Re: [ontolog-forum] CNL's and ConLangs

["Bruce Schuman" <bruceschuman@xxxxxxx>]

“It seems to me that there should be a taxonomy that includes all languages and what I call "language shorthands" such as chemical, math, Feynman diagrams, etc”

 

“I don’t see the grist for an ontology in math”

 

 

Just to postulate a slightly contrarian view – I think I DO see “grist for an ontology in math”.

 

The very simple and perhaps obvious statement from Peter Wegner’s Programming Languages, Information Structures, and Machine Organization might point in this direction, where he says (p.4) that “Any specific instance of an information structure must have a physical existence in some information-storage medium. The information storage medium contains primitive information-storage devices for storing primitive information units.”

 

So, we ordinarily think of “the real number line” as the foundation of mathematics – the bedrock of the “ontology” for math.  What is the constructivist mapping from the real number line to the symbolism of math, as actually instantiated somewhere?

 

Wegner, p.4:

 

“In order to build up information structures it is necessary to introduce one or more primitive components, out of which more complex information structures are constructed.  Information structures may be constructed in terms of a single primitive unit of information called the binary digit or bit.  A bit is characterized by the fact that it can take on one of two states, which will be here represented by  0 and 1.”

 

“Information structures are constructed from bits by grouping ordered sequences into fields and by grouping fields into successively larger information units.  Specific fields of an information structure are usually interpreted as identifiable components of the information structure as a whole.  A specification of an information structure in terms of lower-level components is referred to as a structure definition.”

 

This is a basic and perhaps obvious description of the build-up of any computer language, through a succession of layers or levels, as “bits” are combined into “bytes” and bytes become an alphabet and – in the case of natural language -- an alphabet becomes words, and words become sentences or paragraphs or books.  This form is “absolutely linearly taxonomic”.

 

It seems appropriate to me to insist that mathematical symbolism be “constructed” in the same way, as we define what “A” means, and what “A + B” means, and what “=” means – all given direct mechanical/electronic interpretation at the machine level, defined in bits.  Anything else, I am suggesting, is floating in an imaginary cognitive/visual space in an individual human mind, in a way that cannot be objectively tested or independently confirmed.

 

Seen this way, all these so-called “primitive” and “indefinable” mathematical elements could indeed and in fact be given hard-core mechanistic and compositional definitions, in a form that ought to make engineers happy.  Stephen Wolfram’s “Mathematica” might be pointing in this direction.

 

At an abstract level, we can argue that “all concepts are constructed assemblies of distinctions” – in an exact analogy with the device/state bit/byte hierarchical assembly of any language in a machine.  Just as a “cut” in the real number line is the foundational distinction of all abstract concepts defined in dimensions, bits (0 or 1) are the fundamental distinction at the bottom of the machine representation.

 

All logic, sometimes defined today in terms of “unknowable or indefinable or irreducible primitives”, ought to be analyzed and decomposed to a deeper level – recognizing that in most or all cases, these objects are not truly “primitive”, but are in fact constructed constituent assemblies of sub-components.

 

Mathematics – and the theory of language – should be built up from this kind of bedrock – rather than presuming that somehow a term like ”A” has an irreducible meaning in some Boolean or algebraic _expression_.

 

And – as regards the question asked in a different context as to “whether it is useful to do this” – my guess is, it is essential to do this.  And doing it – I am guessing, opens an explosive and integral analytic power that is simply not available when so-called “primitive elements” are defined in highly composite (and hence lumpy and incommensurate and highly confusing) terms.

 

What we actually want, in our analysis of natural language, is a comprehensive model of semantic structure that is 100% linearly recursive from top to bottom – such that every level in a descending (taxonomic) stipulative cascade of abstractions is defined in the exact same terms, with zero loss of data in the decomposition cascade until it terminates at some acceptable lowest level (number of decimal places).

 

Define all the elements in this descending cascade with the simple precision outlined by Wegner, and there might be some hope of revolution and “the great simplification”.  My instinct is: enforce this simplicity on system definitions.

 

This, it seems to me, begins to point to the “pure form” – the immaculate ideal of “the neats” and the bane of “the scruffies”.  Get all the internal structures of all these interdependent cascading objects defined in the same immaculate mathematical/mechanical terms, in 100% linear form, and the thing will run at the speed of light.

 

http://en.wikipedia.org/wiki/Neats_vs._scruffies

 

To paraphrase Wegner, in the words of Keats

 

“Beauty is truth, truth beauty, -- that is all

Ye know on earth, and all ye need to know.”

 

J

 

Bruce Schuman

ORIGIN RESEARCH: http://originresearch.com

BRIDGE ACROSS CONSCIOUSNESS: http://bridgeacrossconsciousness.net

(805) 966-9515, PO Box 23346, Santa Barbara CA 93101

 

From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Rich Cooper
Sent: Wednesday, October 29, 2014 7:47 AM
To: '[ontolog-forum] '
Subject: Re: [ontolog-forum] CNL's and ConLangs

 

Math would have to be considered a language.  People write in it, read it, learn from it, and teach others with it.  So it fits all the socialization needs we have for communicating among ourselves. 

 

But regarding ontologies, math in itself is not much more than symbols plus operators composed to arbitrary nestings.  Math isn’t speakable like English or German, but that doesn’t seem to limit it from being a language.  I don’t see the grist for an ontology in math.  You raised a good point,

 

-Rich

 

Sincerely,

Rich Cooper

EnglishLogicKernel.com

Rich AT EnglishLogicKernel DOT com

9 4 9 \ 5 2 5 - 5 7 1 2

From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of David Whitten
Sent: Wednesday, October 29, 2014 7:26 AM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] CNL's and ConLangs

 

I was taught that the formal definition of language in discrete math is a set of strings that can be matched according to a pattern or procedure.

 

So any picture that can be represented (perhaps in SVG ?) as a string can be an instance in the set of strings of a language.

 

The real question in my mind, is whether it is useful to do this. It seems that we want pictures to be their own representation. And that begs the question how you will recognize sub-pictures.  Which is an entire branch of 

AI research, as I recall. 

 

David Whitten

713-870-3834

 

On Tue, Oct 28, 2014 at 8:06 PM, John Bottoms <john@xxxxxxxxxxxxxxxxxxxx> wrote:

On 10/28/2014 7:03 PM, Rich Cooper wrote:

John, you raised some interesting questions, but I can’t read the labeled arcs in your imagery, even after expanding it in Paint:

Rich,
This should be more readable. But, no, I am not a physicist so I can't come up with the labels beyond the caption on the image:

  "The Feynman diagram for the Coulomb interaction (electric force), along with the parts of the Feynman integral they correspond too. Every part of this is really nasty. For example, that "g" is actually 16 numbers."

An explanation of the diagram can be found at:

http://www.askamathematician.com/2010/10/q-what-are-feynman-diagrams-how-are-they-used-theoreticallypractically-and-are-there-alternativecompeting-diagrams-to-feynman%E2%80%99s/

  The diagram was meant to be an illustration of a "shorthand" physics symbol, similar to what we do in math. Perhaps I should have used something more universal such as the quadratic equation:

Now it becomes easier to discuss what is needed. One of the difficulties with this type of notation is that it is first introduced orally and then drawn on a blackboard and we intuit the use of the symbols. The professor says, "Let 'X' be the set of sales of rutabagas on each Thursday'". We know we need to create a symbol table entry for X. This quadratic equation needs a small symbol table in order to be useful. All this, we learn to do mentally.

If, and when we want to publish it we must use another form to translate the symbols to the typography of choice. Today, the preferred typography is MathML developed by the AAP and borrowed by the W3C.

So, in the math "domain" we work with this notation and a large community benefits from that use. Now, along come the ontologists and decide to squirrel it away in a data set. Should we discuss this with the mathematician SME's or do we, of our own expertise, already have a notion of how to catalog it? Are their social or cultural issues that need to be aired?

My main concern is that while we know how to markup equation, we have little understanding of the KR for math. We understand that the symbols need to be defined in a NL, but what else? Is an "info" field needed? Is a meta-definition required? Is this part of a language. Either way, how is it integrated into speech?

I am not asking to resolve the implementation questions just now. I am solely looking at the issue of whether these things we have been discussing, (CNL's) and representational shorthands, are languages, or should they be handled as special cases (labeled sets). My hope is that away, in some dusty tome, there is a treatise by Aristotle in which he explains how this is done.

-John

 

It would help answer your question if your identified the labels (I see a lot of blurs where text should be), and defined Feynman’s reference to each of those labels, then a paragraph about the Feynman diagram and what physicists use it for, perhaps we could begin to identify some elements of the ontology you propose for the imagery. 

 

 

But it’s an interesting idea; thanks,

-Rich

 

Sincerely,

Rich Cooper

EnglishLogicKernel.com

Rich AT EnglishLogicKernel DOT com

9 4 9 \ 5 2 5 - 5 7 1 2

From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John Bottoms
Sent: Tuesday, October 28, 2014 11:03 AM
To: ontolog-forum@xxxxxxxxxxxxxxxx
Subject: [ontolog-forum] CNL's and ConLangs

 

There have been a few discussions on www.reddit.com about "Constructed Languages". It surprised me that there are such graduate programs. There is also a reference to The Language Creation Society (www.conlang.org) Mostly, these studies apply to artificial natural languages such as Esperanto and Klingon.

http://www.reddit.com/r/linguistics/comments/2evjri/graduate_programs_for_constructed_languages/

Most of the Reddit discussions pertain to whether Constructed Languages are really languages. Some seem to believe that a language must have an evolved history and been in use by a community before it is meat for a linguistics discussion.

The linguistics community has no consensus on an appropriate criteria for acceptance as a language. However, for me, the overall discussion of Constructed Languages seems to touch on Controlled/Constrained Natural Languages. This is important, I believe, because we are in for an extended era of many CNL's as people partition core and technical vocabularies in various ways, trying to satisfy needs for particular disciplines and markets.

Chomsky defines a set of sets of languages that have formal grammars are a hierarchy.

Chomsky Formal Grammar Language Hierarchy

http://en.wikipedia.org/wiki/Chomsky_hierarchy

It seems to me that there should be a taxonomy that includes all languages and what I call "language shorthands" such as chemical, math, Feynman diagrams, etc. My question is whether ConLangs, shorthands and CNL's are entities of Chomsky's hierarchy of languages? He seems to say that there must be start and end symbols and these are not represented in mathematics notation. The difficulty with this is that in many shallow/deep constructions, the start and terminal symbols are understood according to some protocol. SGML allows <cr> as a terminal in some cases and  speech is terminated when someone stops talking, or it can be semantically terminated when someone says, "That's all I have to say."

Is there a more complete grammar in existance that includes additional forms of sentences? Should we define a super-set of all languages that is more inclusive such as might be found in semiotics? Finally, would we segregate the taxonomy and its elements in an ontology?

A Feynman Diagram

-John Bottoms
 FirstStar Systems
 Concord, MA USA

 

 

_________________________________________________________________

Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  

Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  

Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx

Shared Files: http://ontolog.cim3.net/file/

Community Wiki: http://ontolog.cim3.net/wiki/ 

To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J

 

_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
 

 

_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/ 
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J    (01)