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 zIntelligent System  Semiotic System zKey issue : ydiscovery of elementary/minimum units of intelligence  relation to Semiotics zCurrent Efforts: yAlbus’ Outline for a Theory of Intelligence yMeystel’s GFACS algorithm zAlternative 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” zHow does a system obtain knowledge units ? yEnvironment - xset of dynamical continuous phenomena running in parallel xcannot be known as a whole ySensors - xprovide a partial and continuous source of information yUmwelt (Uexkull, 1986) - sensible environment yHow to encode such information into knowledge ? ySingularities Extraction  knowledge units

Knowledge Units zSingularities ydiscrete entities that model, in a specific level of resolution, phenomena occurring in the world yneed to be encoded to become knowledge units zCodification yrepresentation space yembodiment vehicle (structure) zStructures ynumbers ylists ytrees ygraphs

zRepresentation Space yafter interpretation ybefore interpretation : focus of attention mechanism Knowledge Units

zInterpretation Problems: ystructural identification problem ysemantic identification problem xicon - data represents a direct model of phenomenon xindex - data points to a localization within representation space where it is stored the direct model of phenomenon xsymbol - 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

zFormation of Knowledge Units yElementary Knowledge Units xsingularity extraction mechanisms yMore elaborate Knowledge Units xapplication of knowledge processing operators zA Taxonomy for Knowledge Units Knowledge Units RIcSeSp RIcObG RIcSeG RInRSy Actuator Sensors DSy DIc RIcObSp

zAbstraction partial order relation ( ) za b - b is an abstraction of a zextensional definition: ynominate each particular element belonging to a set ygood for finite sets only zintensional definition: ydefine a set as the collection of all possible elements satisfying a condition ygood for infinite sets yrequires an encoding/decoding in order to convert from intensional to extensional representations zExamples: yS = {(x,y)  R 2 | y = 2x 3 +7x+1 } yS can be encoded by b = (2,0,7,1) ya = (1,10), b = (2,0,7,1)  a b yc = (0,1,1,10,2,31)  T = {(0,1),(1,10),(2,31)}  c b ya c b Packing Knowledge S = {,,,,, ) S = { } ={,,,,, )

Knowledge Extraction zP - Set of Premises zC - Set of Conclusions zC P zThe blue knowledge units in P correspond to a packing of various red knowledge units zObtaining C corresponds to the extraction of such knowledge units, compressed into P’s blue units

Knowledge Generation zP - Set of Premises zC - Set of Conclusions zP C zObtaining C corresponds to the generation of new knowledge, using knowledge in P as a seed zThis generation can happen by different ways: ycombination, yfusion, ytransformation (including insertion of noise, mutation, etc) yinterpolation, yfitting, ytopologic expansion

Knowledge Selection zP - Set of Premises zC - Set of Conclusions zH - Set of Hypothesis zC P zObtaining C corresponds to a selection among candidates in H, using elements in P as a criteria zElements in H can be obtained by any way: by a prior knowledge generation, randomly, etc.

Knowledge Operators x Reasoning Operators zSimilarity between knowledge operators and classical reasoning operators (deduction, induction, abduction) zKnowledge Extraction  Generalized Deduction yDeduction : normally applied within logic (dicent knowledge units) yKE extends it to all types of knowledge units zKnowledge Generation  Generalized Induction yInduction : process of producing a general proposition on the ground of a limited number of particular propositions yKG 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 zKnowledge Selection  Generalized Abduction yThe process of abduction can be decomposed into many phases: xanomaly detection  deduction xexplanatory hypothesis construction  generalized induction xhypothesis verification xselection of best hypothesis generalized abduction

zKnowledge Units  Mathematical Objects zArgumentative Knowledge Units  Active Objects zIntelligent Systems  Object Networks zIntelligent System for an AGV Building Intelligent Systems

Conclusions zGFACS and argumentative knowledge yGrouping  generalized induction yFocusing Attention  generalized deduction yCombinatorial Search  generalized induction and abduction zFinal Conclusions yFormalization of important issues regarding the intersection of semiotics and intelligent systems yIdentification of three knowledge operators that are “atomic” for any type of intelligent system development yFoundations for a computational implementation of the semiosis loop under artificial systems yBackground for the construction for intelligent systems theory, enhanced and sustained by computational semiotics