progress update, 2013 October

[YKY (Yan King Yin, 甄景贤)]

Sorry for the long silence... =)

1.  Learned more maths.  I now start to understand universal algebra, in particular, how an "ideal" is used as a structure for logical consequence.  I also start to understand categorical logic as a generalization of universal algebra using categorical notions, particularly functorial semantics.

But I am a bit disappointed because I was looking for a way to transition binary logic to something "fuzzy", but neither universal algebra nor categorical logic offer ready-made solutions (perhaps they could help in some ways, but not yet very obvious).

The idea of topoi in categorical logic looks tantalizingly like fuzzy logic, but it may take a lot of efforts to work it out.  Also, my idea is not just to make the logic's truth values fuzzy, but also take the logic's deduction or inference apparatus to the fuzzy realm (ie, to perform deduction in some continuous space).  That looks even harder.

The ability of an ideal to model logical consequence is due to the fact that in boolean algebra, implication (the arrow ->) can be converted to "not A or B" which is basically a conjunction.  And the con- or dis-junction is mapped to addition and multiplication in algebra.  The ideal is a structure closed under addition.  So, the ideal can model logical consequences in boolean algebra.

However, this is all lost if the implication arrow cannot be reduced to boolean conjunctions.  And also if the conjunctions are somehow "fuzzy", we're not sure how to define ideals that way.

I'm learning more about modules... somehow they fascinate me because they can be regarded as rings of transformations over themselves, and that sounds like "logical functions defined by the logic itself".

Also learning more about tensors... Riemannian geometry... relational algebra... schemes... etc..

2.  I am developing a Chinese input method based on concepts or pictures.  For example, to input the word "tennis", one may go through the categories "leisure activities -> sports -> ball games" etc.  It may be hard for western people to understand why an input method is needed (other than the keyboard), but we Chinese people are not used to phonetic spelling, and so typing can be a headache-causing problem for us, even now.

The input method requires clustering user sentences as training data, and this clustering process could be helped by an ontology.  So potentially, I may use this as a platform to build a crowd-sourced ontology.

The Conceptual Keyboard project on Github.

************

In mid-September I got hospitalized for acute pancreatitis for 12 days (maybe caused by too much stess)... I seem to have fully recovered now but I fear I may have pancreatic cancer!

Well.... so far so good... =]

YKY

[William Taysom]

Hi YKY,

Glad to hear you're back.

> Also, my idea is not just to make the logic's truth values fuzzy, but also take the logic's deduction or inference apparatus to the fuzzy realm (ie, to perform deduction in some continuous space). That looks even harder.

Perhaps a solution is hidden in plain sight. Bayes' Rule, after all, generalizes Modus Ponens to probability distributions. I recently read "Probabilistic Programming & Bayesian Methods for Hackers" <http://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/>, which does a far better job of giving one the feel for Baysian inference than anything I've encountered before.

As for categories and such, I wonder how one conceptualizes probability theory from a categorical point of view. I guess others have wondered this as well <http://mathoverflow.net/questions/20740/is-there-an-introduction-to-probability-theory-from-a-structuralist-categorical>.

> 2. I am developing a Chinese input method based on concepts or pictures.

Call it a "conceptual dictionary" – that way people won't get hung up and confused,
William

[SeH]

i'm enthusiastic about connecting our tools http://netention.org and jcog http://github.com/automenta somehow

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[Ivan Vodišek]

just thinking about Netention and artificial intelligence.

If we know what end-goal should be reached, we can easily calculate what beginning and intermediate goals should be satisfied to reach it. For simple structures, this should be obvious, but in multiuser environment with tens of goals, a help from computers should do the magic.

Like a function which returns goals that aren't yet satisfied and should be satisfied for end goal to show up among livings.

2013/10/28 SeH <seh...@gmail.com>

[SeH]

step by step, all the details will appear before us like a staircase spiraling towards infinity ;P

[Linas Vepstas]

On 27 October 2013 01:15, YKY (Yan King Yin, 甄景贤) <generic.in...@gmail.com> wrote:

But I am a bit disappointed because I was looking for a way to transition binary logic to something "fuzzy", but neither universal algebra nor categorical logic offer ready-made solutions (perhaps they could help in some ways, but not yet very obvious).

A better, more productive direction would probably be looking at markov logic networks, and the background needed for that: a little bit of model theory, a lot of entropy maximization ideas; in particular, understanding the "partition function" is critical; its a wildly complex beast, and it takes a while to appreciate it. Its a very different direction.

  

The idea of topoi in categorical logic looks tantalizingly like fuzzy logic, but it may take a lot of efforts to work it out.  

It is an area of current research by mathematicians. In particular, there is no good categorization of probability at this time. One of our very finest mathematicians, Misha Gromov, has taken a stab at it.  

The ability of an ideal to model logical consequence 

Indeed, it is sometimes said that "model theory is algebraic geometry without the numbers".  

-- linas