knowledge processing and genAI

[Alex Shkotin]

John and all,

The theme of knowledge processing (KP) is so important.

We first need to classify a little what kind of KP we use in science, technology and everyday life. 

And then which of them are now available through genAI, DL-reasoner, math-prover and other algorithms. 

When we are problem solving, i.e. every time we have a goal, what kind of rules do we follow to get a solution? 

Let me share my findings when investigating undirected graph tasks.

I just want to emphasize that the "inference" rules that we use when constructing a solution to a problem are very diverse. And this is not deduction, abduction and induction at all.

Here is a summary of the rules that I encountered, and in the basement there is a description for those who are interested.

Summary of rules used

rule	short description	use and comment
"quantifier expansion"	finitistic development by run-in ∧, +.	2:_INC00 CLC8_4
"subtask"	separating a subtask into a separate block	26: found in almost all solutions.
"substitution"	DEFINITIONS	4: FCT4_1-1 подзадача
"split"	statements using "and" (2), "equal" (2), "plus"	5:FCT8_6 FCT4_1 FCT4_1 …
"reformulation"	to standard form	2: FCT4_1-1 подзадача
"interpretation"	transition from the terminology of theory to the terminology of structures	FCT4_1-1 подзадача FCT4_1-1 подзадача … FCT4_1-1 подзадача
"choice"	it is determined whether there is an element in the set that satisfies a given condition	2: FCT4_1-1 подзадача
"selection"	subset from set	2:
"obviously"	mental action with elements, parts of phrase	3: FCT4_1 FCT4_1-1 подзадача   ...
"count"	in the mind	2:

I want to emphasize that the list of rules is not complete and it would be great to discuss what other rules there are.

We use theoretical knowledge to solve our problems.

Alex

Rules for transforming propositions and phrases

There are many ways to get from one text to another or several others. It is assumed that the processing of the original text is replaced by the processing of those obtained from it, and we know how to process the received ones, i.e. having received their values, get the value of the original one. We will call such processing methods rules. 

The texts resulting from applying the rules are called subtasks.

The following are descriptions of different rules.

"subtask"

A rule named “subtask” only indicates that this subtask is separated into a separate task, i.e. must have its own solution block, and if it exists, it is indicated in the “parameters” column (see below), and if the cell keeps "???", then the corresponding task has not yet been added to the framework! Strictly speaking, the task block has not been completed to the end.

"interpretation"

This rule makes the transition from terms of theory to terms of structures.

For example, in "There exists x in U such that _e1 is incident to x." the term "incident" is introduced in the theories of Biria and used in Ugraphia for inc global variable. Knowing its “binding” with inc, we can interpret the statement as “There exists x in U such that (_e1 x) in inc.” where the term “incident” is not used.

It is important to emphasize that no terms of theories are used in the resulting statement!

"substitution" 

This rule refers to the substitution of the definition of a term at the place of its use. Typically, a definition consists of a precondition formulated in a sentence beginning with the word “Let” and the definition itself, consisting of a phrase using the term, a syntactic connective (for example, “if and only if”) and a determinant - a phrase that specifies the meaning of the term. Definitions of terms are given in one theory or another - in our case, it is Ugraphia. From a programming point of view, a definition is a macro command, and a “substitution” is a macro substitution, and sometimes, the substituted text itself (preconditions and determinant) is modified.

The substitution comes down to the fact that the statements of the precondition form a linear block, and the determinant - a node of the decision tree.

For example, consider the statement

_e1 parallel to _e4.

It uses the term from Ugraphia - “parallel”.

Applying his definition:

eng	Let e1 e2 denote edges. e1 is parallel to e2 if and only if e1 and e2 denote different edges and e1 has the same endpoints as e2.

We get two precondition statements:

_e1 is an edge.

_e4 is an edge.

which need to be checked for truth, 

and a subtask:

_e1 and _e4 are different and _e1 has the same endpoints as _e4.

It is easy to see that the actual parameters of the place where the term is used, _e1 and _e4, are substituted in place of the formal parameters e1, e2 of the “macro command” of the definition.

+$+"quantifier expansion"

A quantifier always runs over some set or sequence and is expanded by running into an operation on statements or phrases written for each element of the set - an excellent move to finitism.

For example, consider the expansion of the second quantifier "every" in

"every member of every pair of inc belongs to U."

we need to run by inc and, in our case, see the __inc block of the framework; we will get from inc for the first element:

"every member of (_e1 _v1) belongs to U." 

etc., for each pair in inc.

Notes. For example, the finitistic way for the quantifier expansion in mathematical logic can be found in Esenin-Volpin's works. And it can be stated using an example like this

Let S is {e1 e2} and p() is an unary predicate on S. Then

"∀x:S p(x)" expands into "p(e1)∧p(e2)"

the generalization to the case of any finite number of elements in non-empty S is obvious.

Thus, the quantifier statement is expanded into several more specific statements and the meaning of the original statement is obtained by applying the operation ∧ or +, etc., to the expanded values.

"split"

This is a situation when a conjunction such as “and” or the words “equals”, “plus”, and the like is applied to two specific statements or phrases in the original statement.

For example, in 

"_e1 and _e4 are different and _e1 has the same endpoints as _e4." 

we split along the second “and”, obtaining two statements - subtasks: 

"_e1 and _e4 are different."

"_e1 has the same end vertices as _e4."

"reformulation"

According to this rule, various free texts in NL are converted into equivalent but more regular ones.

For example, 

"_e1 is incident to some element from U."

becomes

"there exists x in U such that _e1 is incident to x."

"choice"

Execution of a rule consists of SEARCHING in a set and determining the presence or absence of an element that satisfies a given condition.

For example, applying the "choice" rule to a statement

" there is x in U such that (_e1 x) in inc. "

consists of running through U and checking for the current element that it, paired with _e1, is present in inc. If such an element is found, then the statement is considered valid; otherwise - it is false.

"selection"

A subset of elements is selected from a specific set according to some criterion.

for example, in the phrase 

" number of elements of U such that it's an edge and simple and incident _v1."

Before counting the quantity, it is necessary to obtain a subset of U with the described elements, and then the phrase is converted into

" number of elements in list (_e1, _e2, _e4) ".

"obviously"

With text, the mental action of obtaining its value is performed.

For example, it is obvious that the following statements are true:

"_e1 and _e4 are different."

"_e1 is an element of U."

"(_e1 _v1) in inc."

However, you need to look at U and inc in the last two cases, respectively.

"count"

The calculation formulated in the phrase is performed in the mind.

For example, 

counting "number of elements in list (_e1, _e2, _e4)" will give the result 3.

---------- Forwarded message ---------
От: John F Sowa <so...@bestweb.net>
Date: ср, 20 нояб. 2024 г. в 01:21
Subject: Re: [ontolog-forum] Accelerating Knowledge Graph and Ontology Engineering with Large Language Models
To: <ontolo...@googlegroups.com>

Alex,

I agree that there are many hybrid systems that combine LLMs with more traditional kinds of processing.

Google developed the LLM technology for machine translation (MT), and that is its best and most reliable application.  Since the source and target language are just one step away, the error rate is quite low.

However, the LLM algorithms cannot be used without further processing even for MT in cases where absolute accuracy is essential.  Critical issues are translations at the UN and EU.  International treaties must use exact translations of tiny details.

For many applications of LLM technology, hybrid methods are used, which can make errors in certain kinds of combinations,    Your example of arithmetic is one such special case.  Another example involves problems on exams, where almost every textbook uses very similar methods. As a result the computer gets a score of 98% on an exam.  That's good enough for an A.

But that 2% error, on a design of an airplane or a rocket, could cause a disaster.     A score of 98% can be fatal. 

Another serious problem is that the larger the volume of text that is processed, the more likely that some weird or unusual application somewhere might insert some strange little item.  That one item might then link to some other strange application.  After a few steps, you can get a serious error.  Hallucinations are extremely bad, but they are obviously wrong.  But those tiny little things often go unnoticed.  They  can be more dangerous than a hallucination.

John

 

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From: "Alex Shkotin" <alex.s...@gmail.com>

John,

A kind of knowledge processing genAI can do is not only abduction. 

Look at this example [1] where I have talked with Gemini in Russian but asked to translate one part in English.

I am not about translation itself, though for me this is not abduction. I am about knowledge processing by Gemini.

Alex

[1] https://gemini.google.com/app/a59f16a9a7044419

THE TEXT IS GEMINI PRODUCTION

English Translation of the Problem and Solution

Problem: Let's work with only natural numbers. One number is 35 more than another number. A third number is such that, if it is subtracted from the first number and added to the second number, the first and second numbers become equal. What is the third number?

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