Transcript Diapositiva 1

Workshop on Abduction and Induction in AI and Scientific Modeling (AIAI06),
ECAI2006, Riva del Garda, Italy, August 29, 2006
Hasty Generalizers and Hybrid Abducers
External Semiotic Anchors and Multimodal Representations
Department of Philosophy and Computational
Philosophy Laboratory, University of Pavia, Italy
Department of Philosophy, Sun Yat-sen University,
Canton, China
Integrating Induction and Abduction
• Induction in Organic Agents
• Mimetic Inductions
• Ideal and Computational Inductive Agents
• Mimetic Abductions
• Ideal and Computational Abductive Agents
• Sentential, Model-Based and Manipulative
Abduction
• A Cognitive Integration:
Samples, Induction, and Abduction
Organic Induction
The Human agent is
Human beings mess thing up
genetically and culturally
above the simplest levels of
endowed with a kind of
complexity. This is particularly
Van
Benthem
(2000)iton Abduction
Induction
rationaland
survival
kit
true of
inductive
inferences:
kid on touching
the
(Woods, 2004) also
seems there •
is aThe
tendency
for
element
his to
mother’s
containing
some strategic
• Indeed,
it is noton
easy
give a
crystal-clear
hasty and
unfounded
kitchen
stove
learns
inuses
one of fallacies.
definition
of them,
either
independently
or in
generalizations.
case never to do that
again this is not
their inter-relationship.
(Of course,
For example:
But not every generalization
(primitive
induction)
easy for
“Deduction”
either)
from a single case is bad (that
Hasty
This is not an offense
to generalization
is a fallacy). Hasty
inductive
reasoning.
in Organic
1. Agents
Cynthia is a bad driver.
generalization Induction
is
a prudent
strategy, especially
when risks
MILL provides
“Methods”
for
2. Women
are bad drivers.
are high:
skills are
• survival
HastyInduction
Generalization,
Secundum Quid, Biased
sometimes
exercisedOther Fallacies It is sometimes worse not to
Statistics,
PEIRCE
integrates Abduction
and
generalize
in this way.
successfully but
not rationally.
• aStrategic
versus
Rationalthe
thinking (conscious
Induction
We have
cognitive
error through
but
but often
tacit)
syllogistic
where
not a strategic
error.
This framework
fact
the two non-deductive
always •stimulated
Mill says the
that institutions rather than
inferences
can be clearly
theorists to
say something
individuals
are the embodiment of inductive
distinguished.
helpful about
the
problem of
logics
induction – MILL - (and on
abduction - PEIRCE) both
fallacious but strong.
Mimetic Induction – Mimetic
Abduction
Ideal Agents
• Kid’s performance is a strategic success and a
cognitive failure.
• Human beings are hardwired for survival and
for truth alike so best strategies can be built
and made explicit, through self-correction and
re-consideration (for example Mill’s methods).
• Mill’s methods for induction, Peirce’s
syllogistic and inferential models for abduction
Inductive and Abductive Agents
• Ideal Logical Inductive and Abductive Agents
• Ideal Computational Inductive, Abductive, and
Hybrid Agents
• Merely successful strategies are replaced with
successful strategies that also tell the more
precise truth about things.
Agent-Based reasoning and
Agent-based Logic
• We will exploit the framework of agent-based
reasoning as illustrated by Gabbay and Woods
(Woods 2004; Gabbay, Woods 2005), so adopting
the perspective of a cognitive agent.
• In the agent-based reasoning above (Gabbay and
Woods, 2001) logic can be considered a
formalization of what is done by a cognitive
agent: logic is agent-based.
Agent-Based reasoning
Agent Based Reasoning consist in describing and analyzing the
reasoning occurring in problem solving situations where the
agent access to cognitive resources encounters limitations such
as
1.
Bounded Information
2.
Lack of Time
3.
Limited Computational Capacity.
Actually Happens Rule: to see what agent should do we should
have to look first to what they actually do. Then, if there is
particular reason to do so, we would have to repair the account
(Woods, 2005).
Agent-Based logic and the framework
of Non-Monotonic Logic
• Classical logic as a complete system
• Deduction and modus ponens (the “truth
preserving feature”)
• Non Monotonic Logic: new information can
compel us to revise previous generated
hypotheses (Decision-Making Process and the
“casual truth preserving feature”)
• Not-only-deductive reasoning
Agent-based reasoning and
Actually happens rule
This rule is a particular attractive assumption
about human cognitive behaviour mainly for two
reasons:
• beings like us make a lot of errors
• cognition is something that we are actually very
good at (strategic rationality and cognitive
economies)
Fallacies I
• It is in this framework that fallacious ways of
reasoning are seen as widespread in human
beings’ cognitive performances, and nevertheless
they can in some cases be redefined and
considered as good ways of reasoning.
• A fallacy is a pattern of poor reasoning which
appear to be a pattern of good reasoning (
Hansen, 2002).
Fallacies II
Formal fallacy
Informal fallacy
Deductive argument
Any other invalid
which has an invalid
mode of reasoning
form (not Truth
whose failing is not in
Preserving
the shape of the
Reasoning)
argument
(expl. Affirming the
Consequent)
(expl. Ad hominem, Hasty
Generalization,…)
The Toddler and the Stove
• A sample of Hasty Generalization
•X% of all observed A's are B''s:
(The stove touched burns)
•Therefore X% of all A's are Bs:
(All the stoves burn)
THE STOVE
TOUCHED BURNS
HASTY
GENERALIZATION
ALL THE STOVES
BURN
DEDUCTIVE INVALID
ARGUMENTS (NOT TRUTH
PRESERVING
FEATURES)
FORMAL
FALLACIES I
(LOGICAL
PERSPECTIVE)
INFORMAL
BAD REASONIGS
INDUCTIVE INVALID
ARGUMENTS
GOOD EPISTEMIC
ACTIONS IN PRESENCE OF
“BAD” REASONINGS
ACTUALLY HAPPENS
RULE
LIMITED COGNITIVE
SETTING
FALLACIES II
(AGENT-BASED
PERSPECTIVE)
BEING-LIKE-US AS HASTY
GENERALIZERS
ABDUCTION AS A FALLACIOUS
ARGUMENT
FALLACIES ARE
“BETTER THAN
NOTHING”
(RATIONAL
SURVIVAL KIT)
CASUAL TRUTH PRESERVING
FEATURE OF FALLACIES
COGNITIVE ECONOMIES
Abduction as an example of fallacy
considered in Agent-Based
Reasoning
Abduction
Affirming the Consequent
Abduction that only
generate plausible
hypotheses
(selective or creative)
Abduction considered as
“Inference to
the Best Explanation.”
creative, selective
• what is abduction?
• theoretical abduction
(sentential, model-based)
scientific
discovery
diagnosis
• manipulative abduction
(mathematical diagrams, construals)
creative, selective
• what is abduction?
• theoretical abduction
(sentential, model-based)
scientific
discovery
diagnosis
• manipulative abduction
(mathematical diagrams, construals)
SENTENTIAL
Theoretical Abduction
MODEL-BASED
Model-based cognition
•Simulative reasoning
•Analogy
SENTENTIAL
•Visual-iconic reasoning
•Spatial thinking
Peirce stated that all thinking is•Thought
in signs,experiment
sense activities
and signs can be icons, indices,•Perception,
or
•Visual imagery
symbols. Moreover, all inference
is a
•Deductive reasoning(Beth’s
form of sign activity, where the word
method of semantic tableaux,
sign includes “feeling, image, Girard’s “geometry” of proofs, etc.)
•Emotion
conception, and other representation”
Theoretical Abduction
(CP 5.283), and, in Kantian words, all
synthetic forms of cognition. That is, a
considerable part of the thinking activity
is model-based. Of course modelbased reasoning
acquires its peculiar
MODEL-BASED
creative relevance when embedded in
abductive processes
Mathematical Diagrams
(also Model-Based)
manipulative abduction nicely
introduces to
hypothesis generation in active,
distributed, and embodied cognition
The activity of “thinking through
doing” is made possible not simply
by mediating cognitive artifacts and
tools, but by active process of
testing and manipulation.
Thinking through doing
Construals
Manipulative Abduction
Thinking through doing
Construals
Manipulative Abduction
Samples, Induction, Abduction
“If we think that a sampling
“If we do not think of inductive
method is fair and unbiased,
generalizations as abductions
then straight generalization
we are at a loss to explain why
gives the best explanation of the
such inference is made stronger
sample frequencies. But if the
and more warranted, if in
size is small, alternative
connecting data we make a
explanations, where the
systematic search for counterfrequencies differ, may still be
instances and cannot find any,
plausible. These alternative
than it would be just take the
explanations become less and
observation passively. Why is
less plausible as the sample size
the generalization made
Manipulative
abduction
can
be
considered
a kind
grows,
because
theand
sample
stronger
by of
making an effort to
•
Samples
Manipulative
Abduction
basisbeing
for further
meaningful
inductive
generalizations.
unrepresentative due to
examine a wide variety of types
For example
different
construals
give
riseThe
tothe
chance
becomes
more
and morecanabduction
of A’s?
answer
is way
that for
it is
• Construals
Manipulative
is
correct
improbable.
Thus
viewing
made
stronger
because
the
different
inductive
generalizations.
If “an
describing
the features of what
areinductive
called
``smart
inductive
inductive
generalization
as
the active
search of
generalization
is an inference
that goesfailure
from
the
generalizations'',
as contrasted
to
the of
trivial
ones. For
abductions
show
why
sample
counter-instances
tend
to rule
characteristics
of some
observed
samples
of
example,
in
science
construals
can
shed light on this
process
size is important.
Again,
we see and ``appraisal'':
out various hypotheses
about
of sample
``production''
through
individuals to
a conclusion
about the distribution of
that analyzing
inductive
ways
in which
the sample might
construals,
manipulative
creative
abduction
generates
thosegeneralizations
characteristics
in
some
larger
populations”
as
abductions
be biased, can
thatoriginate
is, is
abstract
hypotheses
butthe
in the
meantime
(Josephson)
what
characterizes
sample
as
shows us
how tobases
evaluate
the
strengthens
the abductive
possible
for further
meaningful
inductive
“representative”
is itsinferences
effect (sample frequency)
byruling out
strengths
of these
conclusion of
by
generalizations
through the identification
new samples
(Josephson,
p.
42).”
alternative
explanations
for the
reference
to(or
part
of
its
cause
(populations
frequency):
of new features of already available sample, for instance
observed
this should be
considered
a conclusion
aboutcircumstances).
itsfrequency
cause. (Josephson
in terms
of the detection
of relevant
2000)”
Different generated construals can
give rise to different
plausible inductive generalizations.
LOGICAL IDEAL ABDUCTIVE and INDUCTIVE SYSTEMS
Flach and Kakas (2000). A useful
- symbolic:
they activate
and “anchor”
meanings in
perspective
on integration
of
material communicative
and intersubjective mediators in
abduction and induction:
the framework of the phylogenetic, ontogenetic, and
• explanation (hypothesis does not
cultural
reality
of the human
being
and its language. They
• refer
cf. thetocognitive
analysis
of
observables
– selective
originatedabduction
in origin
embodied
cognitioncreates
and gestures we share
the
of
theabduction
[but
with some
mammals
but
also non mammals animals (cf.
mathematical
continuous
new
hypotheses
too])
monkey knots
pigeon categorization, Grialou, Longo,
line asand
a pre-conceptual
• generalization – genuinely new
invariant
and Okada,
2005);of three cognitive
(hypothesis can entail additional
practices
2005),are in turn sets of proof invariants,
• (Theissier,
logical systems
observable
information
on
- abstract:
they
arenumeric
based
on
independence
and
of the
linea maximal
sets
of structures
that are
preserved from one proof
unobserved
individual,
extending
regarding(Châtelet,
sensory 1993;
modality;
strongly
stabilize
experience
Dehaene,
to another
or which are
preserved
by proof
the
theory
T)
1997;
Butterworth,
1999).
and common
categorization.
The maximality
especially
transformations.
They are theisresult
of a distilled
praxis
of and
proof:
it is made of maximally
Imagine
wepraxis,
have
athe
new
abductive
important:
it refers
to
their
practical
historical
regularities. by
theory
T’ =stable
T  H constructed
invariance
and stability;
induction: an inductive extension
-rigorous:ofthe
rigor can
of proof
is reached
through a difficult
a theory
be viewed
as set of
practical experience.
For instance,
in MEMORYLESSNESS
the case of
abductive
of the OF
• extensions
MAXIMIZATION
characterizes
original
T.
mathematics,
as theory
thedemonstrative
maximal
place
for convincing
reasoning.
Its properties do not yield
information
the
past, contrarily
for instance to
reasoning.
Rigor lies
in
of proofs
and in the
controversies
onthe
IAIstability
areabout
of course
the narrative and not logical descriptions of nonfact they open
can be
iterated.
and
alive
demonstrative processes, which often involve
Mathematics is the best
example
of maximal
stability
andmemories.
“historical”,
“contextual”,
and
“heuristic”
conceptual invariance.
Thanks
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