Future directions for ontology (JFS topic)

[Alex Shkotin]

Colleagues,

It may be worth exchanging views on this topic which JFS has raised elsewhere.

My opinion goes like this.

The direction of future development of formal ontologies can be found already in the DL “egg”, which, as is known, consists of a T-box (Terminology) and an A-box (Assertions). In the future, the decoding will be changed as follows: T - Theoretical knowledge, A - fActual knowledge.

Since all we do is formalize the knowledge acquired by others, theoretical and factual knowledge for the purpose of algorithmic processing of knowledge by computers. At the same time, factual and even theoretical knowledge does not have to be from our reality and does not even have to be feasible in our reality.

All we need is the ability and usefulness of their algorithmic processing.

It is also worth noting that despite the noise around GenAI, these are just algorithms obtained in a new way. Which make mistakes and to work with the results of which we need error-free algorithms.

It will be interesting to hear other opinions.

Alex

[Kingsley Idehen]

Hi Alex,

Yes, and they make 'mistakes' or 'hallucinate' because LLMs use probabilistic algorithms applied to training data (which may also be of questionable quality). This problem is solved by loosely coupling them with trusted data, information, and knowledge, then encapsulating them as subsystems within a larger system controlled by a main orchestrator i.e., John's 'executive.'.

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[Alex Shkotin]

Exactly. And the study of these algorithms is only at the beginning https://www.anthropic.com/news/mapping-mind-language-model

ср, 22 мая 2024 г. в 15:28, 'Kingsley Idehen' via ontolog-forum <ontolo...@googlegroups.com>:

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[Ravi Sharma]

Alex

There were useful discussions today

What is important is how to put constraints on those algorithms to make them more relevant to Assertions and proven or accepted facts at a given time.

Thanks.

Ravi

(Dr. Ravi Sharma, Ph.D. USA)

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[Alex Shkotin]

Ravi,

As usual, we have a black box approach: check and correct GenAI's results. And the white open box approach: figure out how the hell it works?!!:

"Today we report a significant advance in understanding the inner workings of AI models. We have identified how millions of concepts are represented inside Claude Sonnet, one of our deployed large language models. This is the first ever detailed look inside a modern, production-grade large language model. This interpretability discovery could, in future, help us make AI models safer."

https://www.anthropic.com/news/mapping-mind-language-model

Alex

ср, 22 мая 2024 г. в 20:20, Ravi Sharma <drravi...@gmail.com>:

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[John F Sowa]

Alex,

There are much more complex issues to discuss than just that point:

Alex:  The direction of future development of formal ontologies can  be found already in the DL “egg”, which, as is known, consists of a T-box (Terminology) and an A-box (Assertions). In the future, the decoding will be  changed as follows: T - Theoretical knowledge, A -  fActual knowledge. 

First, by "DL egg", I assume that you mean "description logic".   The first version of so-called Description logic by Ron Brachman and his thesis adviser Bill Woods emphasized the type hierarchy.  Later they added first-order logic as the constraint language.  Since the type hierarchy could be defined in FOL, that seemed to make it redundant.

But the difference between the two was priority or precedence:   The type hierarchy was the basis for the ontology.  In case of any conflict, the type hierarchy was considered to be correct, and the constraint language had to be modified to make it consistent with the hierarchy.

I believe that stage of DL development was a very good start.  Unfortunately, the decidability gang took over and persuaded most (but not all) DL proponents to restrict the constraint logic to the decidable subset.  Very few people who had real work to do adopted that restriction.  Unfortunately, the gang packed the voting process and forced decidability on the Semantic Web.  That was a terrible blunder.

However, the original idea of using FOL as the foundation was good.  The partitioning into a type hierarchy that took precedence over the constraint language was also good.  In practical applications, they also used database languages (SQL or object-oriented DB)  for storing and querying episodic information.

That led to a three-way partitioning:   (1) Type hierarchy (ontology); (2) Constraint logic (also a part of ontology); (3) Episodic information (raw data and information of any kind).

In case of conflicts, #1 had precedence over #2, which had precedence over #3.  The strategy for resolving conflicts depended on informing the system developers or managers, who would make the final decisions about what to change.

As for Claude Sonnet, I don't know enough about their inner workings.  In order to make LLMs safe, the constraints must be applied by technology that is independent of the tensor calculus that processes LLMs.  If they are using something like the above constraint hierarchy, that would be good.  Perhaps they have some other method.  But whatever it is, it must be some kind of method that is outside the basic tensor calculus that processes the LLLMs.

There is more to say, and I'll send another note later.

John

 

---

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

[Alex Shkotin]

John,

Description Logic is a theoretic basis for OWL2 - the most used formal language for ontologies. And at the very beginning they distinguished theoretical and factological (aka structural) propositions. Axioms and assertions in their terminology.

What we need on the way to formal theoretical knowledge is a pattern for formal definitions and formal proofs.

Like this here

definition

rus	Пусть g есть граф, v есть вершина, такая что v принадлежит g. степень [вершины] v в [графе] g есть количество простых рёбер графа g инцидентных v плюс умноженное на два количество петель графа g инцидентных v.
eng	Let g be a graph, v is a vertex such that v belongs to g. The degree of a vertex v in a graph g is the number of simple edges of the graph g that are incident with v plus the number of loops of the graph g that are incident with v multiplied by two.
yfl	declaration d func(Nat graph vertex) (g v) ≝ {vertex(g)(v)} (#e:edge(g) simple(e) & (e inc v)) + 2*(#e:edge(g) loop(e) & (e inc v)).

proof

rus	1	каждое простое ребро даёт вклад 2 в сумму степеней вершин графа.	[simpleE]	"по определению"
rus	2	каждая петля даёт вклад 2 в степень своей вершины.	[d]	"по определению"
rus	3	каждое ребро графа даёт вклад равный двум в сумму степеней вершин графа.	[1 2]	"объединение"
rus	4	Во всяком графе g сумма степеней вершин графа g равна удвоенному числу рёбер графа g.	[3]	"суммирование"
eng	1	each simple edge contributes 2 to the sum of the degrees of the vertices of the graph.	[simpleE]	"a-priory"
eng	2	each loop contributes 2 to the degree of its vertex.	[d]	"a-priory"
eng	3	Each edge of the graph makes a contribution equal to two to the sum of the degrees of the vertices of the graph.	[1 2]	"union"
eng	4	In any graph g, the sum of the degrees of the vertices of the graph g is equal to twice the number of edges of the graph g.	[3]	"summation"

And we need to formalize one or another structure like this

just set of ur-elements

rus	U содержит множество состоящее из шести элементов: _v1, _v2, _v3, _v4, _v5, _v6 и пяти элементов: _e1, _e2, _e3, _e4, _e5.
eng	U contains a set consisting of six elements: _v1, _v2, _v3, _v4, _v5, _v6 and five elements: _e1, _e2, _e3, _e4, _e5.
yfl	declaration U fset(Ide) primary (_e1 _e2 _e3 _e4 _e5 _v1 _v2 _v3 _v4 _v5 _v6 _v5). –rus:(+)здесь добавлено в Y!L2.0 из Y!L.скос ;-)
fl0	declaration U (_e1 _e2 _e3 _e4 _e5 _v1 _v2 _v3 _v4 _v5 _v6 _v5). axiom Set(U). axiom U_1 ∀(≝e:U Ide(e)).

and binary relation on it

rus	inc содержит бинарное отношение заданное так: (_e1 _v1, _v2); (_e2 _v1, _v4); (_e3 _v5, _v6); (_e4 _v1, _v2); (_e5 _v5).
eng	inc contains a binary relation defined as follows: (_e1 _v1, _v2); (_e2 _v1, _v4); (_e3 _v5, _v6); (_e4 _v1, _v2); (_e5 _v5).
yfl	declaration inc frel(U U) primary ((_e1 _v1) (_e1 _v2) (_e2 _v1) (_e2 _v4) (_e3 _v5) (_e3 _v6) (_e4 _v1) (_e4 _v2) (_e5 _v5)). –rus:(+) добавлена возможность из fl0 ;-)
fl0	declaration inc ((_e1 _v1) (_e1 _v2) (_e2 _v1) (_e2 _v4) (_e3 _v5) (_e3 _v6) (_e4 _v1) (_e4 _v2) (_e5 _v5)) . axiom inc_1 Rel(inc). axiom inc_2 ∀(≝p:inc U(1(p))&U(2(p))).

and now we may solve some task on this structure using our theory

rus	0.=	сумма степеней вершин графа U равна удвоенному числу рёбер графа U.	TRUE		"расщепление"
rus	1.	сумма степеней вершин графа U	10	CLC8_4	"подзадача"
rus	2.	удвоенное число рёбер графа U	10	???	"подзадача"
yfl	o.	(Σx:vertex(U) d(x U))=2*Card(edges(U))	TRUE		Yp
yf0	o.	Σ(λx:vertex(U) d(x U))=2*Card(edges(U))	TRUE		Yp0
eng	0.=	the sum of the degrees of the vertices of a graph U equals twice the number of edges of the graph U.	TRUE		"split"
eng	1.	sum of degrees of vertices of graph U	10	CLC8_4	"subtask"
eng	2.	double the number of edges of the graph U	10	???	"subtask"

This is a future of formal ontologies.

We have a task and need a solution. We create a structure to keep task information. We use theory to formulate a task properly. We use knowledge processing rules to create solutions.

All these components should be in ontology or near.

In this particular case our application area is ugraphs like this

But it may be any ⚗️

Alex

чт, 23 мая 2024 г. в 22:23, John F Sowa <so...@bestweb.net>:

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[John F Sowa]

Alex,

We have to make a clear distinction of (1) Historical developments, (2) Particular implementations, (3) Logical foundations, (4) Practical usage and development.

Alex:  Description Logic is a theoretic basis for OWL2 - the most used formal language for ontologies. 

If we consider point #1, the type hierarchy for DLs was specified by Aristotle with his syllogisms, which are more readable today than any current implementation of OWL (Point #2).   There are four rules (A I E O), which can be expressed in Greek, English, or any other natural language.  These rules have been widely used for centuries, and they are a highly readable notation for the OWL hierarchy:

A:  Every  S is P.    (S is the subject, and P is the predicate)

I:   Some S is P.

E;  No S is P,

O:  Some S is not P.

For an introduction and examples, see slides 25 to 30 of https://jfsowa.com/talks/patolog1.pdf .  For theoretical issues (Point #3), see slides 26 to 33.   The Stoic logicians introduced Greek sentence patterns (#2 and #3) for assertions in a subset of first-order logic.  In the 14th century, Ockham introduced a more complete range of sentence patterns in Latin that could represent the full expressive power of first-order logic (#3 and #4).  His notation was very readable (by anyone who could read Latin or its translation to English and other languages).  But he didn't have all the reasoning methods of modern FOL for proving the expressive power. 

In addition to the type hierarchy, Brachman and Fikes (1979) wrote a paper about KL-ONE (Knowledge Language 1),

which consisted of a terminology (T-Box) for the equivalent of Aristotle's syllogisms, and a notation for assertions (A-Box).

This covers points #1, #2, #3, and #4 as a superset of OWL4.  

Anything and everything that can be represented in OWL2 can be represented  in KL-ONE, or in Latin according to Ockham's Summa Logicae.   But the Greek and Latin versions or their translation to modern languages had the same advantage as KL-ONE:  The full expressive power of first-order logic.

And by the way, C. S. Peirce was familiar with all the logic methods by the ancient Greeks and the medieval Latins.  He took pride in having the largest collection of medieval manuscripts on logic in the Boston area (which included the Harvard libraries).  When he specified his versions of logic, he was familiar with all the earlier options.

By comparison, however, OWL2 was a major step BACKWARDS from the Greeks, the Latins, and KL-ONE by the hopelessly misguided idea that decidabiity was important.  It just made the notation more complex, harder to read, harder to write, harder to implement, and much less expressive.  

Recommendation for OWL3:  An upward compatible version that allows any statements in Turtle or other notations plus any statements in pure and simple first-order logic.  That means that all current implementations can continue to be used without change.  The user notation can be a highly readable controlled natural language, such as ACE.  

This gives us the best of all options #1, #2, #3, and #4 -- plus upward compatibility with current implementations.

John

PS:  Since the word 'sowa' means owl in Polish, this version of OWL3 would rescue my totem animal from the ignominy of a horrible version of logic.  That's another plus.

 

---

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

[Alex Shkotin]

John,

What is the reason we formalize our knowledge?

Because we have algorithms for formal knowledge processing implemented in comps.

Look at ability of knowledge processing by DL-reasoner

I marked in pink the ability of DL-Reasoner to calculate. Following Igor's example list_sum.owl.

The simplest example is 

has_price(book, ?p), has_price(bag, ?s), add(?xs, ?s, ?p) -> has_price(SUM, ?xs)

or if we use FOL with numbers as interlingua

∀p,s,xs:Rational price(book)=p ∧ price(bag)=s ∧ xs=s+p -> price(SUM)=xs

And this is a way to write axiom

price(SUM)=price(book)+price(bag)

If we need a DL-Reasoner to calculate.

OMG⛲

For any language in hets.eu or DOL the question #1. What kind of knowledge processing is possible after formalization?

By the way, it is known from math that FOL is not enough to express all kinds of problems they have.

For example let me cite Barwise 

Languages from FOL  to HOL are good to express theoretical knowledge. The languages to introduce a particular math object are of a special kind.

Igor partially touches on this question in his list_sum.owl introducing two "follows" binary predicates (aka object properties).

How to formalize representation of one or another structure we have got from reality?

DB, KG? etc?

Alex

IN ADDITION from Barwise == FOL is good but HOL is used (OWL2 is HOL, by the way. As well as English)

сб, 25 мая 2024 г. в 23:21, John F Sowa <so...@bestweb.net>:

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