On the Generalized Deduction, Induction and Abduction as the Elementary Reasoning Operators within Computational Semiotics

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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
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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
• Meystels GFACS algorithm
• Alternative Set of Operators
• knowledge extraction (abstraction for deduction)
• knowledge generation (abstraction for induction)
• knowledge selection (abstraction for abduction)

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Knowledge Units

• Duality Information x Knowledge
  (whats 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

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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

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Knowledge Units

• Representation Space
• after interpretation
• before interpretation focus of attention
  mechanism

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Knowledge Units

• Interpretation Problems
• structural identification problem
• 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

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Knowledge Units

• Formation of Knowledge Units
• Elementary Knowledge Units
• singularity extraction mechanisms
• More elaborate Knowledge Units
• application of knowledge processing operators
• A Taxonomy for Knowledge Units

RIcObSp
RIcSeG
Sensors
RIcObG
RIn
RSy
DSy
DIc
RIcSeSp
Actuator
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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
• 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
• Examples
• S (x,y) ? R2 y 2x37x1
• 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

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Knowledge Extraction

• P - Set of Premises
• C - Set of Conclusions
• 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 Ps blue units

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Knowledge Generation

• P - Set of Premises
• C - Set of Conclusions
• 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

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Knowledge Selection

• P - Set of Premises
• C - Set of Conclusions
• H - Set of Hypothesis
• 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.

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Knowledge Operators xReasoning 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
• selection of best hypothesis

generalized abduction
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Building Intelligent Systems

• Knowledge Units ? Mathematical Objects
• Argumentative Knowledge Units ? Active Objects
• Intelligent Systems ? Object Networks
• Intelligent System for an AGV

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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