Dynamic Learning Situations

blabbedharborIA et Robotique

23 févr. 2014 (il y a 3 années et 3 mois)

45 vue(s)

Interpretations of the Growth of Knowledge in
Dynamic Learning Situations

András Benedek

Inst. of Philosophy, Research Centre for the Humanities, HAS


Cranach,
Tree of Knowledge

(1472)



benedek@webmail.phil
-
inst.hu

Motto:



If you have an idea and I have an idea and we exchange these ideas,

then will each of us have two ideas…?”

(After G.B. Show)

A Plausible
Thes
is

Motivation:

A

common assumption lurking behind the debates of the 60ies
:


"If you have an apple and I have an apple and we exchange apples then you and I will still each have one apple.

But if you have an idea and I have an idea and we exchange these ideas, then each of us will have two ideas
.
"

K
nowledge does grow as a result of collaboration and information exchange

Attributed to G.B. Show

Trivial

(local)
counterexample
s:

…to (re)interpret the


Growth of
Knowledge

in dynamic (logical) terms


Good old
-
fashioned Questions

(to be reconsidered)



What
is it
that is growing?


What

constitutes knowledge
?


What
kinds

of knowledge are growing?


What exactly is ‘
growing

(if anything)

in case of the different types

of knowledge
?


What is ‘Growth’?


What do we mean by
(
the)


growth
’ (of knowledge)?


What does
‘growth’

consist
of?


How is it measured?


How do we detect growth?

(
Triggers, Statistics, Indicators
)


How do we represent growth?

(
Orderings,
Patterns,
Measures
?)


How could the ‘
mechanics’ of growth processes be described
?


Temporal

dynamics of learning?


What kind of dynamic models we have for the description of changes in
epistemic states as growth of knowledge?



Does Human
Knowledge
d
ouble
in
e
very 5
>3>…

y
ears?

What is growing?



Knowledge in „object(tive)” forms
(Books, Data Stores, Wikis,
Scientific Journals, Papers, Cross References, etc.)


The ‘Third World’
(Sets of Propositions, Problems, Theories,
Models, Proofs, Methods,…)


The Fields of inquiry

(New Questions, Subjects, Frameworks)


Knowledge collectives
(Shared understandings, Reflection,

Awareness, Common (Global) Knowledge


What

kind

of
knowledge
?



Theoretical



Tacit



Propositional



Empirical



Organizational


/Institutional/Social/



Procedural


/Strategic, Methodological/

What

constitutes knowledge
?


-
Types of

propositional(ly based) knowledge




Individual
/Single
-
agent/Multi
-
agent/



Factual /
Hypotetical/Normativ/


Collective
/Distributed/Group /Common/Knowledge Networks



Explicit/Implicit

-
Conceptions of knowledge


Theoretically grounded accumulating

evidence /
Warranted belief



Justified True Belief,


Defeasable/Undefeasible knowledge


Perceptual

(enactive)

knowledge, etc.


A
ny piece of information that promotes

the solution of a task

(AI)



Reflexive
/Mutual/Higher Order/…

What

kind

of
knowledge
?

What
is

G
rowth’
?


What

does Growth consist
of? /
How is it measured?



Closeness / Convergence to the truth



Changes in
Relations bw. Theories

and Models /
Theory change




More people know it / # of

Knowers/Organizations/
CoP/
Networks



Higher Degree of Belief /
Plausibility

/



Higher levels of
reflexivity



Increase in
truthlikeness/verisimiltude
/factual content,

etc.



Higher Measure of
P
robability / Utility




Elimination of possibilities

/ possible worlds / uncertainity



Inductive generalization

Dynamics of learning


Changes in knowledge states are triggered by


incoming semantic information, and


epistemic action(s), including


higher order reflection on the knowledge states of
others

Formal description of the effects of semantic
information

on
communicating agents require
epistemic models

of

change


in

knowledge s
tates,
(represented by

logic structures
)

Brookes’ ‘fundamental equation’:

K
[
S
] +
Δ
I
=
K
[
S
+ Δ
S
]

Δ
I
changes
K
[
S
]

to
K
[
S

+ Δ
S
]
where
K
[
S
+ Δ
S
]
is the changed
knowledge structure
, i.e.,


information

modifies

knowledge
states/
structures



Dynamic logic models of

changing knowledge states as a result of
communication



A: “B, do you have red?”


Bob:“No”


„Dynamics”:

Temporal development
of
agents’ knowledge states

restr
i
cted by „rules”


L
abeled transition system
s


represented by graphs

Other typical examples
: ‘100

prisoners

and a
light bulb’, ‘Russian cards
’, etc.

Epistemic
L
ogic
s

emerging from Hintikka’s Knowledge and Belief (1962)
set the
background of
modeling

information flow

AND

knowledge


in

a
common
framework

model the effect of information as a
dynamic process
.

Updates

Upgrades

Revisions

Various operations in
Dynamic Epistemic Logic
(DEL)

represent
the changes:


Current issues: Models of information flow describe meaningful
interactions between agents as abstract models of “
social software
”.

Dynamic L
ogic
M
odels

of
I
nformation
E
xchange

Tools for Modeling Growth

Growth process
:

(iterated)
belief revision

/ upgrades

with
new
(
true
/reliable)

information

Group level

revision induced by
communication

between

members of the group

Assumptions
: e.g. s
incerity:
members

already accept th
e

information
(before

sharing it).

Higher
-
level (doxastic) information
: may refer to the

agents' own
beliefs
, or even to their
belief
-
revision plans
.


Construction of semantic representations

Local epistemic states / states of the the environment

(shared statemens + public announcements
,

e.g.
)

Representation of communication protocols (e.g.
in
PAL)

Interpreted scenarios of
information flow

(transitions
of knowledge
)

Kripke
structures

in DEL


In finite models, any announcement with a proposition ϕ has an update which
can be generated equivalently by a proposition which becomes common
knowledge after its announcement.

Epistemic Models

Dynamic Consequence


Conclusion
ϕ follows dynamically
from
P
1
, . . . , Pk
if, after public announcements of
the successive premises, all worlds in the new information state satisfy
ϕ

:


Group Knowledge

Combining individual knowledge to
explicit Group Level


Summative Collective Attitudes (defined in terms of individual attitudes)


Shared Belief


Mutual Belief


Distributed Knowledge


Common Knowledge

But we also have Non
-
Summative Collective Attitudes

(The fact that all of the group members believe that P is neither sufficient nor necessary

for a group belief that P)

.


Group Knowledge and Full Communication

There is a way of choosing the parameters such that distributivity is not trivialised.

Full communication, as a weak variant of distributivity may not be guaranteed.

Van der Hoek, van Linder and Meyer gave properties on Kripke models that guarantee

that group knowledge does allow full communication.

Their results can be extended to models equipped with specific communication structures.

Instead of being able to communicate with each other, we may say that the G
-
knowledge
is just the knowledge of one distinct agent, (the `wise man') to whom all the agents
communicate their knowledge that he combines to end up with the knowledge that
previously was implicit. (Growth: implicit knowledge upgraded to explicit knowledge)

Communication Structures


C
ommunication
graphs


R
elational algebras


Galois lattice
s


H
yper graphs

CS
:
Relations
bw.

communicating agents (
learners
,
players of a
game, CoP
, etc)

represented by various relational structures

L
ogic
M
odels of the dynamics of information exchange
,

may depend on


-

communication structures (CS),

and


-

communication protocols (CP)


N.B.: Applications to social
networks

Communication Protocols

(CP)

E.g.:


Security policies, Secrecy


Rules
for

making private information
public
,



Sincerity conditions,


Orders of
epistemic actions, c
ommunication
s
,

temporal or historical possibilities


Restrictions: e.g., o
nly (hard) factual information is communicated,


Soft (
e.g.
communicated
, non
-
reliable
)
i
nformation is allowed,


Higher order epistemic information is communicated/restricted,


Bounds on levels

of Reflection

Rules/Regulations/Patterns
/Procedures

that govern

knowledge
transfer

Communication Protocols in DEL

Freedom of Speech:

No Hiding:

Telling the Truth:

PAL


The language of
public announcement logic PAL
can be considered as the prototipical
epistemic language, with added expressions of epistemic actions:

The modal operator [
ϕ
] (‘after publicly announcing ’) is interpreted as an epistemic state
transformer: the model
M

|
ϕ

is the model
M

restricted so as to only contain worlds in
which
ϕ

is true.


Schematic validities

Common Knowledge




DEL
provides the techniques for carrying

out the epistemic updates

Gives logical means to reason

about
and
express common knowledge of groups of agents:

' is common knowledge in group G if ' is true in all worlds that are

reachable by a series of g
-
steps (with g 2 G) from the current world.

Example:

Modelling what goes on in Card Games

Alice

(1)
, Bob
(2)

and Carol

(3)

each hold one of cards p, q, r.

The actual deal is:

1
holds p,
2
holds q,
3
holds r.

After all players have looked

at their own cards they consider

what the others may know.

For common knowl
edge you have to compute
the transitive closure of the union of the

accessibility relations

A

fi
xpoint procedure for making a relation tran
sitive

goes like this:

1. Check if all two
-
step transitions can be done in a single step.

2.
If so,the relation is transitive, and done.

3
. If not, add all two
-
step transitions as new links, and go back to 1.


Coordinated

Attack Problem
: Common knowledge cannot be achieved in the absence
of a simultaneous event (Public Announcement)

Problems


Formalize higher
-
order cognition for
different agent
types

Resource
-
bounded logics by capabilities


dynamic inference, induction


reflection,


recursion,


update


revision,


upgrade

Extend with realistic components for
group reasoning


Common belief


Common knowledge


Collective intention


Collective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge


􀂊

logical omniscience


􀂊

positive and negative introspection


􀂊

unbounded recursion


Upgrades


Upgrades that may represent
Growth

Gierasimczuk, N. (2009) Bridging learning theory and dynamic epistemic logic
:

the elimination process of learning by erasing can be seen as iterated belief
-
revision

Pacuit. E. and Simon, S. (2011): Reasoning with Protocols under Imperfect Information.


Our
k
nowledge
R

of what the others know

depends

on


CP


CS


K
i
(CS)

Dependencies

of

R
eflexive
K
nowledge
(K
R
)

Synchronous communication = message sent to a whole group

As
ynchronous communication = message sent in serial/temporal order


Alternative (refined!) solutions to „Coordinated Attac Problems”


There are formulas that the agents may come to know that are not explicitly
contained in their communications.



Essentially, these are facts that the agents can derive given their knowledge of
the
structure of the communication graph

and

the
initial distribution of facts
.

Thank you

!

Questions
?

Comments
?

References

T.
Ågotnes
, P.
Balbiani
, H. van
Ditmarsch

and P.
Seban
, 2010,
Group
Announcement

Logic
, Journal of
Applied

Logic

8
(1).

van
Benthem
, J. 2010,
Logical

Dynamics of
Information

and
Interaction
,
Cambridge University Press.

J. van
Benthem
, J. van
Eijck

& B.
Kooi
, 2006, ‘
Logics

of
Communication

and
Change
’,
Information

and

Computation

204, 1620

1662.

van
Benthem
, J., T.
Hoshi
, J,
Gerbrandy
, E.
Pacuit
, 2009, ‘
Merging

Frameworks

for

Interaction
’,
Journal of
Philosophical

Logic

38(5)
, 491

526.

van
Benthem
, J., and
Pacuit
, E. 2006, ‘The
tree

of
knowledge

in

action
:
Towards

a
common

perspective
.’
In

Proceedings

of
Advances

in

Modal

Logic

Volume

6
, G.
Governatori
,
I.
Hodkinson
, and Y.
Venema
,
Eds
.
King's

College Press.

H. van
Ditmarsch
, W. van der
Hoek

& B.
Kooi
, 2007,
Dynamic
-
Epistemic

Logic
,
Synthese

Library

337, Springer, Berlin.

Bird
, A. (2008): ‘
Scientific

Progress

as

Accumulation

of
Knowledge

A
Reply

to

Rowbottom
’,
Studies

in

History

and
Philosophy

of Science
39, 279

281.

Fahrbach
, L. (2011):
How

the

Growth

of Science Ended
Theory

Change
.
Synthese
, 180(2):139
-
155.

J.Y.
Halpern

and Y.O.
Moses
. (1990):
Knowledge

and
common

knowledge

in

a
distributed

environment
. Journal of
the

ACM,
37(3):549
-
587.

R. Fagin and J.Y.
Halpern
, 1989, ‘Modelling
knowledge

and
action

in

distributed

systems
. ’
Distrib
.
Comput
. 34, pp. 159

179.

Fagin, R,
Halpern
, J.Y, Moses, Y, and
Vardi
, M.Y., 1995,
Reasoning about knowledge
. The MIT Press: Cambridge, MA.

Floridi
, L
, 2004, "
Outline

of a
Theory

of
Strongly

Semantic

Information
",
Minds

and
Machines
, 14(2), 197
-
222.

Floridi
, L
, 2005, "Is
Information

Meaningful

Data?"
Philosophy

and
Phenomenological

Research
, 70(2): 351

370.

Hendricks
, V .F. and
Symons
, J., 2006, ‘
Where

is
the

Bridge
?
Epistemology

and
Epistemic

Logic

Philosophical

Studies
,
Vol
. 128, pp 137
-
167.

T
Hoshi

& A.
Yap
, 2009, ‘
Dynamic

Epistemic

Logic

with

Branching

Temporal

Structure
’,
Synthese

169, 259

281.

Th.
Icard
, E.
Pacuit

& Y.
Shoham
, 2009, ‘
Intention

Based

Belief

Revision
’,
Departments

of
Philosophy

and Computer Science, Stanford University.

D. Israel & J.
Perry
, 1990, ‘
What

is
Information
?’,
in

P. Hanson,
ed
.,
Information
,
Language

and
Cognition
. University of British Columbia Press, Vancouver.

Meyer, Ch. and van
der

Hoek
, W., 1995,
Epistemic Logic for AI and Computer

Science
. Cambridge University Press: Cambridge, England.

van
Ditmarsch
, H, van
der

Hoek
, W, and
Kooi
, B., 2007,
Dynamic Epistemic Logic,
Springer, Berlin.

Fitzgerald
, L.A. and van
Eijnatten
, F.M., 1998, “
Letting

Go
For

Control
: The Art of
Managing

the

Chaothic

Enterprise
”,
The International Journal of Business
Transformation
,
Vol
. 1, No. 4,
April
, pp 261
-
270.

K
ing,
Wr
.

(2006) Knowledge transfer. In Encyclopedia of Knowledge

Management (SCHWARTZ DG, Ed), pp 538

543, Idea Group Reference,

Hershey
, PA.

S. van
Otterloo
, 2005,
A
Strategic

Analysis

of
Multi
-
Agent

Protocols
,
Dissertation

DS
-
2005
-
05, ILLC, University of Amsterdam & University of Liverpool.

Nonaka

I. and
Takeuchi

H., (1995) The
Knowledge

Creating

Company
. Oxford University Press.

Oxford, New York. UK.

R.
Parikh
, 2002, ‘
Social

Software’,
Synthese

132, 187

211.

Parikh
, R., &
Ramanujam
,
R
. (2003). A
knowledge

based

semantics

of
messages
.
Journal

of
Logic
,
Language

and
Information
,
12
, 453

467.

M.
Pauly
, 2001,
Logic

for

Social

Software
,
dissertation

DS
-
2001
-
10, Institute

for

Logic
,
Language

and
Computation
, University of Amsterdam.

J.
Peregrin

(
ed
.), 2003,
Meaning
:
the

Dynamic

Turn
,
Elsevier
, Amsterdam

O. Roy, 2008,
Thinking

before

Acting
:
Intentions
,
Logic
, and
Rational

Choice
,
Dissertation
, Institute
for

Logic
,
Language

and
Computation
, University of Amsterdam.

J.
Sack
, 2008, ‘
Temporal

Language

for

Epistemic

Programs
’,
Journal of
Logic
,
Language

and
Information

17, 183

216.