The Metaphysical Nature of the Non-adequacy Claim: An Epistemological Analysis of the Debate on Probability in Artificial Intelligence

152 Pages·2013·1.38 MB·English

by  Carlotta Piscopo (auth.)

Studies in Computational Intelligence 464
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Carlotta Piscopo
The Metaphysical Nature
of the Non-adequacy Claim
An Epistemological Analysis of the Debate
on Probability in Artificial Intelligence
ABC
Author
CarlottaPiscopo
UniversitéLibredeBruxelles
Bruxelles
Belgium
ISSN1860-949X e-ISSN1860-9503
ISBN978-3-642-35358-1 e-ISBN978-3-642-35359-8
DOI10.1007/978-3-642-35359-8
SpringerHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2012953287
(cid:2)c Springer-VerlagBerlinHeidelberg2013
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To my grandmother Irene
Preface
Overthelasttwodecades,the fieldofartificialintelligencehasexperienceda
separation into two schools that hold opposite opinions on how uncertainty
shouldbe treated.Thisseparationis the resultofadebate thatbeganatthe
end of the 1960’s when AI first faced the problem of building machines re-
quiredtomakedecisionsandactintherealworld.Thisdebatewitnessedthe
contraposition between the mainstream school, which relied on probability
for handling uncertainty,and an alternative school,which criticized the ade-
quacyofprobabilityinAIapplicationsanddevelopedalternativeformalisms.
It is my contention that the reason why the uncertainty field has split
into two schools is that a crucial element on which the two schools diverge
has not been properly addressed. The debate has focused on the technical
aspects of the criticisms raised against probability while neglecting an im-
portant element of contrast. This element is of an epistemological nature,
and is therefore exquisitely philosophical. In this book, I present the histori-
cal context in which the debate on probability developed and I illustrate the
key components of the technical criticisms therein. I then analyze in detail,
by referring to the original texts, what I identify to be the epistemological
elementthathasbeenneglectedinthedebate.Throughaphilosophicalanal-
ysis of the epistemological element I argue that this element is metaphysical
inPopper’ssense.Ishowthatthiselementcannotbetestednorpossiblydis-
provedon the basis of experience and is therefore extra-scientific.I establish
that a philosophical analysis is now compelling in order to both solve the
problematic division that characterizes the uncertainty field and to secure
the foundations of the field itself.
This book is based on my doctoral dissertation and would not have been
possible without inspiration, support, and guidance from many people.
I am grateful to my supervisor Prof. Michel Ghins, and to the members
of my examination committee: Prof. Danielle Lories, Prof. Bernard Feltz,
Prof.MarcoSaerens,andProf.VincenzoFano.IamalsogratefultoProf.Jean
VIII Preface
Bricmontforthe inspiringdiscussionsthatwehadonthe historyandphilos-
ophy of science.
I am greatly indebted to Dr. Mauro Birattari for his guidance and super-
vision.Maurotaughtmehowtobuildaresearchidea,putitintoperspective
andturnitintoa researchresult.His contagiouspassionfor researchandhis
precious advice had an impact on my work that words can hardly tell.
I developed my dissertation in collaboration with IRIDIA, the artificial
intelligence laboratory of the Université Libre de Bruxelles. At IRIDIA, I
collaborated directly with Dr. Birattari and I had the opportunity to inter-
act and discuss with many brilliant researchers. I am particularly indebted
with Prof. Philippe Smets, Prof. Marco Dorigo, Prof. Hugues Bersini, and
Dr. Thomas Stützle.
I am also grateful to Prof. Gianluca Bontempi, Prof. Alessandro Saffiotti,
and Prof. Pascal Delwit.
I thank Daniel, my professor of french boxing, for teaching me the im-
portance of perseverance;and Patrick,my professorof brazilianjiu-jitsu, for
emphasizing the importance of technique over strength. I wish to thank also
my friends Elena and Vittorio, Stella, Emanuele and Mary, Andrea, Laura,
Cristina, Pascale, Nick and Candice, Bruno, Danae, Antoine, and Gianni.
Ithankmyfamily:mymotherGiulia,myfatherFrancesco,andmybrother
Filippo; Lorena,Anna, Claudio,Luca, Stefania; Franco,Valeria,Meri, Nino,
Fiorella; Maria, Rita, Giuseppe, and Pina; the kids of my family: Louise,
Fabio,Adriano,andLudovico;mycousins,aunts,anduncles:Marita,Borina,
Margherita,Rachele,Bernardo,Andrea,andStefano,China,Libera,Pasqua,
Mariella, Cristina, Letizia, Maria, Francesco, Pino and Giacomo; and my
grandparentsthat always keep their eyes on me: Filippo, Carmela,Siro, and
Irene.FrommygrandmotherIreneIhaveinheritedthepassionforphilosophy.
This book of mine is dedicated to her.
The last word is for Mauro, the companion of my life. I thank him for
always pushing me to search for more and always do my best while keeping
smiling.
Brussels, Belgium Carlotta Piscopo
October 2012
Contents
1 Introduction............................................. 1
2 Historical and Philosophical Background ................ 7
2.1 Uncertainty as a Scientific Concern ...................... 7
2.2 The Issue of Modelling in Science........................ 16
2.2.1 The Notion of Model ............................ 16
2.2.2 Probability Theory and Probabilistic Models........ 22
2.2.3 On the Status of Empirical Models ................ 25
2.3 In a Nutshell.......................................... 38
3 Uncertainty in AI and the Debate
on Probability ........................................... 39
3.1 The Emergence of Uncertainty in Artificial Intelligence..... 39
3.1.1 Artificial Intelligence............................. 40
3.1.2 Uncertainty in AI ............................... 43
3.1.3 The Abstract AI ................................ 46
3.1.4 The Shift toward the nouvelle AI.................. 50
3.2 The Debate on Probability ............................. 53
3.2.1 The Criticisms against Probability................. 53
3.2.2 The Impact of the Debate ........................ 66
3.3 In a Nutshell.......................................... 68
4 The Non-adequacy Claim
in the Literature......................................... 69
4.1 The Structure of the Non-adequacy Claim ................ 69
4.2 The Non-adequacy Claim in Zadeh ...................... 73
4.2.1 The Discrimination Hypothesis in Zadeh ........... 76
4.2.2 The Correspondence Hypothesis in Zadeh .......... 79
4.3 The Non-adequacy Claim in Shafer ...................... 83
4.3.1 The Discrimination Hypothesis in Shafer ........... 86
4.3.2 The Correspondence Hypothesis in Shafer .......... 91
X Contents
4.4 Other Instances of the Non-adequacy Claim .............. 95
4.5 In a Nutshell.......................................... 97
5 The Metaphysical Character
of the Non-adequacy Claim.............................. 99
5.1 The Discrimination and the Correspondence Hypothesis.... 99
5.1.1 The Discrimination between Deterministic and
Stochastic Phenomena ........................... 100
5.1.2 The Correspondence between Models and Reality.... 104
5.2 Implications of the Non-adequacy Claim.................. 112
5.3 In a Nutshell.......................................... 122
6 Conclusion .............................................. 123
Appendices
A The Probabilistic Framework ............................ 127
B The Alternative Framework ............................. 131
References................................................... 135
1
Introduction
Chi vuol esser lieto, sia:
di doman non c’è certezza†
Lorenzode’Medici
CanzonadiBacco,ca.1490
Uncertaintypervadesourlives.Becauseourknowledgeoftheworldislimited,
our reasoning and our decisions are necessarily affected by uncertainty.
For centuries, both philosophy and science dealt with the problem of un-
certainty.Philosophyhasfocusedontheepistemologicalissueofinvestigating
the limits ofhumanknowledge.Science,onthe otherhand,hasconcentrated
on modeling nature on the basis of available knowledge in order to make
predictions.
In this book, we discuss the emergence of the problem of uncertainty and
howithasbeenaddressedinthefieldofartificialintelligence(hereinafterAI).
Officially born in the 1950’s, AI research embodies the long-held dream of
humanity to develop artificial systems that are able to act in the real world
without human intervention. Within AI, robotics best realizes this dream.
Theaimofthisfieldistocreatemachinesthatareabletosubstitutehumans
in activities that are dirty, dangerous, or degrading. Think, for instance, of
rescuemissionsindisasterareasortheexplorationofdistantplanets.Insome
respects,this dreamisnownearlyareality.Indeed,thetechnologyisalready
availabletobuildthemechanicalandelectronicdevicesofwhicharobotcould
becomposed.Nevertheless,thisisnotenough:inordertoperformataskand
effectively substitute humans,arobotmustbe ableto autonomouslyacquire
and processempiricalinformation.Typically,the real-worldenvironments in
which a robot would operate are dynamic and unstructured, that is, they
would not be modified in order to simplify the robot’s work.There is, there-
fore,littlehope toequiptherobotwithacompleteanddefinitive description
oftheseenvironments.Arobotisrequiredtocontinuouslygatherandupdate
empiricalknowledgeontheenvironment,andthenframeitintoaformalrep-
resentationthatallowsdecisionmakingandrobotaction.Asanydecisionwill
be made on the basis of partial knowledge, the decision-making mechanisms
should be robust to uncertainty and yield acceptable action nonetheless.
† Be happyif you wish: the futureis uncertain.
C.Piscopo:TheMetaphysicalNatureoftheNon-adequacy Claim,SCI464,pp.1–6.
DOI:10.1007/978-3-642-35359-8_1 (cid:2)c Springer-Verlag BerlinHeidelberg2013
2 1 Introduction
InthefieldofAI,researcherslongreliedupontheimplicitassumptionthat
the methodsdevelopedforsolvingdecision-makingproblemsundercomplete
and perfect information, as those, for example, encountered in chess play-
ing, could also be directly extended to decision making in real-world en-
vironments. Therefore, in the initial phases of AI development, real-world
applications were not of concern and research concentrated on solutions for
situationsentailingcompleteandperfectknowledge.Inacrescendoculminat-
ingintheearly1990’s,AIresearchersshiftedtothedevelopmentofmachines
intended to operate autonomously in dynamic and unstructured real-world
environments. Thus, a problem emerged: the techniques designed for sim-
plified world like that of chess could not be directly generalized to the real
world.Indeed,decisionmakingunderuncertaintyrequiresspecificallydevised
methods.Uncertaintywasthereforerecognizedas oneofthe keyproblemsin
AI and contributed to a radical transformationof the field, its goals,and its
methods.
AsuncertaintyrosetotheforefrontofAI,researchersfocusedonthedefini-
tionofformalmethods to managethe problem.Atthatmoment,probability
appearedtobethenaturalchoicetoaddresstheproblembecause,inaddition
to being mathematically well founded, it had already been proved effective
in different scientific fields ranging from statistical mechanics to informa-
tion theory. Nevertheless, some researchers criticized the use of probability
in AI applications. They declared probabilistic models unfit and developed
alternative models. The decision of part of AI researchers to give birth to
alternativemodels determineda sharpseparationofthe researchcommunity
intotwoschools:theprobabilisticandthealternativeschool.Thisseparation
persists and it is perceived as problematic by the researchers in the AI field
of uncertainty (hereinafter uncertainty field).
In this book, we analyze the reasons for this separation and its persis-
tence. Our analysis stems from the understanding that the criticisms raised
against the probabilistic framework are composite. We single out two ele-
ments in these criticisms.The firstis relatedto technicalissuesonthe use of
the probabilistic framework, while the second is philosophical and concerns
the epistemological foundations of this framework. In the book, we argue
that what we call the technical element has been fully analyzed in existing
AI literature. As a result, the majority of AI researchers believe that the
debate concerning the adequacy of probability has been extinguished, and
thus consider it adequate and sufficient to handle uncertainty. Nevertheless,
some researchers remain unsatisfied with the probabilistic models and have
developed alternatives.We consider the existence of these two schools devel-
oping in distinct research directions, as evidence of the fact that some key
issue upon which they diverge has not been properly addressed. Our thesis
is that the key issue rests within what we call the philosophical element of
the criticisms raised against probability. We identify this philosophical ele-
ment in a collection of claims made, with different nuances, by a number of