Mathematical Mapping Theory of Truth

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PeteOlcott
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Mathematical Mapping Theory of Truth

Post by PeteOlcott » Mon Jul 25, 2016 6:58 pm

The one directional mathematical mapping from representations of actuality (within language or memories of physical sensations) to actuality itself is TRUTH Copyright 1997 by Pete Olcott.

In laymen’s terms the curly braces indicate a term that is further defined elsewhere. When this term is on the left side of a specified axiom this axiom is defining one aspect of the meaning of this term.

This is very similar to the way that an ordinary dictionary works. We have words (terms) and their defined meanings (meaning postulates). Unlike a dictionary these meaning postulates build up a single unique meaning for a term. They do not specify different shades of meaning for a word.

The most significant key distinction between an (information science) knowledge ontology and a dictionary is that the latter is a mathematical formalization of the meanings of natural language words such that a machine can achieve understanding of these words fully equivalent to human comprehension.

(Technically the curly braces indicate a specific node in an acyclic directed graph inheritance hierarchy knowledge ontology such as the CYC project. This node is the root of the connected meaning postulates for the specified concept.)

A key distinction that we have been making is that a {DeclarativeSentence} can be incoherent, and a {Proposition} cannot be incoherent. We can determine that a {DeclarativeSentence} is incoherent because it can not be correctly mathematically mapped to a {Proposition}.

Translate {DeclarativeSentence} into {Proposition.Assertion} and {Proposition.BooleanValue}.

Axioms (meaning postulates) related to Propositions
---------------------------------------------------
(1) {BooleanValue} {elementOfSet} {true, false}.
(2) {Thing} Single element of the {UniversalSet}.
(3) {AbstractRepresentation} The encoding of certain aspects of a {Thing} using language.
(4) {Truth} The set of Propositions with a {BooleanValue} of {true}.

// Converting a {DeclarativeSentence} presupposition into an axiom
(5) {DeclarativeSentence} {claimsToBe} {Proposition}.
typeOf( thisThing, {TypeOfThing} )
{DeclarativeSentence} assert( typeOf( thisThing, {Proposition} )

// Converting a {DeclarativeSentence} presupposition into an axiom
(6) {DeclarativeSentence} {claimsToHave} {Proposition.BooleanValue.true}.
hasProperty( thisThing, Property)
{DeclarativeSentence} assert( hasProperty( thisThing, {Proposition.BooleanValue.true} ) )

(7) {Proposition} {hasProperty} {Assertion}.
(8) {Proposition} {hasProperty} {BooleanValue}.
(9) {Proposition} Asserted mathematical mapping from an {AbstractRepresentation} to {Thing}.

The notion of {grounded} in Saul Kripke's famous paper is formalized by the above specifications, leaving everything else as {ungrounded}.

http://www.jstor.org/stable/2024634?seq ... b_contents

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Arising_uk
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Re: Mathematical Mapping Theory of Truth

Post by Arising_uk » Mon Jul 25, 2016 11:20 pm

Is this the same or trying to do the same as Wittgenstein's general propositional variable?

sthitapragya
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Re: Mathematical Mapping Theory of Truth

Post by sthitapragya » Tue Jul 26, 2016 1:07 am

Arising_uk wrote:Is this the same or trying to do the same as Wittgenstein's general propositional variable?
I am just impressed that you know whatever you said above exists.

PeteOlcott
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Re: Mathematical Mapping Theory of Truth

Post by PeteOlcott » Tue Jul 26, 2016 4:02 am

Arising_uk wrote:Is this the same or trying to do the same as Wittgenstein's general propositional variable?
I have no idea. Almost all of my knowledge of these things comes from many years of essentially mathematically interpolating on the best answer. I began this in 1986. I have done very little reading. One key book Formal Semantics An Introduction by Ronnie Cann that elaborated the details of Montague Semantics was enormously helpful.

This quote is just about the only other thing that I found very helpful:
History of type theory From Wikipedia, the free encyclopedia
Kurt Gödel in his 1944 Russell's mathematical logic gave the following definition of the "theory of simple types" in a footnote:

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.

Once I figured that the essential structure of the set of all conceptual knowledge was a single acyclic directed graph organized as an inheritance hierarchy most everything else began to fit into place. The original 1997 version of the Mathematical Mapping Theory of Truth was the key missing piece.

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A_Seagull
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Re: Mathematical Mapping Theory of Truth

Post by A_Seagull » Thu Jul 28, 2016 9:50 am

Does this have anything to do with anything??

Does it relate to mathematics?, to the real world? To some other abstract system?? If so how and to what purpose?

What do you mean by 'truth' in your treatise??

PeteOlcott
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Re: Mathematical Mapping Theory of Truth

Post by PeteOlcott » Thu Jul 28, 2016 2:09 pm

A_Seagull wrote:Does this have anything to do with anything??

Does it relate to mathematics?, to the real world? To some other abstract system?? If so how and to what purpose?

What do you mean by 'truth' in your treatise??
This is a key aspect of the mathematics of the meaning of words that I have been working on for two decades.
It creates a the precise road map required to complete the Cyc Project: http://www.cyc.com/thing/
The Cyc project is the only AI project that will have success in creating a fully operational human mind,
and thus creating strong AI.

The 1997 Theory provides the fundamental basis for mathematically formalizing the concept of truth.
It was on this basis that I recently formalized the error of the Liar Paradox showing that it was never
actually paradoxical at all it was only erroneous.

I have also applied this same proof to the English Words form of the Incompleteness Theorem:
This sentence can not be proven true.

I have formalized the steps to transform the above sentence into the following sentence:
This sentence is not true.

So basically the above words will unravel key theorems at the foundation of mathematics
and computer science showing them to simply be incorrect.

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Arising_uk
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Re: Mathematical Mapping Theory of Truth

Post by Arising_uk » Thu Jul 28, 2016 5:30 pm

You're assuming intelligence is based upon language?

PeteOlcott
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Re: Mathematical Mapping Theory of Truth

Post by PeteOlcott » Thu Jul 28, 2016 6:24 pm

Arising_uk wrote:You're assuming intelligence is based upon language?
I am assuming nothing.

I am comprehending that conceptual knowledge necessarily(modal logic) cannot exist unless it is represented.

Building a wooden chair is a little tricky (logically impossible) if one has no wood.

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Arising_uk
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Re: Mathematical Mapping Theory of Truth

Post by Arising_uk » Thu Jul 28, 2016 7:29 pm

PeteOlcott wrote:I am assuming nothing. ...
The Cyc project is the only AI project that will have success in creating a fully operational human mind,
and thus creating strong AI. ...
?
I am comprehending that conceptual knowledge necessarily(modal logic) cannot exist unless it is represented. ...
But you are assuming the base representation has to be semantical when building a strong AI?
Building a wooden chair is a little tricky (logically impossible) if one has no wood.
But if you build it right couldn't a strong AI just read?

PeteOlcott
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Re: Mathematical Mapping Theory of Truth

Post by PeteOlcott » Thu Jul 28, 2016 9:36 pm

Arising_uk wrote:
PeteOlcott wrote:I am assuming nothing. ...
The Cyc project is the only AI project that will have success in creating a fully operational human mind,
and thus creating strong AI. ...
?
I am comprehending that conceptual knowledge necessarily(modal logic) cannot exist unless it is represented. ...
But you are assuming the base representation has to be semantical when building a strong AI?
Building a wooden chair is a little tricky (logically impossible) if one has no wood.
But if you build it right couldn't a strong AI just read?
Strong AI absolutely requires some fundamental comprehension of language before it can begin to read.
People are accustomed to simply looking up a work in a dictionary to find its meaning, totally
forgetting that every word is only defined in terms of other words.

A computer has not the slightest inkling of what even the word "the" means until after
someone totally explains every infinitesimally minute detail explicitly to it.

The only one that can possibly succeed at creating strong AI is Doug Lenat's Cyc project.
http://www.cyc.com/thing/
This requires building a comprehensive knowledge ontology.

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Arising_uk
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Re: Mathematical Mapping Theory of Truth

Post by Arising_uk » Fri Jul 29, 2016 12:46 am

PeteOlcott wrote:Strong AI absolutely requires some fundamental comprehension of language before it can begin to read. ...
Why do you think a fundamental comprehension of language involves actual having a comprehension of language? Why is it not a by-product of some other pattern-learning process.
People are accustomed to simply looking up a work in a dictionary to find its meaning, totally
forgetting that every word is only defined in terms of other words.
I agree, but why do you think meaning lies in words?
A computer has not the slightest inkling of what even the word "the" means until after
someone totally explains every infinitesimally minute detail explicitly to it. ...
Maybe we're just building the wrong computers?
The only one that can possibly succeed at creating strong AI is Doug Lenat's Cyc project.
http://www.cyc.com/thing/
This requires building a comprehensive knowledge ontology.
If you are building an expert system I'd maybe agree but strong A.I.?

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