Faculty of Electrical and Computer Engineering State University of Campinas

1. 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

2. 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)

3. 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

4. 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

5. Knowledge Units • Representation Space • after interpretation • before interpretation : focus of attention mechanism

6. 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 • symbol - data is only a key to be used in a conversion table (an auxiliary structure) that points to the direct model of phenomenon

7. 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

8. S = { , , , , , ) S = { } = { , , , , , ) Packing Knowledge • Abstraction partial order relation ( ) • ab - 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)  ab • c = (0,1,1,10,2,31)  T = {(0,1),(1,10),(2,31)} cb • a c b

9. 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

10. 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

11. 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.

12. 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

13. Building Intelligent Systems • Knowledge Units  Mathematical Objects • Argumentative Knowledge Units  Active Objects • Intelligent Systems  Object Networks • Intelligent System for an AGV

14. 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