Discussion:
My inspiration for sub atomic semantic compositionality (SASC)
(too old to reply)
Pete Olcott
2017-06-10 19:20:35 UTC
Permalink
Raw Message
<html>
<head>

<meta http-equiv="content-type" content="text/html; charset=utf-8">
</head>
<body bgcolor="#FFFFFF" text="#000000">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<p class="MsoNormal"><span style="font-family:&quot;Segoe UI
Symbol&quot;"><a class="moz-txt-link-freetext" href="https://en.wikipedia.org/wiki/History_of_type_theory#G.C3.B6del_1944">https://en.wikipedia.org/wiki/History_of_type_theory#G.C3.B6del_1944</a><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:&quot;Segoe UI
Symbol&quot;"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:&quot;Segoe UI
Symbol&quot;"><b>Kurt Gödel (1944)</b><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:&quot;Segoe UI
Symbol&quot;">By the theory of
simple types I mean the doctrine which says that the objects of
thought (or, in
another interpretation, the symbolic expressions) are divided
into types,
namely: individuals, properties of individuals, relations
between individuals,
properties of such relations, etc. (with a similar hierarchy for
extensions),
and that sentences of the form: " a has the property φ ", " b
bears the relation R to c ", etc. are meaningless, if a, b, c,
R, φ are
not of types fitting together.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:&quot;Segoe UI
Symbol&quot;"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:&quot;Segoe UI
Symbol&quot;">The above was
the inspiration for my theory of <b><span
style="background:yellow;mso-highlight:
yellow">sub atomic semantic compositionality</span></b>. I
reduced it further to simply relations between units-of-thought.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:&quot;Segoe UI
Symbol&quot;"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:&quot;Segoe UI
Symbol&quot;">The units-of-thought
are formalized as the nodes of a directed acyclic graph and the
relations
between them are formalized as its edges. A <b><span
style="background:yellow;
mso-highlight:yellow">unit-of-thought (DAG node)</span></b><b>
</b>and a <b><span
style="background:yellow;mso-highlight:yellow">relation
between units-of-thought
(DAG edge)</span></b> form the sub atomic particle smallest
possible constituent part of
semantic compositionality.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family:&quot;Segoe UI
Symbol&quot;"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family:&quot;Segoe UI
Symbol&quot;">I created a
whole branch of mathematics (Minimal Type Theory) to formalize
the details of this. I am currently
implementing this as software knowledge ontology capable of
processing semantic
logical entailment.<o:p></o:p></span></p>
<meta name="ProgId" content="Word.Document">
<meta name="Generator" content="Microsoft Word 10">
<meta name="Originator" content="Microsoft Word 10">
<link rel="File-List"
href="file:///C:%5CUsers%5CPETEOL%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml">
<!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:ApplyBreakingRules/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:UseFELayout/>
</w:Compatibility>
<w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel>
</w:WordDocument>
</xml><![endif]-->
<style>
<!--
/* Font Definitions */
@font-face
{font-family:SimSun;
panose-1:2 1 6 0 3 1 1 1 1 1;
mso-font-alt:宋体;
mso-font-charset:134;
mso-generic-font-family:auto;
mso-font-pitch:variable;
mso-font-signature:3 680460288 22 0 262145 0;}
@font-face
{font-family:"Segoe UI Symbol";
panose-1:2 11 5 2 4 2 4 2 2 3;
mso-font-charset:0;
mso-generic-font-family:swiss;
mso-font-pitch:variable;
mso-font-signature:-2147483165 302055407 262144 0 1 0;}
@font-face
{font-family:"\@SimSun";
panose-1:2 1 6 0 3 1 1 1 1 1;
mso-font-charset:134;
mso-generic-font-family:auto;
mso-font-pitch:variable;
mso-font-signature:3 680460288 22 0 262145 0;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{mso-style-parent:"";
margin:0in;
margin-bottom:.0001pt;
mso-pagination:widow-orphan;
font-size:12.0pt;
font-family:"Times New Roman";
mso-fareast-font-family:SimSun;}
@page Section1
{size:8.5in 11.0in;
margin:1.0in 1.25in 1.0in 1.25in;
mso-header-margin:.5in;
mso-footer-margin:.5in;
mso-paper-source:0;}
div.Section1
{page:Section1;}
-->
</style><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin:0in;
mso-para-margin-bottom:.0001pt;
mso-pagination:widow-orphan;
font-size:10.0pt;
font-family:"Times New Roman";}
</style>
<![endif]-->
<p><br>
</p>
<br>
</body>
</html>
Pete Olcott
2017-06-11 03:06:26 UTC
Permalink
Raw Message
Post by Pete Olcott
https://en.wikipedia.org/wiki/History_of_type_theory#G.C3.B6del_1944
Kurt Gödel (1944)
By the theory of
simple types I mean the doctrine which says that the objects of
thought (or, in
another interpretation, the symbolic expressions) are divided
into types,
namely: individuals, properties of individuals, relations
between individuals,
properties of such relations, etc. (with a similar hierarchy for
extensions),
and that sentences of the form: " a has the property φ ", " b
bears the relation R to c ", etc. are meaningless, if a, b, c,
R, φ are
not of types fitting together.
The above was
the inspiration for my theory of sub atomic semantic compositionality. I
reduced it further to simply relations between units-of-thought.
The units-of-thought
are formalized as the nodes of a directed acyclic graph and the
relations
between them are formalized as its edges. A unit-of-thought (DAG node)
and a relation
between units-of-thought
(DAG edge) form the sub atomic particle smallest
possible constituent part of
semantic compositionality.
I created a
whole branch of mathematics (Minimal Type Theory) to formalize
the details of this. I am currently
implementing this as software knowledge ontology capable of
processing semantic
logical entailment.
Gödel was too off-hand in his "definition" of simple types. He
enumerates "individuals, properties of individuals, relations
between individuals, properties of such relations" drops off
into "etc.
That is, he has I (individuals), P(I) properties of I, R(I1, I2)
relations between I (ignoring the possibility of relationship
among more then two I) and P(R). It is not clear what "etc."
includes. Perhaps R(P1, P2), perhaps P(P), perhaps R(P, I).
Which, if any, of these possibilities do you admit?
I will explain it using different terms. In Minimal type theory there are really only two most fundamental types of things:
(1) Relations
(2) Non-Relations

The whole hierarchy that KG referred to is not separately specified, and a property is merely a type of Relation.
--
(Γ ⊨ _FS A) ≡ (Γ ⊢ _FS A)
Kaz Kylheku
2017-06-11 04:50:37 UTC
Permalink
Raw Message
Post by Pete Olcott
I will explain it
That would be an amazing first, calling for champagne.
Peter Percival
2017-06-11 11:43:24 UTC
Permalink
Raw Message
Post by Pete Olcott
I will explain it using different terms. In Minimal type theory there
(1) Relations
(2) Non-Relations
I think this was your first (first posted to sci.logic, anyway) account
of what MTT types are, but you've also claimed that numbers and strings
are among MTT's types. When will we get the definitive account?

And if those are the fundamental types, you still need rules saying how
types in general are built up from those fundamental types.
Post by Pete Olcott
The whole hierarchy that KG referred to is not separately specified, and
a property is merely a type of Relation.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
Pete Olcott
2017-06-11 13:40:18 UTC
Permalink
Raw Message
<html>
<head>
<meta content="text/html; charset=utf-8" http-equiv="Content-Type">
</head>
<body bgcolor="#FFFFFF" text="#000000">
<div class="moz-cite-prefix">On 6/10/2017 5:46 PM, David Kleinecke
wrote:<br>
</div>
<blockquote
cite="mid:a524f1c1-8c1d-4f1c-a511-***@googlegroups.com"
type="cite">
<pre wrap="">On Saturday, June 10, 2017 at 12:20:44 PM UTC-7, Pete Olcott wrote:
</pre>
<blockquote type="cite">
<pre wrap=""><a class="moz-txt-link-freetext" href="https://en.wikipedia.org/wiki/History_of_type_theory#G.C3.B6del_1944">https://en.wikipedia.org/wiki/History_of_type_theory#G.C3.B6del_1944</a>

 

Kurt Gödel (1944)

By the theory of
simple types I mean the doctrine which says that the objects of
thought (or, in
another interpretation, the symbolic expressions) are divided
into types,
namely: individuals, properties of individuals, relations
between individuals,
properties of such relations, etc. (with a similar hierarchy for
extensions),
and that sentences of the form: " a has the property φ ", " b
bears the relation R to c ", etc. are meaningless, if a, b, c,
R, φ are
not of types fitting together.

 

The above was
the inspiration for my theory of sub atomic semantic compositionality. I
reduced it further to simply relations between units-of-thought.


 

The units-of-thought
are formalized as the nodes of a directed acyclic graph and the
relations
between them are formalized as its edges. A unit-of-thought (DAG node)
and a relation
between units-of-thought
(DAG edge) form the sub atomic particle smallest
possible constituent part of
semantic compositionality.

 

I created a
whole branch of mathematics (Minimal Type Theory) to formalize
the details of this. I am currently
implementing this as software knowledge ontology capable of
processing semantic
logical entailment.
</pre>
</blockquote>
<pre wrap="">
Gödel was too off-hand in his "definition" of simple types. He
enumerates "individuals, properties of individuals, relations
between individuals, properties of such relations" drops off
into "etc.

That is, he has I (individuals), P(I) properties of I, R(I1, I2)
relations between I (ignoring the possibility of relationship
among more then two I) and P(R). It is not clear what "etc."
includes. Perhaps R(P1, P2), perhaps P(P), perhaps R(P, I).

Which, if any, of these possibilities do you admit?
</pre>
</blockquote>
<br>
<p><br>
<font face="Segoe UI Symbol">
<meta http-equiv="Content-Type" content="text/html;
charset=utf-8">
<meta name="ProgId" content="Word.Document">
<meta name="Generator" content="Microsoft Word 10">
<meta name="Originator" content="Microsoft Word 10">
<link rel="File-List"
href="file:///C:%5CUsers%5CPETEOL%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml">
<!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:ApplyBreakingRules/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:UseFELayout/>
</w:Compatibility>
<w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel>
</w:WordDocument>
</xml><![endif]-->
<style>
<!--
/* Font Definitions */
@font-face
{font-family:SimSun;
panose-1:2 1 6 0 3 1 1 1 1 1;
mso-font-alt:宋体;
mso-font-charset:134;
mso-generic-font-family:auto;
mso-font-pitch:variable;
mso-font-signature:3 680460288 22 0 262145 0;}
@font-face
{font-family:"Segoe UI Symbol";
panose-1:2 11 5 2 4 2 4 2 2 3;
mso-font-charset:0;
mso-generic-font-family:swiss;
mso-font-pitch:variable;
mso-font-signature:-2147483165 302055407 262144 0 1 0;}
@font-face
{font-family:"\@SimSun";
panose-1:2 1 6 0 3 1 1 1 1 1;
mso-font-charset:134;
mso-generic-font-family:auto;
mso-font-pitch:variable;
mso-font-signature:3 680460288 22 0 262145 0;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{mso-style-parent:"";
margin:0in;
margin-bottom:.0001pt;
mso-pagination:widow-orphan;
font-size:12.0pt;
font-family:"Times New Roman";
mso-fareast-font-family:SimSun;}
@page Section1
{size:8.5in 11.0in;
margin:1.0in 1.25in 1.0in 1.25in;
mso-header-margin:.5in;
mso-footer-margin:.5in;
mso-paper-source:0;}
div.Section1
{page:Section1;}
-->
</style><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin:0in;
mso-para-margin-bottom:.0001pt;
mso-pagination:widow-orphan;
font-size:10.0pt;
font-family:"Times New Roman";}
</style>
<![endif]-->
<p class="MsoNormal"><b><span style="font-family:&quot;Segoe UI
Symbol&quot;;background:
yellow;mso-highlight:yellow">Now that I have analyzed this
again I will say it
a little differently.</span></b></p>
<font size="+1"><b>
Minimal Type Theory has only two fundamental types of
things:</b></font><font size="+1"><b><br>
</b></font>(1) Things that can have Relations to other things,
representing as directed acyclic graph nodes.<br>
(2) Relations to other things, representing as directed acyclic
graph edges.<br>
<br>
Although MTT has an inheritance hierarchy of the sub-types of
other types, any MTT predicate can express a relation between
anything else without distinguishing the order of these types. <br>
<br>
The relation between what would otherwise be an individual and
the relation between properties of relations is treated
uniformly in MTT as simply a relation between things. <br>
</font></p>
<p>When Minimal Type Theory is expressed in language so that people
can write MTT axioms or a computer can process logical entailment
deductions, MTT is expressed as finite string transformation rules
(for people) and relations between integer values (for computers).
<br>
</p>
<p>Because MTT decomposes semantic meaning into the smallest
possible constituent parts (sub atomic units of semantic
compositionality) MTT has unlimited expressiveness and
flexibility. <br>
</p>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<p><b><span
style="font-size:13.5pt;background:yellow;mso-highlight:yellow">MTT
is essentially the machine language of thought.</span></b><b><span
style="font-size:13.5pt"> </span></b><o:p></o:p></p>
<meta name="ProgId" content="Word.Document">
<meta name="Generator" content="Microsoft Word 10">
<meta name="Originator" content="Microsoft Word 10">
<link rel="File-List"
href="file:///C:%5CUsers%5CPETEOL%7E1%5CAppData%5CLocal%5CTemp%5Cmsohtml1%5C01%5Cclip_filelist.xml">
<!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:ApplyBreakingRules/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:UseFELayout/>
</w:Compatibility>
<w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel>
</w:WordDocument>
</xml><![endif]-->
<style>
<!--
/* Font Definitions */
@font-face
{font-family:SimSun;
panose-1:2 1 6 0 3 1 1 1 1 1;
mso-font-alt:宋体;
mso-font-charset:134;
mso-generic-font-family:auto;
mso-font-pitch:variable;
mso-font-signature:3 680460288 22 0 262145 0;}
@font-face
{font-family:"\@SimSun";
panose-1:2 1 6 0 3 1 1 1 1 1;
mso-font-charset:134;
mso-generic-font-family:auto;
mso-font-pitch:variable;
mso-font-signature:3 680460288 22 0 262145 0;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{mso-style-parent:"";
margin:0in;
margin-bottom:.0001pt;
mso-pagination:widow-orphan;
font-size:12.0pt;
font-family:"Times New Roman";
mso-fareast-font-family:SimSun;}
p
{mso-margin-top-alt:auto;
margin-right:0in;
mso-margin-bottom-alt:auto;
margin-left:0in;
mso-pagination:widow-orphan;
font-size:12.0pt;
font-family:"Times New Roman";
mso-fareast-font-family:SimSun;}
@page Section1
{size:8.5in 11.0in;
margin:1.0in 1.25in 1.0in 1.25in;
mso-header-margin:.5in;
mso-footer-margin:.5in;
mso-paper-source:0;}
div.Section1
{page:Section1;}
-->
</style><!--[if gte mso 10]>
<style>
/* Style Definitions */
table.MsoNormalTable
{mso-style-name:"Table Normal";
mso-tstyle-rowband-size:0;
mso-tstyle-colband-size:0;
mso-style-noshow:yes;
mso-style-parent:"";
mso-padding-alt:0in 5.4pt 0in 5.4pt;
mso-para-margin:0in;
mso-para-margin-bottom:.0001pt;
mso-pagination:widow-orphan;
font-size:10.0pt;
font-family:"Times New Roman";}
</style>
<![endif]-->-- <br>
<div class="moz-signature">
<p class="western" style="margin-bottom: 0in"><b><font
face="Arial, sans-serif"><font style="font-size: 12pt"
size="2">(Γ
</font><font style="font-size: 12pt" size="2">⊨ </font><sub><font
style="font-size: 8pt" size="2">FS</font></sub><font
style="font-size: 12pt" size="2">
A) ≡ (</font><font style="font-size: 12pt" size="2">Γ </font><font
style="font-size: 12pt" size="2">⊢
</font><sub><font style="font-size: 8pt" size="2">FS</font></sub><font
style="font-size: 12pt" size="2">
A)</font></font></b></p>
<p class="western" style="margin-bottom: 0in"><br>
</p>
</div>
</body>
</html>
Pete Olcott
2017-06-12 13:24:38 UTC
Permalink
Raw Message
Post by Pete Olcott
On 6/10/2017 5:46 PM, David Kleinecke
https://en.wikipedia.org/wiki/History_of_type_theory#G.C3.B6del_1944
Kurt Gödel (1944)
By the theory of
simple types I mean the doctrine which says that the objects of
thought (or, in
another interpretation, the symbolic expressions) are divided
into types,
namely: individuals, properties of individuals, relations
between individuals,
properties of such relations, etc. (with a similar hierarchy for
extensions),
and that sentences of the form: " a has the property φ ", " b
bears the relation R to c ", etc. are meaningless, if a, b, c,
R, φ are
not of types fitting together.
The above was
the inspiration for my theory of sub atomic semantic compositionality. I
reduced it further to simply relations between units-of-thought.
The units-of-thought
are formalized as the nodes of a directed acyclic graph and the
relations
between them are formalized as its edges. A unit-of-thought (DAG node)
and a relation
between units-of-thought
(DAG edge) form the sub atomic particle smallest
possible constituent part of
semantic compositionality.
I created a
whole branch of mathematics (Minimal Type Theory) to formalize
the details of this. I am currently
implementing this as software knowledge ontology capable of
processing semantic
logical entailment.
Gödel was too off-hand in his "definition" of simple types. He
enumerates "individuals, properties of individuals, relations
between individuals, properties of such relations" drops off
into "etc.
That is, he has I (individuals), P(I) properties of I, R(I1, I2)
relations between I (ignoring the possibility of relationship
among more then two I) and P(R). It is not clear what "etc."
includes. Perhaps R(P1, P2), perhaps P(P), perhaps R(P, I).
Which, if any, of these possibilities do you admit?
Now that I have analyzed this
again I will say it
a little differently.
Minimal Type Theory has only two fundamental types of
(1) Things that can have Relations to other things,
representing as directed acyclic graph nodes.
(2) Relations to other things, representing as directed acyclic
graph edges.
Although MTT has an inheritance hierarchy of the sub-types of
other types, any MTT predicate can express a relation between
anything else without distinguishing the order of these types.
The relation between what would otherwise be an individual and
the relation between properties of relations is treated
uniformly in MTT as simply a relation between things.
When Minimal Type Theory is expressed in language so that people
can write MTT axioms or a computer can process logical entailment
deductions, MTT is expressed as finite string transformation rules
(for people) and relations between integer values (for computers).
Because MTT decomposes semantic meaning into the smallest
possible constituent parts (sub atomic units of semantic
compositionality) MTT has unlimited expressiveness and
flexibility.
MTT
is essentially the machine language of thought.
Hence MTT "is" a set of ordered pairs.
MTT is not a set of ordered pairs. Exactly what MTT is will be more clear when I provide its YACC BNF grammar.
But you are not clear about "has only two fundamental
types of things". What you must mean is that the objects
of MTT are members of a set of ordered pair. Does
"fundamental" mean there are other objects - if so how
constructed?
There are things (of the coherent axiomatic set of all things that excludes sets from being members of themselves) that are not relations to other things, and there are things that are relations to other things.
A DAG is a set o ordered pairs with a an acyclic rule
imposed on it. You have yet to justify that acyclic
assumption.
http://liarparadox.org/Provability_with_Minimal_Type_Theory.pdf
If a digraph contains cycles then the evaluation of a syntactically WFF never completes. The evaluation get stuck in an infinite loop, thus is semantically incorrect.
--
(Γ ⊨ _FS A) ≡ (Γ ⊢ _FS A)
Peter Percival
2017-06-12 14:03:16 UTC
Permalink
Raw Message
[...] Exactly what MTT is will be more
clear when I provide its YACC BNF grammar.
Don't you need to decide what it is before you write that grammar?
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan
Loading...