The only 2 unsolved problems in AGI

[YKY (Yan King Yin, 甄景贤)]

1.  The ultimate universal logic

The current situation is like this:

Both Genifer and Opencog (and others) probably have a logic that is capable of near-human-level intelligence.

But currently all our AGI logics have flaws.  For example, the inability to deal with some paradoxes (eg Russell's and Curry's paradoxes).  Notice that some human logicians can reason about them.

What we need is perhaps a formal logic that can reason about paradoxes like humans do.  But we run into a circle because the correctness of formal logic can have no foundation other than human judgement.  Moreover, it seems that formal logics can get more and more sophisticated without bound -- perhaps a consequence of Godel incompleteness.

But then, why is the human brain able to reason about Godel incompleteness, in the first place?

This suggests another scenario:

By "ultimate logic" I mean:

1.  The logic can reason about anything conceivable.  (Similar to Turing universality.)

2.  The logic system itself does not need to be modified, ever.  (It could have some parameters that remain to be machine-learned.)

#2 seems to be very hard, but it is at least plausible that we might be able to invent a logic (or a class of logics) that do not need to be modified for a very, very long time -- eg, as long as Turing universality holds, etc.

Solomonoff induction may be relevant to this pursuit, but I'll have to study it more...

That is the 1st unsolved problem in AGI.

2.  How to learn fast

This is an optimization / algorithmics issue.  It is a more practical / urgent problem that needs to be solved.  I have some ideas of how to do it.  More on it later =)

-- 

KY

"The ultimate goal of mathematics is to eliminate any need for intelligent thought" -- Alfred North Whitehead

 

[Matt Mahoney]

2011/12/18 YKY (Yan King Yin, 甄景贤) <generic.in...@gmail.com>

> But then, why is the human brain able to reason about Godel incompleteness, in the first place?

Because logic is learned natural-language grammar. It is a set of
rules for manipulating symbols, like "if P then Q" = "Q or not P". We
can make up rules if we want, and teach them to others. But Godel
tells us we can't ever make up a complete and consistent set of rules.

> 2.  How to learn fast

Natural language evolved to have a structure that makes it learnable
by a slow but massively parallel neural network. It is just going to
take a lot of computing power. I realize that doing math and logic
with a neural network is vastly slower and less accurate than the well
known algorithms we have developed. But it is necessary to interface
it to the real world.

-- Matt Mahoney, mattma...@gmail.com

[YKY (Yan King Yin, 甄景贤)]

On Sun, Dec 18, 2011 at 11:49 PM, Matt Mahoney <mattma...@gmail.com> wrote:

> But then, why is the human brain able to reason about Godel incompleteness, in the first place?

Because logic is learned natural-language grammar. It is a set of
rules for manipulating symbols, like "if P then Q" = "Q or not P". We
can make up rules if we want, and teach them to others. But Godel
tells us we can't ever make up a complete and consistent set of rules.

Godel incompleteness only affects binary logic.  If the logic is 3-valued or more (such as fuzzy), it may be able to escape Godel incompleteness.

> 2.  How to learn fast

Natural language evolved to have a structure that makes it learnable
by a slow but massively parallel neural network. It is just going to
take a lot of computing power. I realize that doing math and logic
with a neural network is vastly slower and less accurate than the well
known algorithms we have developed. But it is necessary to interface
it to the real world.

We would be using a network of nodes to perform distributive and massively parallel learning.  It's just that the nodes would be using predicate logic rather than propositional logic (equivalent to neural networks).

KY

[Matt Mahoney]

2011/12/25 YKY (Yan King Yin, 甄景贤) <generic.in...@gmail.com>:

> On Sun, Dec 18, 2011 at 11:49 PM, Matt Mahoney <mattma...@gmail.com>
> wrote:
>
>> > But then, why is the human brain able to reason about Godel
>> > incompleteness, in the first place?
>>
>> Because logic is learned natural-language grammar. It is a set of
>> rules for manipulating symbols, like "if P then Q" = "Q or not P". We
>> can make up rules if we want, and teach them to others. But Godel
>> tells us we can't ever make up a complete and consistent set of rules.
>
>
> Godel incompleteness only affects binary logic.  If the logic is 3-valued or
> more (such as fuzzy), it may be able to escape Godel incompleteness.

Godel incompleteness is better understood as the halting problem.
Fuzzy logic doesn't help.

>> > 2.  How to learn fast
>>
>> Natural language evolved to have a structure that makes it learnable
>> by a slow but massively parallel neural network. It is just going to
>> take a lot of computing power. I realize that doing math and logic
>> with a neural network is vastly slower and less accurate than the well
>> known algorithms we have developed. But it is necessary to interface
>> it to the real world.
>
>
> We would be using a network of nodes to perform distributive and massively
> parallel learning.  It's just that the nodes would be using predicate logic
> rather than propositional logic (equivalent to neural networks).
>
> KY

Maybe you have seen the discussion on the OpenCog list about
distributing AtomSpace?

--
-- Matt Mahoney, mattma...@gmail.com

[YKY (Yan King Yin, 甄景贤)]

On Mon, Dec 26, 2011 at 4:51 AM, Matt Mahoney <mattma...@gmail.com> wrote:

> Godel incompleteness only affects binary logic.  If the logic is 3-valued or
> more (such as fuzzy), it may be able to escape Godel incompleteness.

Godel incompleteness is better understood as the halting problem.
Fuzzy logic doesn't help.

In Godel's proof, he considered logics where a statement is either true or false.  I don't think his proof works if some statements can have intermediate truth values.

Let's look at a formal statement of Godel incompleteness:

Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory

The definitions of "true", "provable", "complete", and "consistent" all rely on binary logic.  I've never seen Godel's theorem stated in fuzzy or probabilistic logic.

Maybe you have seen the discussion on the OpenCog list about

distributing AtomSpace?

Yes, I have tried to contribute to their project, but so far they have been very hostile.  They don't want me to check our code into their repository, and they also banned me from their discussion list.

KY

[Matt Mahoney]

2011/12/27 YKY (Yan King Yin, 甄景贤) <generic.in...@gmail.com>:

> In Godel's proof, he considered logics where a statement is either true or
> false.  I don't think his proof works if some statements can have
> intermediate truth values.

Probably so. Humans don't break down on input like "this sentence is
false". We just assign a truth value of 1/2.

The problem doesn't completely go away, because sometimes we need
truth values of 1 to think about math, logic, and programs. But I
don't think this is going to be a major obstacle.

>> Maybe you have seen the discussion on the OpenCog list about
>> distributing AtomSpace?
>
> Yes, I have tried to contribute to their project, but so far they have been
> very hostile.  They don't want me to check our code into their repository,
> and they also banned me from their discussion list.

Then we should proceed separately.

-- Matt Mahoney, mattma...@gmail.com