Semantic Network Programming

1
Semantic Network Programming

• version 2.3, 1st of june 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 categories
Primitive set primitive set I E, U, A, S, B,
T Construction of the first layer L1 L1 is the
power set of I, including Ø and I. All elements
of L1 (all subsets of I) are called categories of
layer 1 or primitive categories (64 categories of
L1). The elements of L1 E, U, A, S,
B, T are called single primitive
categories. Any element of L1 can be expressed as
a union of single primitive categories.Example
E, U, S E ? U ? S Construction of the
second layer L2 L2 is the set of triples of
categories of L1 Elements of L2 are called
categories of L2, or event categories. A triple
of single categories of L1 is called a single
category of L2 Any category of L2 can be
expressed as a union of single categories of
L2 Example E, U, U, A, B, T E,
U, B ? E, U, T ? E, A, B ?
E, A, T ? U, U, B ? U, U,
T ? U, A, B ? U, A,
T Construction of layers 3 to 6 Ln is the set
of triples of categories of layer Ln-1 (2
n6) Elements of Ln are called categories of
layer n (relations, ideas, phrases, semes
respectively for layers 3, 4, 5 and 6). A triple
of single categories of Ln-1 is called a single
category of Ln Any category of Ln can be
expressed as the union of single categories of Ln
4
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
5
Musical Metaphor(semantic music)

• A primitive element is an elementary semantic
  grain
• A primitive category (a note-character) is a
  superposition of 1 to 6 grains.
• A first layer flow is a triadic morphing between
  a source single grain primitive category and a
  destination single grain primitive categorie
  through a translator single grain primitive
  category
• A first layer category is a set of first layer
  flows.
• A flow of layer n is a triadic morphing between
  flows of layer n-1.
• A category of layer n is a set of flows of layer
  n.

6
HEXAGRAMATIC REPRESENTATION OF IEML PRIMITIVE
CATEGORIES (64-1 hexagrams)
EmptinessSilence
Bipolarity. Process. Verb.

?
VirtualizeMinus
Ternarity RepresentationNoun

?
?
ActualizePlus
SignFuture1st person

?
Fullness
BeingPresent2nd person

Complete information
?
ThingPast3rd person
Composed semantic grains(primitive categories)
Elementary semantic grains(primitive elements)
Presence
Absence
7
HEXAGRAMATIC REPRESENTATION OF 1ST LAYER FLOWS
semantic flow (elementary sound at first
transformation frequency)
USE.
semantic category - set of flows -Set of
elementary sounds having same transformation
frequency
OME.
(EOS)TF.
semantic category - set of flows -
blow of semantic wind
Switch ON(grain)
Switch OFF
semantic flow(sound grain transformation)
8
HEXAGRAMATIC REPRESENTATION 2nd LAYER FLOWS2nd
frequency transformation
USE. (EOS)TF. OME.-
semantic flow(elementary sound transformation)
blow of semantic wind
Switch OFF
Switch ON(grain)
9
HEXAGRAMATIC REPRESENTATION OF CHORDSSemantic
harmonium 364 hexagrams disposed on 6 tones
corresponding to a triadic scale of
transformation frequency
ETC.
tone 4
tone 3
tone 2
tone 1
blow of semantic wind
semantic flow(elementary sound transformation)
Switch OFF
Switch ON(grain)
10
IEML Layers
source
translator
destination
Phr. IEML
Phr. IEML
Phr. IEML
Single semes 6243Semes categories 21458
6
I_
Idea
Idea
Idea
Single phrases 681Phrases categories 2486
5
I,
Relation
Relation
Relation
Single ideas 627Ideas categories 2162
4
I
Event
Event
Event
Single relations 69Relations categories 254
3
I-
Primitive
Primitive
Primitive
Single events 63Events categories 218
2
I.
1
Single primitives 6 E U A
S B T Primitive categories 26 64
I
11
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 -1 (26 -
1) different semantic 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 represented
by an emptiness (100000) character, that is a
semantic character, whereas a null character
(000000) denotes the absence of any semantic
character.
Semantic Character
12
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

• NOT Inversion
• 0 1
• 1 0
• is equivalent to 1

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

13
Semantic Space
Definition of a semantic chord Sextuple set of
1 to 6 IEML categories One category per tone. A
semantic chord is a position in IEML semantic
space Functional role of a semantic
chord Variable (operand or result) of semantic
transformations. Semantic space Definition set
of all semantic chords. The semantic space is
organized by a scale of 6 tones (one per IEML
layer) The semantic space has 9.26406 x (10654)
chords.
Semantic Chord (364 semantic characters)
semantic space tones categories Binary
representation A note in tone 1 primitive
category 1 semantic character array A note in
tone 2 event category 3 semantic characters
array A note in tone 3 relation category 9
semantic characters array A note in tone 4 idea
category 27 semantic characters array A note in
tone 5 phrase category 81 semantic characters
array A note in tone 6 seme category 243
semantic characters array
14
Semantic Modes

• Distinction of the notions of layer and tone
• The tone of a category corresponds to its higher
  (or superior) layer
• A category of tone n embeds the layers 1 to n
• Mode of a semantic chord
• IEML categories can be distributed into a scale
  of 6 possible modes.
• One particular chord of the semantic space can be
  made of 1 up to 6 categories, each one in a
  different tone.
• A semantic chord is distributed into a scale of 1
  to 6 tones, according to the higher layers of the
  categories of which it is composed.
• Conversely, a semantic chord can have a null
  category (no category) in 1 to 5 tones.
• The pattern of presence or absence of categories
  in the 6 possible semantic tones of a semantic
  chord is called its mode.
• Number of modes
• There are 63 possible semantic modes of a chord
  (26-1)
• The semantic mode of a chord can be represented
  by a character, since there are 63 possible
  characters.

15
Number of chords in IEML semantic
space(automatic computation made by Biezunski
and Newcomb)

• Considering that there are only 63 semantic
  characters, for each tone n, there is
• 63 power (n-1) x 3 possible categories.
• To get the number of chords for each one of the
  63 possible modes, we have to multiply the number
  of categories per actualized (non zero) mode.
• Adding the 63 possible modes, we get
• 9.26405 x 10654 semantic chords

16
PRIMITIVE AND COMPOSED LOGICAL TRANSFORMATIONS

• ON SEMANTIC CHORDS (POSITIONS or NODES IN
  IEML SEMANTIC SPACE)

17
Primitive Logical Transformation (PLT)

• Definition of an PLT
• Consists of a logical operation on a semantic
  character located in a semantic chord.
• Reminder a character is the binary
  representation of a primitive category
• Properties of a character logical transformation
• Has a semantic chord as operand and a semantic
  chord as result
• Preserves 363 characters (of the 364 in a chord)
  between the operand and the result.
• A character logical function (PL) is a triple
• Operator (OR, AND, XOR) one among 3
• Focus (character address in the chord operand)
  one among 364
• category tone
• 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

operand chord
result chord
Example of primitive logical transformation FUNCTI
ONOperator ORFocus tone 1, unique
characterParameter 000111
- 011000 -... -... -... -... -...
- 011111 -... -... -... -... -...
000111on tone 1
18
Study of Primitive Logical Transformations (PLT)

• Universal composition law
• PLTs can be composed any result of any
  primitive logical transformation can be taken as
  the operand of any primitive logical
  transformation.
• Whatever the transformations Ta and Tb, there is
  always a composed transformation Tab that has the
  same result as the transformation Tb on the
  result of Ta.
• PLT families
• Any set of PLT having the same logical operator
  (3 logical operators) and the same focus (364
  focuses) form a transformation family (1092
  families).
• There are three sets of families according to
  their logical operator (union, intersection,
  symmetric difference).
• Number of distinct PL and PLT
• For the union, inversion and symmetric
  difference, there are 64 possible parameter
  characters for each of the 364 focuses.
• Therefore, there are 69 888 (3 x 64 x 364)
  different Primitive Logical Functions (a PL is a
  triple operand, focus, parameter).
• As there are 64 possible distinct operands (64
  characters), there are 4 472 832 possible
  distinct PLT on a semantic chord.

19
Notation for primitive logical transformations

• Operator 3 sets of PLT families
• There are three sets of PLT families, defined by
  their operation o (OR, AND, XOR)Toi means one
  of these 3 sets, defined by the logical operation
  i
• Focus 1 092 PLT families
• Toifj means a family defined by its logical
  operation oi, and its focus fj 1 lt j lt 364.
• Parameter 69 888 PL
• Toifjpk means a logical function, defined by
  its logical operation oi, its focus fj and its
  parameter pk
• Operand 4 472 832 PLT
• Toifjpk(x) means a transformation defined by
  its logical operation, its focus fj, its
  parameter pk and its operand (a semantic chord)
  x Toifjpk(x) y, where y is the (semantic
  chord) result of the transformation Toifjpk(x)

20
Reflexivity

• Definition
• An identical PLT is such as its result is
  identical to its operand.
• A transformation subgroup Toifj is reflexive if
  there is a parameter p0 such as, for any x,
  Toifjp0(x) x
• For oi OR ()
• p0 000000
• For oi AND ()
• p0 111111
• For oi XOR ()
• p0 any character for which there is a null
  intersection with x or x(x p0 000000)

21
Symmetry

• Definition of symmetry
• Existence of an inverse transformation for any
  transformation
• All PLT families are symmetrical
• ? i, j, k and x, for which Toifjpk(x) y ? i
  and k, for which Toifjpk(y) x
• For T,
• the symmetrical PLTs will be in the T and T
  sets,
• for T and T
• the symmetrical PLTs will be in the T set

22
Associativity of PLTs

• The associativity of PLTs is independant from
  their subgroups
• ? a, b, c defining PLs, Ta.(Tb.Tc) (Ta.Tb).Tc

23
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 Tfipj are necessary
  to perform a subtraction on an focused
  character of a semantic chord
• compositions of PLTs having same logical
  operation can perform logical operations on on
  chords, since chords 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 tones
  substitutions.
• composition of several role player substitutions
  can exchange the role players (like exchange
  role and destination of a flow category)
• composition of substitutions on tones are
  necessary to perform a tone extraction (replace
  all tones by null categories, except one chosen
  tone) as on the example next slide.
• Compositions of PLT (CLT) are still logical
  transformations composable transformations on
  semantic chords.
• Any composed logical transformation can be broken
  down to primitive logical transformations
  (otherwise, it wouldnt be programmable).

24
Example of tone extraction by composition of
replace tone 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 tone.1 by null category
replace tone.3 by null category
replace tone.4 by null category
replace tone.5 by null category
replace tone.6 by null category
tone extraction semantic transformation
performing composed replace tone transformations
000000 FUS. 000000... 000000... 000000... 000
000...
I FUS. M!!- S!!! O!!!!, F!!!!!
_
Extract tone 2 means replace all tones by
corresponding null categories, except tones 2
25
SEMANTIC OPERATIONS AND SEMANTIC FUNCTIONS

• Complex composed logical operations on semantic
  chords

26
Semantic Operation

• A semantic operation is a set of composed logical
  transformations involving - the same operand
  chord - 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)-
  zero or more results

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
MTE
000000 000000... 000000... S!!! 000000... 0000
00...
The example has focus variation on the composed
transformation tone extraction. The operation
of the example is an actual performance of the
semantic function extract categories by their
upper layer, or in short extract by tone
operand
5
6
000000 000000... 000000... 000000... O!!!!, 000
000...
000000 000000... 000000... 000000... 000000... F!
!!!!_
Semantic function example 1 Operator MTE
(multiple tone extraction) Focus tones 1, 2, 3,
4, 5, 6 Parameter none
27
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.

Semantic Function example 2 Operator LAN
(logical analysis) Focus tone 2, role
So Parameter 011000, 000111
SO Example 2
000000 OUS. 000000... 000000... 000000... 00
0000...
parameter i 011000
000000 FUS. 000000... 000000... 000000... 000
000...
LAN
result b
000000 MUS. 000000... 000000... 000000... 00
0000...
parameter j 000111
operand
result a
28
Semantic Functions

• Primitive operators (closed)
• AND intersection
• OR union
• XOR symmetric difference
• Composed operators (open)
• LAN logical analysis
• LEX logical extraction
• LSY logical synthesis
• COM composition from role players
• DEC decomposition into role players
• ROE role exchange
• SUB substitution (replace category)
• MTE multiple tone extraction
• GCE gestalt class extraction
• Instanciated functions
• operator (primitive or composed)
• focus (set of chord roles),
• parameter set (set of categories).

29
Analysis Functions

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

See example in Example of logical analysis
slide
30
Logical Extraction Functions

• Operator LEX (logical extraction)
• Focus (invariant) tone, role of the transformed
  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 chords
display only the members of the parameter set
that are strictly 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 tone 2, role
So Parameter 010000, 001000, 000100,000010,
000001
000010
LSO
result
000000 TUS. 000000... 000000... 000000... 00
0000...
000001
31
Synthesis Functions

• Operator LSY (logical synthesis)
• Focus (invariant) tone, 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...
The focused character should be included in every
element of the parameter set.
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 tone 2, role
So Parameter 000111, 011111, 111111
011111
LSY
result
000000 IUS. 000000... 000000... 000000... 00
0000...
111111
32
Composition Functions

• Operator COM (composition from role players)
• Focus (invariant) one tone except tone 6
• Parameter (variation) list of categories
  including focus in one of their role

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

• The resulting chords are in mode focus tone 1
  only
• Focus tone is null in resulting chords

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 tone 2 Parameter So
(focus) De (BU.) Tr (E.) So (focus) De
(BA.) Tr (E.) So (BS.) De (focus) Tr (E.)
result
000000 000000... BS. FUS.
- 000000... 000000... 000000...
33
Decomposition Functions

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

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

• The results are in mode focus tone - 1 only
• Focus tone 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 tone 2 Parameter So,
De, Tr
result
S 000000... 000000... 000000... 000000... 00000
0...
result
34
Role Exchange Functions

• Operation ROE (role exchange)
• Focus (invariant) tone (except 1), role player
  layer, role of the transformed category
• Parameter (variation) 1, 2 or 3 of the possible
  exchanges (So, De), (De, Tr), (So De)

000000 000000... BA.FUS.- 000000... 00000
0... 000000...
The role of the transformed category is specified
in the focus only if all the role players of the
focused layer are not involved in the
transformation.
operand
000000 000000... FUS. BA.- 000000... 00000
0... 000000...
result
Example of role player exchange function Operator
ROE (Role Exchange) Focus tone 3, layer
2 Parameter (So, De), (De, Tr)
000000 000000... FUS.E.BA.- 000000... 000
000... 000000...
result
35
Substitution Functions

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

result
result
result
... ... b.e.- ... ... ...
... ... b.u.- ... ... ...
... ... b.a.- ... ... ...
... ... b.o.- ... ... ...
Example of Substitution function Operator SUB
(substitution) Focus tone 3, De Parameter y.
o. e. u. a. i.
... ... b.i.- ... ... ...
... ... b.y.- ... ... ...
... ... b.o.- ... ... ...
operand
result
result
result
36
MTE Multiple Tone Extraction Functions

• Operator MTE
• Focus list of tones (variation)
• Parameter none
• See example in slide semantic operation,
  example 1

37
Gestalt Classes

• A gestalt class (of categories) is defined in
  terms of relations between role players.
• Population and Rationality classes are examples
  of gestalt classes (see next slides). Other
  Gestalt classes can be defined.
• 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.

38
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 (exclusive or).

39
Rationality Gestalt Classes

• V Defined in the previous slide (V is at the
  same time a Rationality class and a Population
  Class)
• 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
• 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)

40
Gestalt Class Extraction Function

• Operator GSO (gestalt sorting)
• Focus (invariant) tone, 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 gestalt class extraction function
Operator GEX (gestalt class extraction) Focus
tone 2 Parameter rational gestalt class Z
(FEE., FFE., FFF.)
000000 III. 000000... 000000... 000000... 000
000...
result
000000 FFF. 000000... 000000... 000000... 00
0000...
41
SEMANTIC PROGRAMINGSEMANTIC NETWORKING

• Semantic trees

42
Semantic Trees
Semantic network construction program An SNCP is
a program consisting mainly of semantic functions
used to add a tree of linked semantic chords to a
semantic network. 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 chords (as
represented on the diagram for k l). In the
example, the same functions are run on all the
results of same generation, but an SNCP can
specify any function on any result.
root inputgen.0
first operand
i
gen.1
operands
results
j
j
j
gen.2
operands
Semantic treeTree of semantic chords generated
by a semantic chord input (the root of the tree)
and an SNCP. PipelineSequence of processes that
connects the root input to one of the leaves. It
is a perspective on an SNCP. Generational
OrderOnly the generational order is determined
by the SNCP. A generation is logically
instantaneous.The order of operations of same
generation is optional (renditional), and can be
determined by sorting functions.
results
k
l
k
l
k
l
k
l
k
l
k
l
results
leavesoutputgen.3
results
results
SNCP 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)
43
Semantic programs

• Flow chart of logical functions and semantic
  functions (on semantic chords).
• 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

44
Semantic Networks

• Semantic Link Construction
• Pair
• operand (semantic chord)
• function
• The result (semantic chord) is given
  automatically by the operand and the function

Semantic Link (functional construction)

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

• 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 chord can be an operand
  and a result of several transformations.

goal
origin
operand
ordinarytraversal
result
goal
origin
result
reversetraversal
operand

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