sentences, infer new facts from them like Abby doesn't like herself HUHWHA WHAT THE YOU KIDDING ME I'm lost... And to think this is the tip of the iceberg on my todolist, there's so much involved to do!! This is just some of my work, just /some/ thoughts.

Next, I notice it uses punctuation plus operators, with an order. This defines bond order/structure...and how to assign Truth  O M G... Down the rabbit hole. Essentially we have here a structure with truth assignment, while the proposition/conclusions/inferring/predictions or 'implications' are one part of the AND/OR/NOR/NEGATE/IMPLY/BIIMPLY...not even sure why it jumped from x=y=z to truth assignment despite they are closely used, hmm, maybe it means if x=y then it must be related to its truth to get assignment?

[LOCKSUIT]

Also, need clarification here
http://intrologic.stanford.edu/public/section.php?section=section_02_05

The pattern I found after observing the truth table is that it seems that if p or q on the left is a 1 (true), then both the 2 after the arrow gotta be true, otherwise only one must ex. R.........again: that's what I infer from their truth table at least...

However, it says q & r.....why is the sentence or even the right side half True if both q & r are not true in one row that says it would be?

[Korrelan]

A truth table for a propositional language is a table showing all of the possible truth assignments for the proposition constants in the language

 

[ivan.moony]

P, q and r are not connected anyhow there. If you read on, later you will find out the other side of truth table, and that is an expression that makes a truth table make sense. For example, this is a truth table of `and` operator:

Code

 p   q   |p ∧ q
----------------
 1   1   |  1
 1   0   |  0
 0   1   |  0
 0   0   |  0

Truth table can be constructed for any operator combination. In chapter 5.2, page 5, they put `x` where `p ∨ q ⇒ q ∧ r` is false (instead of making new column containing values of `p ∨ q ⇒ q ∧ r`).

[LOCKSUIT]

No make sense still... You have an input sentence and sum up its Truth to either 0 -or- 1, and there is possible ways it will output a 1 or 0, yes, yes, right?......hmm, but given 4 sentences like the Sorority World example, what if the goal was to find or generate a sentence output that satisfied the input?  ;p3

[LOCKSUIT]

can you give me sentences that would be these? http://intrologic.stanford.edu/public/exercise.php?exercise=exercise_02_02

ex. like "If I eat and sleep then I am alive"

confused here because it says the Truth of    p ⇒ q ∧ r    is False...but the   p ∧ q ⇒ r    should be too...

[ivan.moony]

It's good, implication operator works that way. Expressed differently, A -> B means ~(A & ~B).

Read on, there is a complete truth tables for major logical operators: http://intrologic.stanford.edu/public/section.php?section=section_02_03. You should be able to sing them in the midnight. 

[LOCKSUIT]

Take a close look here: http://intrologic.stanford.edu/public/exercise.php?exercise=exercise_02_02

on some of the results shown (click show results), it implies it is OK if   p & q => r   I.E p & q = 0 and then 0 => 1 wtf? Only 1 => 1 no? How does a false imply a true?

It's like saying if you are alive and smoke then you won't make it. Both conditions must be true - "AND"

[ivan.moony]

on some of the results shown (click show results), it implies it is OK if   p & q => r   I.E p & q = 0 and then 0 => 1 wtf? Only 1 => 1 no? How does a false imply a true?

This is the story about implication: It is possible for cause not to happen, but consequence still to be true (due to some other possible causes). In fact any truth assignment is possible except cause to be true and consequence to be false. If cause is there, consequence must be also there.

False can imply true, here is the proof:

Code

  False -> True
---------------------
  (¬False) ∨ True
---------------------
  True ∨ True
---------------------
  True

The interpretation could be: within lies could be anything, including a truth.

Let's try the other way around:

Code

  True -> False
---------------------
  (¬True) ∨ False
---------------------
  False ∨ False
---------------------
  False

The interpretation would be that within truth there can't be lies.

used rules of inference are:
A -> B ⊢ ¬A ∨ B
¬True ⊢ False
¬False ⊢ True

It's like saying if you are alive and smoke then you won't make it. Both conditions must be true - "AND"

Code

YouSmoke -> YouDontMakeIt

The interpretation is as you read IF you smoke THEN you won't make it. But it is also possible not to smoke, and not to make it anyway because i.e. you regularly run across a highway, or you regularly swim with sharks.

[LOCKSUIT]

Gonna read that wait, but here's something I just realized, it may shock you to see this lol (result at end):

So we can figure out if a sentence or part of it is true or false, we can infer new true or false facts from it ex. if it is true using "p or q" and we have another timbit saying "q => b" and b is true then we know q is true. And if I tell you a sentence saying true and false and unvalidated things like "Food is good. If food is good then I am a billionaire." then of course we first must validate before can discern how true the sentence is. Let's look at "If pigs are cute and alive then clouds are evil or I brush my teeth" - here we have a going to be validated as false fact and a wider fact (If pigs are cute and alive then I brush my teeth) while the small part in it is true yes but  ya this wider one will too be false once validated and hence the sentence is false: c & a => c |  b -------- 1 & 1 => 0 | 1 --------- 1 => 1 --------- 0 !!!!!

Moral of the story: just because 2 facts are both 1s as shown at end, doesn't mean the final number will be 1!
All parts of a node must be validated as either True or False/satisfied.....A....B....and AB....all 3 nodes of the pyramid hierarchy if you want AB node to be true! (all its parts including itself)

  O
O O