Soeterbeeck programma 2006 Het Onbegrensde Intellect

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Soeterbeeck programma 2006Het Onbegrensde
Intellect

• Astrobiologie
• Lingua Cosmica
• Alexander Ollongren

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Astrobiologie

• Leven in het universum
• Oorsprong
• Evolutie
• Waar?
• Toekomst

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Veronderstellingen I

• existentie in de Melkweg van
• aardse exo-planeten waarop
• intelligente nieuwsgierige samenlevingen
• technologisch ontwikkelingsniveau gtgt de onze

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Veronderstellingen II

• Niet universeel
• - grammaticas van talen
• Wel universeel
• - mathematica
• - logica

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Communicatie met ETI

• ?
• gemiddelde afstand
• maximale snelheid info-overdracht
• vorm info
• inhoud info

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Pioneer plaquette 1970-72
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Karakteristieken van natuurlijke talen (op aarde)

• In een natuurlijke taal
• syntaxis en semantiek
• gesproken / geschreven vorm
• mogelijkheid van auto-interpretatie

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Karakteristieken van Lingua Cosmica

• Freudenthal (1960) symbolisch systeem
• het uitdrukken van wiskundige relaties
• voor aliens interpreteerbaar
• traditie Lingua Characteristica
• geen auto-interpretatie
• waarheid via true en false

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Karakteristieken van Lingua Cosmica

• Ollongren (2006) multi level linguistisch
  systeem
• basisniveau tekst
• toelichting op logische relaties
• voor aliens interpreteerbaar
• traditie Lingua Logica/Systematica
• inclusief auto-interpretatie
• waarheid via verificatie

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LINGUA COSMICA (LINCOS)a Multilevel
SystemLowest level Text in Natural
LanguageSecond level Annotations in a Formal
SystemLINCOS, Based on Logic, explains the
logic contents of texts (sentences) written in
ordinary language

• Sentences are split into
• constants, definitions
• conclusions in the form of facts

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MARKERINGSSYMBOLEN

• CONSTANT A Prop.
• In American Standard Code Information
• Interchange (ASCII) met markers
• spatie (20 0010 0000)
• punt (2E 0010 1110)
• 43 4F 4E 53 54 41 4E 54 20 41 20 3A 20
• 50 72 0F 70 2E

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Bits en Bytes

• 0100 0011 0100 1111 0100 1110 0101 0011
• 0101 0100 0100 0001 0100 1110 0101 0100
• 0010 0000 0100 0001 0010 0000 0011 1100
• 0010 0000 0101 0000 0111 0010 0000 1111
• 0111 0000 0010 1110
• 43 4F 4E 53 54 41 4E 54 20 41 20 3A 20
• 50 72 0F 70 2E

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Tree Beard (J.R.R. Tolkien The Lord of the
Rings, Part II)
Hm, but you are hasty folk, I see, said
Treebeard. I a not going to tell you my name. For
one thing it would take a long while my name is
growing all the time, my name is like a story.
Real names tell you the story of the things they
belong to in my language, in the Old Entish. It
is a lovely language, but it takes a very long
time to say anything in it, because we do not say
anything in it, unless it is worth taking a long
time to say, and to listen to.
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Introductie gehele positieve getallen

• CONSTANTS , , , , , ,
• , , , ,
  Etc. Pos.
• DEFINE 0 .
• DEFINE 1 . DEFINE 2 .
• DEFINE 3 . DEFINE 4 .
• DEFINE 5 . DEFINE 6 .
• DEFINE 7 . DEFINE 8 .
• DEFINE 9 . DEFINE 10 .
• DEFINE 11 . Etc.

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Priemgetallen

• Een (onvolledige) lijst van ondeelbare getallen
• DEFINE Prime 1, 2, 3, 5, 7, 11, 13, 17, 19, 23,
  29, 31, 37, 41, 43, 47, Etc.

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Constanten en Variabelen

• CONSTANTS 0, 1, 2, 3, Etc. Pos.
• CONSTANTS , x Pos ? Pos ? Pos.
• ( 2 argumenten, resultaat in Pos)
• Voorbeelden 4 21 Pos. (optelling)
• x 4 21 Pos. (product)
• Variabelen a en b expliciet resp. impliciet
• VARIABLES a, b Pos.
• b Pos( 4 b) Pos ? Pos.
• a, b Pos( a b) Pos ? Pos ? Pos.

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Proposities

• VARIABLES A, B Prop.
• CONSTANT Prop ? Prop. (negatie)
• Conjunctie en disjunctie (en resp. of)
• CONSTANTS ?, V Prop ? Prop ? Prop.
• Voorbeelden
• A Prop.
• (? A) Prop ? Prop.
• (V A B) Prop.

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Proposities, vervolg

• x Prop(? x) Prop ? Prop ? Prop.
• x Prop(? x B) Prop ? Prop.
• (x Prop(? x B)). toepassen op A (applicatie)
  (x Prop(? x B))A. reduceert tot
• (? A B) Prop.

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Modus Ponens

• CONSTANTS A, B Prop.
• zodat (A /\ (A ? B)) ? B Prop.
• FACT MP (A /\ (A ? B)) ? B.

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Example

• all men are human, all women are humanSusan is a
  woman so Susan is human
• John is a man so John is human
• CONSTANTS Susan, John Prop.CONSTANTS
  is-woman, is-man Prop ? Prop.
• DEFINE is-human Prop
• m (ALL x Prop)(is-man x) ? (is-human x)
• w (ALL y Prop)(is-woman y) ? (is-human y).
• FACT (w Susan) (is-woman Susan) ?
• (is-human Susan).
• FACT (m John) (is-man John) ? (is-human John).
• Opm. Susan is een zgn. singulier vlgs.
  Aristoteles

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Aristotelian syllogism, universal case (all)

• Sentences with a single subject S and a single
• predicate P, all S is P (no singular). Example
• if all humans are mortal, if all Greeks are
  humans,
• then all Greeks are mortal
• CONSTANTS is-human, is-Greek, is-mortal
• Prop ? Prop.
• HYPOTHESES 1,2
• (ALL x Prop)(is-human x) ? (is-mortal x),
• (ALL x Prop)(is-Greek x) ? (is-human x).
• FACT 3 (ALL x Prop)(is-Greek x) ? (is-mortal
  x).

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Aristotelian syllogisms (general)

• subject S is predicated by P
• all S is P (ALL x Prop) (is-S x) ? (is-P .
  . .)
• some S is P (EXISTS x Prop) (is-S x) ?
  (is-P . . .)
• no S is P (NOT (EXISTS x Prop) (is-S x) ?
• (is-P . . .))
• not every S is P (NOT (ALL x Prop) (is-S x)
  ?
• (is-P . . .))

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Uit Alice in Wonderland

• You are sad, the knight said in an anxious
  tone let me sing you a song to comfort you.
• Is it very long? Alice asked for she had heard
  a good deal of poetry that day.
• Its long , said the knight, but its very,
  very beautiful. Everybody that hears me sing it
  either it brings the tears into their eyes, or
  else
• Or else what? said Alice, for the knight had
  made a sudden pause.
• Or else it doesnt, you know. The name of the
  song is called Haddocks Eyes.
• Oh, thats the name of the song, is it? Alice
  said, trying to feel interested.

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• No, you dont understand, the Knight said,
  looking a little vexed.
• Thats what the name is called. The name really
  is The Aged Aged Man.
• Then I ought to have said thats what the song
  is called? Alice corrected herself.
• No, you oughtnt thats quite another thing!
  The song is called Ways and means but that is
  only what its called, you know!
• Well, what is the song, then? said Alice, who
  was by this time completely bewildered.
• I was coming to that, the Knight said. The
  song really is A-sitting on A Gate and the
  tunes my own invention.

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Logic structure of the story

• Knights song
• A-sitting on A Gate
• songs name call name of song
• The Aged Aged Man Ways and means
• call name of songs name
• Haddocks Eyes

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Formal logic structure of the story

• Knights song
• DEFINE Knights song
• A-sitting on A Gate
• DEFINE songs name DEFINE call name of
  song
• The Aged Aged Man Ways and means
• DEFINE call name of songs name
• Haddocks Eyes

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Logic of the story in LINCOS

• DEFINE Knights-song songs-name,
  call-name-of-song Prop Prop A-sitting On
  A Gate ?  (DEFINE songs-name
  call-name-of-songs-name Prop The Aged
  Aged Man ? (DEFINE call-name-of-songs-
  name Prop Haddocks Eyes) ) ?
  (DEFINE call-name-of-song Prop Ways and
  Means) ?
• (Knights-song songs-name call-name-of-song).

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Mensenrechten Preambule

• Whereas recognition of the inherent dignity and
  of the equal and inalienable rights of all
  members of the human family is the foundation of
  freedom, justice and peace in the world,
• Whereas it is essential, if man is not to be
  compelled to have recourse, as a last resort, to
  rebellion against tyranny and oppression, that
  human rights should be protected by the rule of
  law,
• Whereas it is essential to promote the
  development of friendly relations between
  nations,

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Universal Declaration of Human Rights (UN 1948)
30 articles

• Article 1.
• All human beings are born free and equal in
  dignity and rights. They are endowed with reason
  and conscience and should act towards one another
  in a spirit of brotherhood.

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PIONEER PLAQUETTE

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• EINDE

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