Information Loss Versus Information Degradation
From: AAAI Technical Report FS-94-02. Compilation copyright © 1994, AAAI (www.aaai.org). All rights reserved.
Information Deductively sense
that
any
conclusion.
It
validity
central
not
always
Elena
it
even
is
prized
preserving
premises
yields
quality
quality,
deductively
of
the
a true
deductive
truth
valid
information
in
being
one
transitions
preserving.
of are
For
from and Alan is in is in Venice.
Sydney
a consistent
and
hundred
Elena
is
in
Rome
conjunct
conclusion
in Rome
deductively
information preserve
true
a much
to be
the
Degradation
truth
preserving
typically
above
- to
from
However
York John
are
truth
transition
conjunction
though
makes
the
Information
transitions
this
is in New . . . and
- imagine
Versus
transition
concerns.
the
(A) Ken and
(B)
is
or
instance
valid such
that
our
Loss
valid
preserving
the
is
in
an
obvious
transition.
information
about
(B),
Alan’s
sense for
not
an
instance,
whereabouts
does
contained
not in
(A). Information in
preservation
inferential
makes
the
transitions.
transition
particular
bit
interest
focused
from
to
(A)
a conclusion though
the However
qualitative conjunct
is not
of
(B)
from
not
a large
information solely
is more
containing latter
Sometimes
on
our
highly
the
the
losses
par.
Compare
conjunction
(A)
whereabouts then 50
has
more
base
transition
to
a
Given
an
a transition
a transition
from
conjuncts
information are from
of (A)
than on our
quality interests
of Elena
or so
of information
84
particular
desirable.
first
the
a desirable
information
appropriate
conclusion all
always
(B).
a hundred
(A) even
(C)
Elena
and
the
(D)
Elena
Both of
transition is
(A) the
in Rome
to
(D)
(A)
to
terms
of ~ is
(DI)
say
is
transition
of
loss
[1994]
is
Sydney. both
How the
are
kind
we
to
a notion
standard
we
of
a diminution
information
that
is
separate
not the
in
shared first
second?
I introduced of the
involve
a degradation
a particular
from
Thus
in
have
of content
defined
deductive
consequence
informal
definition,
the
in
stronger not
than
~ if and
deductively
between
of the
only
entail
content two
if
a deductively
entails
@.
may
be
different
used
to
kinds
characterize
the
of information
loss
above. One
that
thing
while the
However
this
Indeed
that
our
entails
this
characterizes
hundred
conclusion is
equally
gives
transition
(C),
itself
not
entail
(C)
true
of the
criteria
involves
a loss
of information thing
does
second
(A)
of what
information.
one
(C)
deductively
a clear
note,
to
(A)
of
Now
(A)
conjunction
a loss
A.
the
conjunct
involves
entail
not
valid,
transition.
conception
difference noted
Alan
a content part of ~ =df ~ is deductive a consequence of @ and there is no deductive consequence a of ~ such that o is stronger than ~ and a contains only (non-logical) vocabulary that occurs in
~ does This
(A)
there
formulae.
a is
but
in Sydney
deductively
of a partition
classes
is
However
(C)
Gemes
Alan
or
are
of information In
and
from
transitions
kind
We
in Rome
information.
the by
is
A transition if that
85
A entails separates
to (D)
kind
of
from B but the
transition.
transition A to B does two
B not
transitions
is
that
content not
part
from
(A)
(A),
whereas
a transition
to
a content
of (A)
stronger
statable
vocabulary
of
from
does
not
transition
to
(A) have
of
vocabulary).
maximum
then
own is
the
In
(D)
bang
an
On
(A) is
than)
which
is
not
intuitive bang
the
(D) a content
of
(D)
(A)
and
sense
the
(information)
other
hand
a transition
for
to
a consequence
maximum
involves
a consequence
in its
Here
(C)
(D)
(A).
is
(D).
has
from
information
to
to
of
(C)
the
is a transition
transition
instance, more
(A)
(C)
part
(contains
(richness
transition
statable
for
to
the
than
from
buck
that
since,
in
inference the
transition of
part is
the
the
to a consequence
the
buck.
It
the
strongest
is
not
a
consequence
vocabulary.
a way loss
of
and
specifying
the
information
difference
between
mere
information
(D2)
The transition from ~ to ~ involves an entails @ and ~ does not entail ~.
(D3)
The transition from ~ to @ involves a degradation of information when ~ entails ~ but ~ is not a content part
the
degradation information
loss
when
of
8. The
transition
from
(A)
information
degradation.
information
loss
More transition to
an
(D4)
with
polemically that
irrelevant
to
(C)
The
involves transition
information we
involves
might
from
(A)
to
loss
without
(D)
involves
degradation.
say
information
consequence.
information
Thus
that
a deductively
degredation we
have
the
is
valid a transition
definition
~ is an irrelevant consequence of ~ =df. ~ is a consequence of ~ and there is some consequence a of ~ such that a is stronger than ~ and all of a’s (non-logical) vocabulary occurs in ~. (i.e. ~ is consequence but not a content part of ~). Generally
transitions
that
86
involve
information
loss
are
tolerable, the
and
culling
indeed
of
a single
containing
millions
involving
information
consequences, an
checks so
who
his
number
is
882-3232 (DI)
purposes
the
of
that
data
represented
by
For machine
(e.g.
procedure loss.
Gemes
decision
of
is
imagine
Jones
882-3232 way
this
and
"The
a given
demonstrates for
~ to So
testing
87
claim from
no
rather
Jones
is
information
the
the
is
in
detective’s
a content
sets than
in
that
’Jones
longer
there
testing wff
are
other
part
optimally sets
there
that
are if
well
of
the
known
transition
~ is deductively is
transition
if
that
about
beliefs.
for
method).
irrelevant
belief
languages
(wff)
if
it is
for
information
expunged
agent’s
algorithms
testing
[1994]
be
parts
propositional
table
point
that
content
formula
seeking
gets
At
relevant
of
he
suggests
of
banks
utilized
Later
- since
This
be
learns
set
procedure
instance,
number
he
belief
formed
for
base
irrelevant
number
first
may
truth
to
degrading
also
is
Hobart’
of the
the
At
Hobart.
implementable
well
can
or
sets
formal
a data
of
transitions
For
phone
the
information
Sydney.
bank.
consequences
from
in
- his
the
a detective
or
Melbourne
bank
avoided.
information
of content
Jones.
Melbourne
Sydney, data
of
Jones
be
think
or 256-9794."
Suppose
pinpoints
However
realizes
but
from
transitions
about
base
of trimming
whereabouts
Sydney,
queried
notion
information.
to
instance,
number
numbers.
generally
when
For
phone
degradation,
in a truthful
The the
phone
information
replies
desirable.
desired
of
are
operator
often
there
a mechanical involves is
propositional
valid decision
information
a mechanical wff
~ is
a
content
part
decision
of
procedure
To
see
normal
form
entailed
is
for
form
example
ordering
of
If
part
the
conjuncts
of
our
test
the
content
content
of
Gemes extended
its
entailed
more
a mechanical
degradation.
proper
and
is
of ~ put
~ in
(minimal)
sub-disjunct
provided
Boolean
~ itself
normal
disjuncts)
of
’(p&r)’
entails
correct On
since
of
[1994a]
to
some
there
of is
that
entailed
~.
Now
the
’(p&r)’
- is
if
of
So
content
not,
and
’(p&r)’.
sub-disjunction itself
information
’(p&q)v(p&~q)v(~&q)’,
delivers
of
for
(minimal)
’(p&q)v(p&-q)v(~p&q)’. disjunction
@.
the
test
@.
~, ~ is a content For
of
and
by
wff
testing
if ~ is part
Boolean
by
propositional
it
the
minimal
’(p&q)v(p&~q)’, ’(pvq)’
hand
is entailed Boolean
up
a proper
that
other
(unique
’(pvq)’
namely
result
form
’p’
is
not
part
is
part
of
the
by ’(p&r)’
and
no
proper
normal
form
- being
’p’
by ’(p&r)’. shows
complex
how
the
definitions
quantificational
of
content
may
be
languages. Ken Gemes Department of Philosophy Yale University [email protected]
References Gemes,
K.
[1994],
"A
New
JournalofPhilosophicalLogic,
Notion of Content I: September 1994.
Gemes,
K. [1994a], "A New Notion Accounts", forthcoming.
88
of
Content
II:
Basic
Content,"
Model-Theoretic
Information Deductively sense
that
any
conclusion.
It
validity
central
not
always
Elena
it
even
is
prized
preserving
premises
yields
quality
quality,
deductively
of
the
a true
deductive
truth
valid
information
in
being
one
transitions
preserving.
of are
For
from and Alan is in is in Venice.
Sydney
a consistent
and
hundred
Elena
is
in
Rome
conjunct
conclusion
in Rome
deductively
information preserve
true
a much
to be
the
Degradation
truth
preserving
typically
above
- to
from
However
York John
are
truth
transition
conjunction
though
makes
the
Information
transitions
this
is in New . . . and
- imagine
Versus
transition
concerns.
the
(A) Ken and
(B)
is
or
instance
valid such
that
our
Loss
valid
preserving
the
is
in
an
obvious
transition.
information
about
(B),
Alan’s
sense for
not
an
instance,
whereabouts
does
contained
not in
(A). Information in
preservation
inferential
makes
the
transitions.
transition
particular
bit
interest
focused
from
to
(A)
a conclusion though
the However
qualitative conjunct
is not
of
(B)
from
not
a large
information solely
is more
containing latter
Sometimes
on
our
highly
the
the
losses
par.
Compare
conjunction
(A)
whereabouts then 50
has
more
base
transition
to
a
Given
an
a transition
a transition
from
conjuncts
information are from
of (A)
than on our
quality interests
of Elena
or so
of information
84
particular
desirable.
first
the
a desirable
information
appropriate
conclusion all
always
(B).
a hundred
(A) even
(C)
Elena
and
the
(D)
Elena
Both of
transition is
(A) the
in Rome
to
(D)
(A)
to
terms
of ~ is
(DI)
say
is
transition
of
loss
[1994]
is
Sydney. both
How the
are
kind
we
to
a notion
standard
we
of
a diminution
information
that
is
separate
not the
in
shared first
second?
I introduced of the
involve
a degradation
a particular
from
Thus
in
have
of content
defined
deductive
consequence
informal
definition,
the
in
stronger not
than
~ if and
deductively
between
of the
only
entail
content two
if
a deductively
entails
@.
may
be
different
used
to
kinds
characterize
the
of information
loss
above. One
that
thing
while the
However
this
Indeed
that
our
entails
this
characterizes
hundred
conclusion is
equally
gives
transition
(C),
itself
not
entail
(C)
true
of the
criteria
involves
a loss
of information thing
does
second
(A)
of what
information.
one
(C)
deductively
a clear
note,
to
(A)
of
Now
(A)
conjunction
a loss
A.
the
conjunct
involves
entail
not
valid,
transition.
conception
difference noted
Alan
a content part of ~ =df ~ is deductive a consequence of @ and there is no deductive consequence a of ~ such that o is stronger than ~ and a contains only (non-logical) vocabulary that occurs in
~ does This
(A)
there
formulae.
a is
but
in Sydney
deductively
of a partition
classes
is
However
(C)
Gemes
Alan
or
are
of information In
and
from
transitions
kind
We
in Rome
information.
the by
is
A transition if that
85
A entails separates
to (D)
kind
of
from B but the
transition.
transition A to B does two
B not
transitions
is
that
content not
part
from
(A)
(A),
whereas
a transition
to
a content
of (A)
stronger
statable
vocabulary
of
from
does
not
transition
to
(A) have
of
vocabulary).
maximum
then
own is
the
In
(D)
bang
an
On
(A) is
than)
which
is
not
intuitive bang
the
(D) a content
of
(D)
(A)
and
sense
the
(information)
other
hand
a transition
for
to
a consequence
maximum
involves
a consequence
in its
Here
(C)
(D)
(A).
is
(D).
has
from
information
to
to
of
(C)
the
is a transition
transition
instance, more
(A)
(C)
part
(contains
(richness
transition
statable
for
to
the
than
from
buck
that
since,
in
inference the
transition of
part is
the
the
to a consequence
the
buck.
It
the
strongest
is
not
a
consequence
vocabulary.
a way loss
of
and
specifying
the
information
difference
between
mere
information
(D2)
The transition from ~ to ~ involves an entails @ and ~ does not entail ~.
(D3)
The transition from ~ to @ involves a degradation of information when ~ entails ~ but ~ is not a content part
the
degradation information
loss
when
of
8. The
transition
from
(A)
information
degradation.
information
loss
More transition to
an
(D4)
with
polemically that
irrelevant
to
(C)
The
involves transition
information we
involves
might
from
(A)
to
loss
without
(D)
involves
degradation.
say
information
consequence.
information
Thus
that
a deductively
degredation we
have
the
is
valid a transition
definition
~ is an irrelevant consequence of ~ =df. ~ is a consequence of ~ and there is some consequence a of ~ such that a is stronger than ~ and all of a’s (non-logical) vocabulary occurs in ~. (i.e. ~ is consequence but not a content part of ~). Generally
transitions
that
86
involve
information
loss
are
tolerable, the
and
culling
indeed
of
a single
containing
millions
involving
information
consequences, an
checks so
who
his
number
is
882-3232 (DI)
purposes
the
of
that
data
represented
by
For machine
(e.g.
procedure loss.
Gemes
decision
of
is
imagine
Jones
882-3232 way
this
and
"The
a given
demonstrates for
~ to So
testing
87
claim from
no
rather
Jones
is
information
the
the
is
in
detective’s
a content
sets than
in
that
’Jones
longer
there
testing wff
are
other
part
optimally sets
there
that
are if
well
of
the
known
transition
~ is deductively is
transition
if
that
about
beliefs.
for
method).
irrelevant
belief
languages
(wff)
if
it is
for
information
expunged
agent’s
algorithms
testing
[1994]
be
parts
propositional
table
point
that
content
formula
seeking
gets
At
relevant
of
he
suggests
of
banks
utilized
Later
- since
This
be
learns
set
procedure
instance,
number
he
belief
formed
for
base
irrelevant
number
first
may
truth
to
degrading
also
is
Hobart’
of the
the
At
Hobart.
implementable
well
can
or
sets
formal
a data
of
transitions
For
phone
the
information
Sydney.
bank.
consequences
from
in
- his
the
a detective
or
Melbourne
bank
avoided.
information
of content
Jones.
Melbourne
Sydney, data
of
Jones
be
think
or 256-9794."
Suppose
pinpoints
However
realizes
but
from
transitions
about
base
of trimming
whereabouts
Sydney,
queried
notion
information.
to
instance,
number
numbers.
generally
when
For
phone
degradation,
in a truthful
The the
phone
information
replies
desirable.
desired
of
are
operator
often
there
a mechanical involves is
propositional
valid decision
information
a mechanical wff
~ is
a
content
part
decision
of
procedure
To
see
normal
form
entailed
is
for
form
example
ordering
of
If
part
the
conjuncts
of
our
test
the
content
content
of
Gemes extended
its
entailed
more
a mechanical
degradation.
proper
and
is
of ~ put
~ in
(minimal)
sub-disjunct
provided
Boolean
~ itself
normal
disjuncts)
of
’(p&r)’
entails
correct On
since
of
[1994a]
to
some
there
of is
that
entailed
~.
Now
the
’(p&r)’
- is
if
of
So
content
not,
and
’(p&r)’.
sub-disjunction itself
information
’(p&q)v(p&~q)v(~&q)’,
delivers
of
for
(minimal)
’(p&q)v(p&-q)v(~p&q)’. disjunction
@.
the
test
@.
~, ~ is a content For
of
and
by
wff
testing
if ~ is part
Boolean
by
propositional
it
the
minimal
’(p&q)v(p&~q)’, ’(pvq)’
hand
is entailed Boolean
up
a proper
that
other
(unique
’(pvq)’
namely
result
form
’p’
is
not
part
is
part
of
the
by ’(p&r)’
and
no
proper
normal
form
- being
’p’
by ’(p&r)’. shows
complex
how
the
definitions
quantificational
of
content
may
be
languages. Ken Gemes Department of Philosophy Yale University [email protected]
References Gemes,
K.
[1994],
"A
New
JournalofPhilosophicalLogic,
Notion of Content I: September 1994.
Gemes,
K. [1994a], "A New Notion Accounts", forthcoming.
88
of
Content
II:
Basic
Content,"
Model-Theoretic
