Transcript On the Generalized Deduction, Induction and Abduction as

On the Generalized Deduction,
Induction and Abduction as the
Elementary Reasoning Operators
within Computational Semiotics
Faculty of Electrical and
Computer Engineering
State University of Campinas
FEEC - UNICAMP - Brazil
Ricardo R. Gudwin
Introduction
 Computational Semiotics - attempt of emulating the
semiosis cycle within a digital computer
 Intelligent Behavior  semiotic processing within an
autonomous system
 Intelligent System  Semiotic System
 Key issue :
 discovery of elementary/minimum units of intelligence 
relation to Semiotics
 Current Efforts:
 Albus’ Outline for a Theory of Intelligence
 Meystel’s GFACS algorithm
 Alternative Set of Operators:
 knowledge extraction (abstraction for deduction)
 knowledge generation (abstraction for induction)
 knowledge selection (abstraction for abduction)
Knowledge Units
 Duality : Information x Knowledge
(what’s the difference ?)
 Knowledge Unit : “A granule of information encoded
into a structure”
 How does a system obtain knowledge units ?
 Environment  set of dynamical continuous phenomena running in parallel
 cannot be known as a whole
 Sensors  provide a partial and continuous source of information
 Umwelt (Uexkull, 1986) - sensible environment
 How to encode such information into knowledge ?
 Singularities Extraction  knowledge units
REAL
WORLD
UMWELT
SINGULARITIES
Sensors
Knowledge Units
 Singularities
 discrete entities that model, in a specific level of resolution,
phenomena occurring in the world
 need to be encoded to become knowledge units
 Codification
 representation space
 embodiment vehicle (structure)
 Structures




numbers
lists
trees
graphs
A
A
D
A
B
B
C
A
B
D
E
E
C
E
G
G
G
(b)
F
F
F
(a)
D
C
(c)
(d)
Knowledge Units
 Representation Space
 after interpretation
 before interpretation : focus of attention mechanism
A
B
A
B
C
AA
B
C
A
B
A
C
D
F
B
C
G
E
A
E
C
A B
B
D
F
C
GC
F E
E
F
D
A
A
C A B
D
A E
AD
D
E
A
E
C
A
A
B
A
A
G
F
G
G
D
F
FOCUS OF
ATTENTION
D
D
E
GF
F
G
E
G
AA
F
G
A A
A
A
A
A
E
C
E
D G
C
E
G
G
G
D
C C
C
G G
G
D
FE
G
F
G
F
D
F
C
F
C
CC
EE
GG
D
D
E B
E
G
F
A
A
B
A
F
C B
G
A
A
E
D
EA
F
B
A
C
A
B
D
C
A
C
AB
A
B
B B
B
E
EE
B
A
A
A A
A
BB
AA
DD
D D
D
FF
F
FF
Knowledge Units
 Interpretation Problems:
 structural identification problem
D
A
B
C
F
E
D
A
B
C
E
F
G
G
D
A
B
C
E
F
G
D
A
B
C
E
F
G
 semantic identification problem
 icon - data represents a direct model of phenomenon
 index - data points to a localization within representation space
where it is stored the direct model of phenomenon
 symbol - data is only a key to be used in a conversion table (an
auxiliary structure) that points to the direct model of phenomenon
Knowledge Units
 Formation of Knowledge Units
 Elementary Knowledge Units
 singularity extraction mechanisms
 More elaborate Knowledge Units
 application of knowledge processing operators
KNOWLEDGE
EXTRACTION
KNOWLEDGE
SELECTION
KNOWLEDGE
GENERATION
KNOWLEDGE
UNITS
 A Taxonomy for Knowledge Units
RIcObSp
Sensors
RIcSeG
RIcObG
RIn
RSy
DSy
DIc
RIcSeSp
Actuator
Packing Knowledge
 Abstraction partial order relation (  )
 a  b - b is an abstraction of a
 extensional definition:
 nominate each particular element belonging to a set
 good for finite sets only
S={
,
,
,
,
,
)
 intensional definition:
 define a set as the collection of all possible elements satisfying
a condition
 good for infinite sets
 requires an encoding/decoding in order to convert from
intensional to extensional representations
S={
} = { ,
,
,
,
,
)
 Examples:





S = {(x,y)  R2 | y = 2x3+7x+1 }
S can be encoded by b = (2,0,7,1)
a = (1,10) , b = (2,0,7,1)  a  b
c = (0,1,1,10,2,31)  T = {(0,1),(1,10),(2,31)}  c  b
a cb
Knowledge Extraction
 P - Set of Premises
 C - Set of Conclusions
P
KNOWLEDGE
EXTRACTION
C
 C P
 The blue knowledge units in P correspond to a packing
of various red knowledge units
 Obtaining C corresponds to the extraction of such
knowledge units, compressed into P’s blue units
Knowledge Generation
 P - Set of Premises
 C - Set of Conclusions
P
KNOWLEDGE
GENERATION
C
 P C
 Obtaining C corresponds to the generation of new
knowledge, using knowledge in P as a seed
 This generation can happen by different ways:






combination,
fusion,
transformation (including insertion of noise, mutation, etc)
interpolation,
fitting,
topologic expansion
Knowledge Selection
 P - Set of Premises
 C - Set of Conclusions
 H - Set of Hypothesis
H
P
KNOWLEDGE
SELECTION
C
 C P
 Obtaining C corresponds to a selection among
candidates in H, using elements in P as a criteria
 Elements in H can be obtained by any way: by a prior
knowledge generation, randomly, etc.
Knowledge Operators x
Reasoning Operators
 Similarity between knowledge operators and classical
reasoning operators (deduction, induction, abduction)
 Knowledge Extraction  Generalized Deduction
 Deduction : normally applied within logic (dicent knowledge
units)
 KE extends it to all types of knowledge units
 Knowledge Generation  Generalized Induction
 Induction : process of producing a general proposition on the
ground of a limited number of particular propositions
 KG is more than induction. Induction is only one of KG
procedures. KG includes operations (e.g. crossover, mutation)
that are not usually categorized as induction
 Knowledge Selection  Generalized Abduction
 The process of abduction can be decomposed into many
phases:
 anomaly detection  deduction
 explanatory hypothesis construction  generalized induction
 hypothesis verification
generalized abduction
 selection of best hypothesis
Building Intelligent
Systems
 Knowledge Units  Mathematical Objects
 Argumentative Knowledge Units  Active Objects
 Intelligent Systems  Object Networks
Active Place
Instances
of Objects
Input Places
Output Places
 Intelligent System for an AGV
DA1
DA4
EM
SR
SSA
IA1
AKA
DA2
DA5
SS
IV
AA1
AKP
AA2
SSP
DA3
VSP
IA3
VSA
RVC
DA6
OV
PL
IVC
IA2
AA4
CPK
VC
DA9
AD8
PL1
DA7
MC
PL2
AA3
Conclusions
 GFACS and argumentative
knowledge
Grouping  generalized induction
Focusing Attention  generalized deduction
Combinatorial Search  generalized induction
and abduction
 Final Conclusions
Formalization of important issues regarding the
intersection of semiotics and intelligent systems
Identification of three knowledge operators that
are “atomic” for any type of intelligent system
development
Foundations for a computational implementation
of the semiosis loop under artificial systems
Background for the construction for intelligent
systems theory, enhanced and sustained by
computational semiotics