Semantic Network Programming

1
Semantic Network Programming

• version 2.2, 12th of may 2008
• Pierre Lévy, CRC, FRSC
• Dir. Collective Intelligence Lab.University of
  Ottawa

2
SEMANTIC SPACE

• References- www.ieml.org/starparser for the
  IEML syntax and parser - www.ieml.org/spip.php?ru
  brique3langen for Biezunski and Newcombs IEML
  binary

3
IEML REMARKABLE PRIMITIVE CATEGORIES
I Complete set. Information.
Null set.No semantics. Unfit for tagging.
Computation tool only
000000
111111
FFullness
EEmptiness.
100000
011111
OBipolarity. Process. Verb.
MTernarity. Representation. Noun.
011000
000111
SSign. Signifier.
BBeing.Interpreter.
TThing. Referent.
UVirtualization
AActualization
010000
001000
000100
000010
000001
4
IEML Layers
source
translator
destination
Phr. IEML
Phr. IEML
Phr. IEML
Semes 6162Semes categories 21458
6
I_
Idea
Idea
Idea
Phrases 654Phrases categories 2486
5
I,
Relation
Relation
Relation
Ideas 618Ideas categories 2162
4
I
Event
Event
Event
Relations 69Relations categories 254
3
I-
Primitive
Primitive
Primitive
Events 63Events categories 218
2
I.
1
Primitives 6 E U A S B
T Primitive categories 26 64
I
5
IEML Binary Representation
Definition of a semantic character Six digits
unsigned binary integer. Representation A
semantic Character is the binary representation
of a primitive category (a set of IEML
primitives). Each digit represents the
non-occurrence (0) or the occurence (1) of one of
the six IEML primitives. There are 64 (26)
different characters. Null character If all six
bits of a character 0, the character is
null. The null character does not represent the
occurence of any primitive, does not give any
information and has no representation in Star. It
is a computational tool only. An emptiness
category is made of emptiness (100000)
characters, a null category is made of null
(000000) characters.
Semantic Character
6
Logical operations on categories

• Thank to its generative structure, any IEML
  category is composed (recursively) of IEML
  primitive categories.
• Therefore, any IEML category can be represented
  by an array of semantic characters
• 1 (3layer n-1) for layer 1 (primitive
  categories),
• 3 (3layer n-1) for layer 2 (event categories),
• 9 (3layer n-1) for layer 3 (relation categories)
• 27 (3layer n-1) for layer 4 (idea categories)
• 81 (3layer n-1) for layer 5 (phrase categories)
• 243 (3layer n-1) for layer 6 (seme category)
• AND (intersection)
• 00 0
• 01 0
• 11 1

• OR (union)
• 00 0
• 01 1
• 11 1

• XOR (symmetric difference)
• 00 0
• 01 1
• 11 0

• NON Inversion
• 0 1
• 1 0

• Logical operations on IEML categories can be
  performed as operations on their characters.
• Example 010101
• 100100
• ----------
• 110101

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Semantic Space
Definition of a semantic node Sextuple set of 1
to 6 IEML categories One category by
dimension. A semantic node represents the IEML
coordinate of a position in semantic
space Functional role of a semantic
node Variable (operand or result) of semantic
transformations. Semantic space Definition set
of semantic nodes. The semantic space has 6
dimensions (one by IEML layer) The semantic
space has 22184 nodes.
Semantic Node (364 semantic characters)
semantic space dimensions categories Binary
representation dimension 1 primitive category 1
semantic character array dimension 2 event
category 3 semantic characters array dimension
3 relation category 9 semantic characters
array dimension 4 idea category 27 semantic
characters array dimension 5 phrase category 81
semantic characters array dimension 6 seme
category 243 semantic characters array
8
PRIMITIVE AND COMPOSED LOGICAL TRANSFORMATIONS

• ON SEMANTIC NODES (COORDINATES OF POSITIONS IN
  SEMANTIC SPACE)

9
Primitive Logical Transformation (PLT)

• Definition of a PLT
• Consists of a logical operation on a semantic
  character located in a semantic node.
• Properties of a primitive logical transformation
• Has a semantic node as operand and a semantic
  node as result
• Preserves 363 invariant characters (on 364 in a
  node) between the operand and the result.
• A primitive logical function (PL) is a triple
• Logical Operator (OR, AND, XOR, NOT) one among
  4
• Focus (character address in the node operand)
  one among 364
• category dimension
• category role location in the array of
  characters (or generative tree) of the category
• Parameter (second operand for OR, AND, XOR
  logical operations) one among 64 characters
• There is no parameter needed for NON (bit
  inversion)

operand node
result node
Example of primitive logical transformation FUNCTI
ONOperator ORFocus dimension 1, unique
characterParameter 000111
- 011000 -... -... -... -... -...
- 011111 -... -... -... -... -...
000111on dimension 1
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Composed Logical Transformations (CLT)

• A composed logical transformation is a succession
  of primitive logical transformations taking in
  input the result of the previous one.
• For example...
• compositions of Tfipj and Tfipk are necessary
  to perform a substraction on an focused
  character of a semantic node
• compositions of PLTs having same logical
  operation can perform logical operations on
  categories or on nodes, since categories and
  nodes are arrays of characters.
• a substitution (replace character on focus i by
  character j) is the composition of Tfi000000 and
  Tfipj
• compositions of character substitutions can
  perform role players substitutions, or dimensions
  substitutions.
• composition of several role player substitutions
  can perform a role inversion (like inverse
  role and destination of a flow category)
• composition of dimensions substitutions are
  necessary to perform a dimension extraction
  (replace all dimensions by null categories,
  except one chosen dimension) as on the example
  next slide.
• Compositions of PLT (CLT) are still logical
  transformations composable transformations on
  semantic nodes.
• Any composed logical transformation can be broken
  down to primitive logical transformations.

11
Example of dimension extraction by composition
of replace dimension transformations
000000 FUS. 000000... 000000... 000000... 000
000...
I FUS. M!!- S!!! O!!!!, F!!!!!
_
000000 FUS. M!!.- S!!! O!!!!, F!!!
!!_
000000 FUS. 000000... S!!! O!!!!, F!!
!!!_
000000 FUS. 000000... 000000... O!!!!, F!
!!!!_
000000 FUS. 000000... 000000... 000000... F!
!!!!_
replace dim.1 by null category
replace dim.3 by null category
replace dim.4 by null category
replace dim.5 by null category
replace dim.6 by null category
dimension extraction semantic transformation
performing composed replace dimension
transformations
000000 FUS. 000000... 000000... 000000... 000
000...
I FUS. M!!- S!!! O!!!!, F!!!!!
_
Extract dimension 2 means replace all
dimensions by corresponding null categories,
except dimension 2
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SEMANTIC OPERATIONS AND SEMANTIC FUNCTIONS

• Complex composed logical operations on semantic
  nodes

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Semantic Operation

• A semantic operation is a set of composed logical
  transformations involving - the same operand
  node - the same operator,- but a variety of
  focuses or (exclusive or) a variety of
  parameters.- one or several results.
• A semantic operation produces a semantic
  differentiation a set of transformations
  having... - same operand - similar CL
  invariance of operator and focus (or parameter)-
  one or several results
• The rule of a semantic operation is called a
  semantic function (S)

SO Example 1
000000 FUS. 000000... 000000... 000000... 000
000...
I 000000... 000000... 000000... 000000... 0000
00...
000000 000000... M!!- 000000... 000000... 00000
0...
1
2
3
I FUS. M!!- S!!! O!!!!, F!!!!!
_
4
SOD
000000 000000... 000000... S!!! 000000... 0000
00...
The example has focus variation on the composed
transformation dimension extraction. The
operation of the example is an actual performance
of the semantic function sort categories by
their upper layer, or in short sort by
dimension
operand
5
6
000000 000000... 000000... 000000... O!!!!, 000
000...
000000 000000... 000000... 000000... 000000... F!
!!!!_
Semantic function example 1 Operator SOD (sort
by dimension) Focus dimensions 1, 2, 3, 4, 5,
6 Parameter none
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Example of logical analysis SO

• The previous example had focus variation, this
  example has parameter variation.
• In a logical analysis (LAN) SO, the focused
  character is partitioned in such a way that -
  the intersection of resulting characters 000000
  - the union of resulting characters the
  focused character.
• The parameter of a LAN is made of the set of the
  resulting characters.
• If the focused character is different from the
  union of the parameter set, the operation is
  impossible

Semantic Function example 2 Operator LAN
(logical analysis) Focus dimension 2, role
So Parameter 011000, 000111
SO Example 2
000000 OUS. 000000... 000000... 000000... 00
0000...
parameter i000111
000000 FUS. 000000... 000000... 000000... 000
000...
LAN
result b
000000 MUS. 000000... 000000... 000000... 00
0000...
parameter j011000
operand
result a
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Semantic Operators

• Dimension operator
• DSO sort by dimension (multiple dimension
  extraction)
• Generative operators
• COM composition from role players
• DEC decomposition into role players
• Role operator
• ROI role inversion
• Substitution operator
• SUB replace character, role player or dimension
• Logical operators
• LAN logical analysis
• LSY logical synthesis
• LSO logical sorting
• Gestalt operator
• GEX Extract gestalt class categories

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Sort by Dimension Functions

• Operator DSO (sort by dimension)
• Focus list of dimensions (variation)
• Parameter none
• See example in slide Semantic Tree Operation
  (STO)

17
Composition Functions

• Operator COM (composition from role players)
• Focus (invariant) one dimension except
  dimension 6
• Parameter (variation) list of role players pairs

result
000000 000000... FUS.BU.- 000000... 000000
... 000000...

• Parameter pairs should be of same layer than
  focused category
• The composed categories replace focus dimension
  1 in results
• Focus dimension is null in results

result
operand
000000 000000... FUS. BA.- 000000... 00000
0... 000000...
000000 FUS. 000000... 000000... 000000... 000
000...
Example of composition function Operator COM
(composition) Focus dimension 2 Parameter De
(BU.) Tr (E.) De (BA.) Tr (E.) De
(BS.) Tr (E.)
result
000000 000000... FUS. BS.- 000000... 00000
0... 000000...
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Decomposition Functions

• Operator DEC (decomposition into role players)
• Focus (invariant) one dimension except
  dimension 1
• Parameter (variation) list of 1, 2 or 3 roles

F 000000... 000000... 000000... 000000... 00000
0...

• The decomposed role players replace focus
  dimension - 1 in results
• Focus dimension is null in results

result
operand
U 000000... 000000... 000000... 000000... 0000
00...
000000 FUS. 000000... 000000... 000000... 000
000...
Example of composition function Operator DEC
(decomposition) Focus dimension 2 Parameter
So, De, Tr
result
S 000000... 000000... 000000... 000000... 00000
0...
result
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Role Inversion Functions

• Operation ROI (role inversion)
• Focus (invariant) dimension (except 1), role
  player layer, role of the transformed category
• Parameter (variation) 1, 2 or 3 of the possible
  inversions (So, De), (De, Tr), (So De)

000000 000000... BA.FUS.- 000000... 00000
0... 000000...
The role of the transformed category is precised
in the focus only if all the role players of the
focused layer are not concerned by the
transformation.
operand
000000 000000... FUS. BA.- 000000... 00000
0... 000000...
result
Example of Role inversion function Operator ROI
(decomposition) Focus dimension 3, layer
2 Parameter (So, De), (De, Tr)
000000 000000... FUS.E.BA.- 000000... 000
000... 000000...
result
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Substitution Functions

• Operator SUB
• Focus (invariant) dimension, role of the
  transformed category
• Parameter (variation) set of categories of same
  layer than the focus

result
... ... b.e.- ... ... ...
result
... ... b.u.- ... ... ...
If the focused category is not an element of the
parameter set, the operation is impossible
result
... ... b.o.- ... ... ...
... ... b.a.- ... ... ...
result
Example of Substitution function Operator SUB
(substitution) Focus dimension 3, De Parameter
y. o. e. u. a. i.
... ... b.i.- ... ... ...
result
... ... b.y.- ... ... ...
operand
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Analysis Functions

• Operator LAN (logical analysis)
• Focus (invariant) dimension, role of the
  transformed character. The focus can only be one
  character.
• Parameter (variation) set of characters such
  as... - the intersection of resulting characters
  000000 - the union of resulting characters
  the focused character

If the focused character is different from the
union of the parameter set, the operation is
impossible
See example in Example of logical analysis
slide
22
Synthesis Functions

• Operator LSY (logical synthesis)
• Focus (invariant) dimension, role of the
  transformed character. The focus can only be one
  character.
• Parameter (variation) set of characters. Each
  character of the set includes the (focused)
  transformed character

result
000000 MUS. 000000... 000000... 000000... 00
0000...
If the focused character is not included in every
element of the parameter set, the operation is
impossible.
000111
result
000000 FUS. 000000... 000000... 000000... 00
0000...
operand
000000 BUS. 000000... 000000... 000000... 000
000...
Example of synthesis function Operator LSY
(logical synthesis) Focus dimension 2, role
So Parameter 000111, 011111, 111111
011111
LSY
result
000000 IUS. 000000... 000000... 000000... 00
0000...
111111
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Logical Sorting Functions

• Operator LSO (logical sorting)
• Focus (invariant) dimension, role of the
  transformed character. The focus can only be one
  character.
• Parameter (variation) set of characters such as
  their intersection 000000.

result
000000 SUS. 000000... 000000... 000000... 00
0000...
The transformed characters of the result nodes
display only the members of the parameter set
that are included in the focused character
000100
result
000000 BUS. 000000... 000000... 000000... 00
0000...
operand
000000 MUS. 000000... 000000... 000000... 000
000...
Example of logical sorting function Operator
LSO (logical sorting) Focus dimension 2, role
So Parameter 010000, 001000, 000100,000010,
000001
000010
LSO
result
000000 TUS. 000000... 000000... 000000... 00
0000...
000001
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Gestalt Classes

• General definition A gestalt class of flow
  categories is defined in terms of logical
  relations between properties of categories role
  players.
• Population and Rationality classes are examples
  of gestalt classes.
• Semantic functions can manipulate gestalt classes
  using the operator Extract Gestalt Class (GEX).
  
• The following slides give two interconnected
  examples of partition of complete categories into
  gestalt classes.

25
Population Gestalt Classes

• V Set of void categories
• All their characters are single empty 100000.
• J Set of mixed categories
• All their characters have Ebit 1
• P Set of populated categories
• All categories that are neither void nor mixed.
  At least one of their characters have Ebit 0
• All flow categories of layer n belong to V, or to
  J, or to P (exclususive or).

26
Rationality Gestalt Classes

• Z Set of rational categories (subset of
  populated)
• the source player is populated
• AND
• IF the destination player is void, THEN the
  translator player is void
• AND
• IF the translator player is populated, THEN the
  destination player is populated
• Y Set of irrational categories (subset of
  populated)
• the destination player is populated, AND the
  source player is void
• OR
• the translation player is populated, AND the
  destination player is void
• OR
• the translation player is populated AND the
  source player is void
• X Set of ambiguous categories (populated or
  mixed)
• neither irrational, nor rational, nor void
• All categories of layer n belong to Z, or to Y,
  or to X, or to V (exclusive or)

27
Gestalt Class Extraction Function

• Operator GSO (gestalt sorting)
• Focus (invariant) dimension, role of the
  transformed category. The focus can only be one
  flow category.
• Parameter (variation) one gestalt class of flow
  categories, corresponding to one or several
  categories

A gestalt class of flow category is defined in
terms of logical relations between role players
of categories. A gestalt class extraction needs a
prior formal definition of a gestalt class. The
GEX operator extracts, from the focused category,
the distinct categories corresponding to the
parameter definition. Note that the union of the
three results of the example does not give a
rational (Z) category but an ambiguous one (X).
result
000000 FEE. 000000... 000000... 000000... 00
0000...
result
000000 FFE. 000000... 000000... 000000... 00
0000...
operand
Example of logical sorting function Operator
GEX (gestalt class extraction) Focus dimension
2 Parameter rational gestalt class (Z)
000000 III. 000000... 000000... 000000... 000
000...
result
000000 FFF. 000000... 000000... 000000... 00
0000...
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SEMANTIC PROGRAMINGSEMANTIC NETWORKING

• Semantic trees

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Semantic Trees
Semantic tree algorithm Pipeline or flow chart
(sequences, loops, forks, conditional rules) of
semantic functions growing trees of semantic
nodes (semantic trees). Functions of generation
n take as operands the results of functions of
generation n-1. A semantic tree can have as many
generations as needed. Different functions can
operate on the same generation of nodes (as
represented on the diagram for k l)
root inputgen.0
i
gen.1
j
j
j
gen.2
k
l
k
l
k
l
k
l
k
l
k
l
Semantic treeTree of semantic nodes generated by
a semantic node input (the root of the tree) and
a semantic tree algorithm. Generational
OrderOnly the generational order is determined
by the algorithm. A generation is logically
instantaneous.The order of operations of same
generation is optional (renditional), and can be
determined by sorting functions.
leavesoutputgen.3
Algorithm example i j k l i operates
on the rootj operates on the first generation
(resulting of i) k operates on the second
generation (resulting of j) l operates also on
the second generation (resulting of j)
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Semantic programs

• Flow chart of logical functions and semantic
  functions (on semantic nodes).
• Semantic programs can contain complex loops
  involving tests, conditional instructions, and
  incremental conditional transformations (on
  parameters and focuses) of logical and semantic
  functions.
• Semantic programs produce semantic networks

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Semantic Networks

• Semantic Link Construction
• Triple
• operand (semantic node)
• result (semantic node)
• transformation (operated by a function)

Semantic Link (functional construction)

operand
result

• Semantic Network
• Set of semantic links.
• The links of a semantic network can have been
  generated by different types of functions.
• In a semantic network, a node can be an operand
  and a result of several transformations.

Semantic Link (use)
Semantic Link Traversal Triple (origin node,
goal node, transformation traversal). The
traversal can be in the functional reverse
direction. The traversal of different
transformations between the same two nodes makes
different traversals.
origin
traversal
goal

• Semantic Path
• definition one or more contiguous links
  traversals in a semantic network.