Mathematical Mapping Theory of Truth

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Mathematical Mapping Theory of Truth
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
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
 Arising_uk
 Posts: 10664
 Joined: Wed Oct 17, 2007 2:31 am
Re: Mathematical Mapping Theory of Truth
Is this the same or trying to do the same as Wittgenstein's general propositional variable?

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 Joined: Sat Oct 18, 2014 2:55 pm
Re: Mathematical Mapping Theory of Truth
I am just impressed that you know whatever you said above exists.Arising_uk wrote:Is this the same or trying to do the same as Wittgenstein's general propositional variable?

 Posts: 6
 Joined: Mon Jul 25, 2016 6:55 pm
Re: Mathematical Mapping Theory of Truth
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.Arising_uk wrote:Is this the same or trying to do the same as Wittgenstein's general propositional variable?
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.
Re: Mathematical Mapping Theory of Truth
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??
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??

 Posts: 6
 Joined: Mon Jul 25, 2016 6:55 pm
Re: Mathematical Mapping Theory of Truth
This is a key aspect of the mathematics of the meaning of words that I have been working on for two decades.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??
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.
 Arising_uk
 Posts: 10664
 Joined: Wed Oct 17, 2007 2:31 am
Re: Mathematical Mapping Theory of Truth
You're assuming intelligence is based upon language?

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 Joined: Mon Jul 25, 2016 6:55 pm
Re: Mathematical Mapping Theory of Truth
I am assuming nothing.Arising_uk wrote:You're assuming intelligence is based upon language?
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.
 Arising_uk
 Posts: 10664
 Joined: Wed Oct 17, 2007 2:31 am
Re: Mathematical Mapping Theory of Truth
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. ...
But you are assuming the base representation has to be semantical when building a strong AI?I am comprehending that conceptual knowledge necessarily(modal logic) cannot exist unless it is represented. ...
But if you build it right couldn't a strong AI just read?Building a wooden chair is a little tricky (logically impossible) if one has no wood.

 Posts: 6
 Joined: Mon Jul 25, 2016 6:55 pm
Re: Mathematical Mapping Theory of Truth
Strong AI absolutely requires some fundamental comprehension of language before it can begin to read.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. ...But you are assuming the base representation has to be semantical when building a strong AI?I am comprehending that conceptual knowledge necessarily(modal logic) cannot exist unless it is represented. ...But if you build it right couldn't a strong AI just read?Building a wooden chair is a little tricky (logically impossible) if one has no wood.
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.
 Arising_uk
 Posts: 10664
 Joined: Wed Oct 17, 2007 2:31 am
Re: Mathematical Mapping Theory of Truth
Why do you think a fundamental comprehension of language involves actual having a comprehension of language? Why is it not a byproduct of some other patternlearning process.PeteOlcott wrote:Strong AI absolutely requires some fundamental comprehension of language before it can begin to read. ...
I agree, but why do you think meaning lies in words?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.
Maybe we're just building the wrong computers?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. ...
If you are building an expert system I'd maybe agree but strong A.I.?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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