Re: [ontolog-forum] New Postulate formulation on AI KR

Joe,

Let me say this way.
-math structure is a mathematical structure. (Matrix, set of natural
numbers, labeled graph...)
-the theory is a special kind of text with axioms, definitions, theorems,
and proofs.
So they exist separately.
Math structure is a model for theory if we have an interpretation of
theory formulae
such that all axioms are true.
So, a model is a role math structure may play or not play for theory.
And we came to the formula:

Ontology = formal theory + finite structure modeling it:-)

what do you think?

Alex

ср, 28 авг. 2019 г. в 01:57, joseph simpson <jjs0sbw@gmail.com>:

> Alex:
>
> Great question.
>
> "is it possible to say that formal mathematical models you are talking
> about are finite?"
>
> Some models (Formal Theories)  may be finite others may be infinite.
>
> In this case, I assume you are using the terms "models" and "formal
> theory" interchangeably.
>
> To me the important ideas are associated with the model (theory) level of
> abstraction.
>
> Abstract mathematical theories (models) can address both finite (matrix
> theory) and infinite (number theory) abstract models.
>
> These abstract models (theories) may be formally applied to any specific
> domain of science.
>
> When these abstract models (theories) are applied to a specific domain of
> science, the concrete, substantive data and information that populates the
> models transform the theory from "abstract" to "concrete specific."
>
> General Systems Theory is viewed as occupying the space between abstract
> formal mathematical theories (models) and content specific theories
> (models) of specific scientific domains.
>
> I tend to view this area of inquiry along a graded range starting from
> pure abstraction and flowing to specific concrete examples.
>
> As Boulding wrote:
> "General Systems Theory is a name which has come into use to describe a
> level of theoretical model-building which lies somewhere between the highly
> generalized constructions of pure mathematics and the specific theories of
> the specialized disciplines. "
>
> Take care, be good to yourself and have fun,
>
> Joe
>
>
> On Tue, Aug 27, 2019 at 10:49 AM Alex Shkotin <alex.shkotin@gmail.com>
> wrote:
>
>> Joe,
>>
>> is it possible to say that formal mathematical models you are talking
>> about are finite?
>>
>> Alex
>>
>> вт, 27 авг. 2019 г. в 15:13, joseph simpson <jjs0sbw@gmail.com>:
>>
>>> Alex:
>>>
>>> *Figure 1,  Scientific Method and Model Building *is basically a
>>> process flow chart.
>>>
>>> Take care, be good to yourself and have fun,
>>>
>>> Joe
>>>
>>> On Tue, Aug 27, 2019 at 1:25 AM Alex Shkotin <alex.shkotin@gmail.com>
>>> wrote:
>>>
>>>> Joe,
>>>>
>>>> you are happy to work with systems and even in a general way. But who
>>>> will work with not systems? (joke)
>>>>
>>>> It's a pity Fig.1 in "System Concepts and Theories" does not have
>>>> rectangles for formal mathematical models, as it's better to keep theory
>>>> and models separately.
>>>>
>>>> Alex
>>>>
>>>> вт, 27 авг. 2019 г. в 03:58, joseph simpson <jjs0sbw@gmail.com>:
>>>>
>>>>> All:
>>>>>
>>>>> The statement:
>>>>>
>>>>> "Interdisciplinarity is fundamental to problem solving in most
>>>>> domains, and applied science and engineering are concerned primarily with
>>>>> problem solving, rather than purely theoretical formulations"
>>>>>
>>>>> Appears to relate directly to General Systems Theory.  See:
>>>>>
>>>>>
>>>>> https://www.researchgate.net/publication/323387658_A_General_Systems_Context_for_Structural_Modeling
>>>>>
>>>>> https://www.panarchy.org/boulding/systems.1956.html
>>>>>
>>>>> The proper alignment of natural language and formal language may be
>>>>> addressed in a range of view points.
>>>>>
>>>>> Some issues and ideas are outlined at:
>>>>>
>>>>>
>>>>> https://www.researchgate.net/publication/324138184_System_Concepts_and_Theories
>>>>>
>>>>> Take care, be good to yourself and have fun,
>>>>>
>>>>> Joe
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>> On Mon, Aug 26, 2019 at 1:42 AM Paola Di Maio <paola.dimaio@gmail.com>
>>>>> wrote:
>>>>>
>>>>>> Thank you Alex
>>>>>>
>>>>>> variations/elaborations  welcome (Vx)
>>>>>>
>>>>>> There is a problem with math KR tho - which has been discussed forever
>>>>>> I ll summarise it briefly hoping to put things to rest:
>>>>>>
>>>>>> Interdisciplinarity is fundamental to problem solving in most
>>>>>> domains, and applied science and engineering are concerned primarily with
>>>>>> problem solving, rather than purely theoretical formulations
>>>>>>
>>>>>> Interdisciplinarity means not everyone uses maths (  apparently even
>>>>>> mathematicians sometimes use different types of maths) Most domain experts
>>>>>> are not mathematicians
>>>>>>
>>>>>> Therefore, maths, like ml should also be translatable/mappable to to
>>>>>> plain natural language, even better to some diagrammatic notation  or
>>>>>> logical language that reproduces the logical schema ideally, problems and
>>>>>> solutions should be represented in a multiplicity of ways
>>>>>>
>>>>>> This particular postulate - luckily I dont wake up early morning to
>>>>>> postulate very often - has been prompted but the need to fill a gap between
>>>>>> symbolic an subsymbolic KR as per the posts, and having a citable reference
>>>>>> I am sure it can be refined further
>>>>>> PDM
>>>>>>
>>>>>>
>>>>>>
>>>>>> On Mon, Aug 26, 2019 at 4:29 PM Alex Shkotin <alex.shkotin@gmail.com>
>>>>>> wrote:
>>>>>>
>>>>>>> Paola,
>>>>>>>
>>>>>>> I keep in mind a variation of your postulate:
>>>>>>> Any algorithm (including MLA) has math representation.
>>>>>>>
>>>>>>> This is all that we have been talking about since Leibniz: math
>>>>>>> knowledge representation:-)
>>>>>>> The problem is that computer programs and DBs are not mathematical structures
>>>>>>> but they work:-)
>>>>>>>
>>>>>>> Alex
>>>>>>>
>>>>>>> пн, 26 авг. 2019 г. в 05:27, Paola Di Maio <paola.dimaio@gmail.com>:
>>>>>>>
>>>>>>>> Since posting  discussions about bridging the gap between symbolic
>>>>>>>> and subsymbolic, (see related posts) I have formulated a simple postulate,
>>>>>>>> and assigned a DOI so that anone following up on these discussions can cite
>>>>>>>> the contribution accordingly. I ll be happy to review the postulate with
>>>>>>>> comments and suggestions if any
>>>>>>>>
>>>>>>>> To support AI explainability, learnability,verifiability and
>>>>>>>> reproducibility, it is postulated that
>>>>>>>> for each MLA *machine learning algorithm,
>>>>>>>> there should correspond a natural language expression or other type
>>>>>>>> of symbolic knowledge representation
>>>>>>>>
>>>>>>>> https://doi.org/10.6084/m9.figshare.9730268.v2
>>>>>>>>
>>>>>>>> https://figshare.com/articles/A_New_Postulate_for_Knowledge_Representation_in_AI/9730268
>>>>>>>>
>>>>>>>>
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>>>>>>>> .
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>>>>>>> .
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>>>>>> .
>>>>>>
>>>>>
>>>>>
>>>>> --
>>>>> Joe Simpson
>>>>> “Reasonable people adapt themselves to the world. Unreasonable people
>>>>> attempt to adapt the world to themselves. All progress, therefore,
>>>>> depends on unreasonable people.”
>>>>> George Bernard Shaw
>>>>> Git Hub link:
>>>>> https://github.com/jjs0sbw
>>>>> Research Gate link:
>>>>> https://www.researchgate.net/profile/Joseph_Simpson3
>>>>> YouTube Channel
>>>>> https://www.youtube.com/user/jjs0sbw
>>>>> Web Site:
>>>>> https://systemsconcept.org/
>>>>>
>>>>>
>>>>> --
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>>>>> .
>>>>>
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>>>> .
>>>>
>>>
>>>
>>> --
>>> Joe Simpson
>>> “Reasonable people adapt themselves to the world. Unreasonable people
>>> attempt to adapt the world to themselves. All progress, therefore,
>>> depends on unreasonable people.”
>>> George Bernard Shaw
>>> Git Hub link:
>>> https://github.com/jjs0sbw
>>> Research Gate link:
>>> https://www.researchgate.net/profile/Joseph_Simpson3
>>> YouTube Channel
>>> https://www.youtube.com/user/jjs0sbw
>>> Web Site:
>>> https://systemsconcept.org/
>>>
>>>
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>>> .
>>>
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>> .
>>
>
>
> --
> Joe Simpson
> “Reasonable people adapt themselves to the world. Unreasonable people
> attempt to adapt the world to themselves. All progress, therefore,
> depends on unreasonable people.”
> George Bernard Shaw
> Git Hub link:
> https://github.com/jjs0sbw
> Research Gate link:
> https://www.researchgate.net/profile/Joseph_Simpson3
> YouTube Channel
> https://www.youtube.com/user/jjs0sbw
> Web Site:
> https://systemsconcept.org/
>
>
> --
> All contributions to this forum are covered by an open-source license.
> For information about the wiki, the license, and how to subscribe or
> unsubscribe to the forum, see http://ontologforum.org/info/
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> .
>