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

REALWORLD UMWELT

Sensors

SINGULARITIES

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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Representation Space after interpretation

before interpretation : focus of attention mechanism

Knowledge Units

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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 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

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Formation of Knowledge Units Elementary Knowledge Units

singularity extraction mechanisms More elaborate Knowledge Units

application of knowledge processing operators

A Taxonomy for Knowledge Units

Knowledge Units

KNOWLEDGEUNITS

KNOWLEDGEEXTRACTION

KNOWLEDGEGENERATION

KNOWLEDGESELECTION

RIcSeSp

RIcObG

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Actuator

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sors

DSyDIc

RIcObSp

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 = 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

Packing Knowledge

S = { , , , , , )

S = { } = { , , , , , )

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 P’s blue units

KNOWLEDGEEXTRACTION

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C

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

KNOWLEDGEGENERATION

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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.

KNOWLEDGESELECTION

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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

Knowledge Units Mathematical Objects

Argumentative Knowledge Units Active Objects

Intelligent Systems Object Networks

Intelligent System for an AGV

Building Intelligent Systems

Input Places

Active Place

Instancesof Objects

Output Places

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CPK

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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