Diapositiva 1

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
Lorenzo Magnani
Department of Philosophy and Computational
Philosophy Laboratory, University of Pavia,
Italy Department of Philosophy, Sun Yat-sen
University, Canton, China
2
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

3
Organic Induction
Human beings mess thing up above the simplest
levels of complexity. This is particularly true
of inductive inferences it seems there is a
tendency for hasty and unfounded
generalizations. But not every generalization
from a single case is bad (that is a fallacy).
Hasty generalization is a prudent strategy,
especially when risks are high survival skills
are sometimes exercised successfully but not
rationally. We have a cognitive error but not a
strategic error. This fact always stimulated the
theorists to say something helpful about the
problem of induction MILL - (and on abduction -
PEIRCE) both fallacious but strong.

• The Human agent is genetically and culturally
  endowed with a kind of rational survival kit
  (Woods, 2004) also containing some strategic uses
  of fallacies.
• For example
• Hasty generalization
• Cynthia is a bad driver.
• Women are bad drivers.
• It is sometimes worse not to generalize in this
  way.

Van Benthem (2000) on Abduction and Induction

• The kid on touching the element on his mothers
  kitchen stove learns in one case never to do that
  again (primitive induction)
• This is not an offense to inductive reasoning.
• MILL provides Methods for Induction
• PEIRCE integrates Abduction and Induction through
  the syllogistic framework where the two
  non-deductive inferences can be clearly
  distinguished.

• Indeed, it is not easy to give a crystal-clear
  definition of them, either independently or in
  their inter-relationship. (Of course, this is not
  easy for Deduction either)

Induction in Organic Agents

• Hasty Generalization, Secundum Quid, Biased
  Statistics, Other Fallacies
• Strategic versus Rational thinking (conscious but
  often tacit)
• Mill says that institutions rather than
  individuals are the embodiment of inductive logics

4
Mimetic Induction Mimetic Abduction Ideal
Agents

• Kids 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 Mills methods).
• Mills methods for induction, Peirces
  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.

5
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.

6
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
• Bounded Information
• Lack of Time
• 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).

7
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

8
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)

9
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).

10
Fallacies II
Formal fallacy Informal fallacy
Deductive argument which has an invalid form (not Truth Preserving Reasoning) (expl. Affirming the Consequent) Any other invalid mode of reasoning whose failing is not in the shape of the argument (expl. Ad hominem, Hasty Generalization,)
11
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)

12
Hasty Generalization Scheme
THE STOVE TOUCHED BURNS
HASTY GENERALIZATION
ALL THE STOVES BURN
13
DEDUCTIVE INVALID ARGUMENTS (NOT TRUTH
PRESERVING FEATURES)
FORMAL
FALLACIES I (LOGICAL PERSPECTIVE)
INFORMAL
BAD REASONIGS
INDUCTIVE INVALID ARGUMENTS
14
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)
COGNITIVE ECONOMIES
CASUAL TRUTH PRESERVING FEATURE OF FALLACIES
15
Abduction as an example of fallacy considered in
Agent-Based Reasoning
16
creative, selective

• what is abduction?
• theoretical abduction
• (sentential, model-based)
• manipulative abduction
• (mathematical diagrams, construals)

scientific discovery
diagnosis
17
creative, selective

• what is abduction?
• theoretical abduction
• (sentential, model-based)
• manipulative abduction
• (mathematical diagrams, construals)

scientific discovery
diagnosis
18
SENTENTIAL
Theoretical Abduction
MODEL-BASED
19
Model-based cognition

• Simulative reasoning
• Analogy
• Visual-iconic reasoning
• Spatial thinking
• Thought experiment
• Perception, sense activities
• Visual imagery
• Deductive reasoning(Beths
• method of semantic tableaux,
• Girards geometry of proofs, etc.)
• Emotion

SENTENTIAL
Peirce stated that all thinking is in signs, and
signs can be icons, indices, or symbols.
Moreover, all inference is a form of sign
activity, where the word sign includes feeling,
image, conception, and other representation (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 model-based reasoning acquires its
peculiar creative relevance when embedded in
abductive processes
Theoretical Abduction
MODEL-BASED
20
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
21
Thinking through doing
Construals
Manipulative Abduction
22
Cognitive Mediators and External Models and
Representations
CONJECTURAL TEMPLATES I (they act on external
representation and originate epistemic mediators)
Ampére frame

• curious and anomalous phenomena
• dynamical aspects
• artificial apparatus
• epistemic acting

turbulent dissipation and diffusivity
apparatus to measure paleomagnetization of samples
Turing Universal Practical Computing Machine (PCM)
looking
re-ordering, changing relationships
choosing, discarting, imaging further
manipulations
checking the information
comparing events
23
CONJECTURAL TEMPLATES II

• simplification of the reasoning task
• treatment of incomplete and inconsistent
  information
• control of sense data
• external artifactual models
• natural objects and phenomena

24
Samples, Induction, Abduction
If we do not think of inductive generalizations
as abductions we are at a loss to explain why
such inference is made stronger and more
warranted, if in connecting data we make a
systematic search for counter-instances and
cannot find any, than it would be just take the
observation passively. Why is the generalization
made stronger by making an effort to examine a
wide variety of types of As? The answer is that
it is made stronger because the failure of the
active search of counter-instances tend to rule
out various hypotheses about ways in which the
sample might be biased, that is, is strengthens
the abductive conclusion by ruling out
alternative explanations for the observed
frequency (Josephson 2000)
If we think that a sampling method is fair and
unbiased, then straight generalization gives the
best explanation of the sample frequencies. But
if the size is small, alternative explanations,
where the frequencies differ, may still be
plausible. These alternative explanations become
less and less plausible as the sample size grows,
because the sample being unrepresentative due to
chance becomes more and more improbable. Thus
viewing inductive generalization as abductions
show why sample size is important. Again, we see
that analyzing inductive generalizations as
abductions shows us how to evaluate the strengths
of these inferences (Josephson, p. 42).
Manipulative abduction can be considered a kind
of basis for further meaningful inductive
generalizations. For example different construals
can give rise to different inductive
generalizations. If an inductive generalization
is an inference that goes from the
characteristics of some observed samples of
individuals to a conclusion about the
distribution of those characteristics in some
larger populations (Josephson) what
characterizes the sample as representative is
its effect (sample frequency) by reference to
part of its cause (populations frequency) this
should be considered a conclusion about its
cause.

• Samples and Manipulative Abduction
• Construals Manipulative abduction is the correct
  way for describing the features of what are
  called smart inductive generalizations'', as
  contrasted to the trivial ones. For example, in
  science construals can shed light on this process
  of sample production'' and appraisal''
  through construals, manipulative creative
  abduction generates abstract hypotheses but in
  the meantime can originate possible bases for
  further meaningful inductive generalizations
  through the identification of new samples (or of
  new features of already available sample, for
  instance in terms of the detection of relevant
  circumstances). Different generated construals
  can give rise to different plausible inductive
  generalizations.

25
mimetic external representations mirror
concepts and problems that are already
represented in the brain and need to be enhanced,
solved, further complicated, etc. MANIPULATIVE
ABDUCTION - NON-DEMONSTRATIVE - IS AN ASPECT OF
THIS INTERPLAY MIND transcends the boundary of
the individual and includes parts of that
individuals environment
Mimetic Representationsand their Non-Deductive
Effect
At this stage the patterns of neural activation
no longer need a direct stimulus from the
environment for their construction and fixation.
In a certain sense they can be viewed as fixed
internal records of external structures that can
exist also in the absence of such external
structures. These patterns of neural activation
that constitute the First-Level Representations
always keep record of the experience that
generated them and, thus, always carry the
Second-Level Representation associated to them,
even if in a different form, the form of memory
and not the form of a vivid sensorial experience.
Now, the human agent, via neural mechanisms, can
retrieve these Second-Level Representations and
use them as internal representations or use parts
of them to construct new internal representations
very different from the ones stored in memory.
This explains why human beings seem to perform
both computations of a connectionist type such as
the ones involving representations as - (I
LEVEL) patterns of neural activation that arise
as the result of the interaction between body and
environment (and suitably shaped by the evolution
and the individual history) pattern completion
or image recognition, and computations that use
representations as - (II LEVEL) derived
combinatorial syntax and semantics dynamically
shaped by the various external representations
and reasoning devices found or constructed in the
environment (for example geometrical diagrams)
they are neurologically represented contingently
as pattern of neural activations that sometimes
tend to become stabilized structures - stabilized
thoughts - and to fix and so to permanently
belong to the I LEVEL
the I level originates those sensations (they
constitute a kind of face we think the world
has), that provide room for the II level to
reflect the structure of the environment, and,
most important, that can follow the computations
suggested by these external structures. the
growth of the brain and especially the synaptic
and dendritic growth are profoundly determined by
the environment
- external representations are formed by
external materials that express (through
reification) concepts and problems that do not
have a natural home in the brain. - internalized
representations are internal re-projections, a
kind of recapitulations, (learning) of external
representations in terms of neural patterns of
activation in the brain. They can be internally
manipulated like external objects and can
originate new internal reconstructed
representations through the neural activity of
transformation and integration.
we no longer need Descartes dualism we only have
brains that make up large, integrated, material
cognitive systems like demonstrative systems,
non-demonstrative tools, LCMs and PCMs, etc. the
only problem is How meat knows (sum ergo
cogito?)
DESCARTES mind-body dualism
26

• LOGICAL IDEAL ABDUCTIVE and INDUCTIVE SYSTEMS
• - symbolic they activate and anchor meanings
  in material communicative and intersubjective
  mediators in the framework of the phylogenetic,
  ontogenetic, and cultural reality of the human
  being and its language. They originated in
  embodied cognition and gestures we share with
  some mammals but also non mammals animals (cf.
  monkey knots and pigeon categorization, Grialou,
  Longo, and Okada, 2005)
• - abstract they are based on a maximal
  independence regarding sensory modality strongly
  stabilize experience and common categorization.
  The maximality is especially important it refers
  to their practical and historical invariance and
  stability
• rigorous the rigor of proof is reached through a
  difficult practical experience. For instance, in
  the case of mathematics, as the maximal place for
  convincing reasoning. Rigor lies in the stability
  of proofs and in the fact they can be iterated.
• Mathematics is the best example of maximal
  stability and conceptual invariance.

• Flach and Kakas (2000). A useful perspective on
  integration of abduction and induction
• explanation (hypothesis does not refer to
  observables selective abduction but abduction
  creates new hypotheses too)
• generalization genuinely new (hypothesis can
  entail additional observable information on
  unobserved individual, extending the theory T)
• Imagine we have a new abductive theory T T ?
  H constructed by induction an inductive
  extension of a theory can be viewed as set of
  abductive extensions of the original theory T.
• controversies on IAI are of course open and alive

• cf. the cognitive analysis of the origin of the
  mathematical continuous line as a pre-conceptual
  invariant of three cognitive practices
  (Theissier, 2005), and of the numeric line
  (Châtelet, 1993 Dehaene, 1997 Butterworth,
  1999).

• logical systems are in turn sets of proof
  invariants, sets of structures that are preserved
  from one proof to another or which are preserved
  by proof transformations. They are the result of
  a distilled praxis, the praxis of proof it is
  made of maximally stable regularities.

• MAXIMIZATION OF MEMORYLESSNESS characterizes
  demonstrative reasoning. Its properties do not
  yield information about the past, contrarily for
  instance to the narrative and not logical
  descriptions of non-demonstrative processes,
  which often involve historical, contextual,
  and heuristic memories.

27
Thanks lorenzo.magnani_at_unipv.it