Transcript The logic of Existence - ORION Active Structure

The Logic of
Existence
The Legend of the Unicorn
We need to be able to talk about and control the
existence and nonexistence of objects and
relations
Objects can be created or destroyed, but
sometimes we need to create objects and
relations, then “send them dark” - act as though
they do not exist and see what that causes - or
evaluate a probability of existence given other
information, in the same way we have Bayesian
logical values
We Use It All The Time
The tiger can escape
The system shall be capable of...
He doubted the existence of a cure
He was able to do it
It was possible
It is commonplace in our everyday
language and is a vital part of
language modelling
Several Forms of Existence
• The patient was born without a liver
• The liver may stop working at any time
• Only consider diseases related to the liver
The object may be not present, not functioning or
present but not relevant
Existence in a Database
Cost
Cost > 20
Length
10
15
2
6
23
45
44
56
78
23
11
6
A database handles current existence by marking records in
or out of a working set - this works when the records are
static and independent. It also makes a closed world
assumption - no record, doesn’t exist
Marking the Structure
In a huge active structure, we have to block
propagation into areas that are not relevant, by
indicating they do not exist for the current
analysis
Existence needs to be computable and
propagatable
Orthogonal Properties
Existence
State
Value
We need to determine existence before we determine logical
state before we determine value - a value on one object may
determine existence on another if glycosine_level > 0.3 then Antibody is present
Existence Web
Does
Not
Exist
Exist
Leg
Some links only transmit existence, some
links transmit the object, its existence and
its state - the existence web is interleaved
with other webs for logic and objects
Types of Existence
• Does Exist
• May Exist - values 0 - 1.0
• Does Not Exist
This matches Bayesian logical values of True/False.
The midpoint of the range - 0.5 - has a special significance
of DontCare or Ignore. This value can be propagated over
the top of existing values when existence is to be ignored.
The EXISTS Operator
False
DoesNotExist
EXISTS
UKE 0.5
MayExist 0.5
The EXISTS operator links between True/False and
DoesExist/DoesNotExist, with Bayesian values on
one side represented on the other side by MayExist
values
Conversion is automatic at logical connectives - AND,
OR, IF...THEN etc.
Operators Handling Existence
A
X
PLUS
If B does not exist, the PLUS operator
assumes zero. If B may exist, the operator
assumes a range of B,0
The MULTIPLY operator behaves differently,
passing along the DoesNotExist
B
C
The Cause Operator
Existence
Control
Mutation
Relation
Object
CAUSE
Logical
Control
Disease
This is shorthand for IF Mutation EXISTS AND Other Conditions
THEN Disease (an object) EXISTS
If Disease is to be ignored, then Mutation will be
ignored, and vice versa
Relation Operator
Fred can cross the bridge
The RELATION operator has both logical and existential
control linked together in the operator so the logical control
cannot have a greater probability than the existence value
- here “can” asserts existence, so the logical value can be
anything
Relation Operator
Fred can’t cross the bridge
Here we build a structure, then say it does not exist and let
it affect whatever it may
As a corollary, it must be logically false (within the
timeframe of its nonexistence)
He Failed …
He failed to prevent a riot
There is an implication that it was possible for him to prevent
a riot, otherwise he would not have failed, he would have
been unable to prevent a riot. ToFail puts out a
propositional False and an Existential True, so ToPrevent
exists.
Multiple Causes and Effects
Mutation1
A
N
D
CAUSE
Mutation2
CAUSE
Mutation3
CAUSE
Logic operators now handle
existence interchangeably with
logic - they combine causes and
effects around variables.
Disease
O
R
Other
Causes
No Effect - No Existence
Mutation1
CAUSE
Disease_1
CAUSE
Disease_2
A
N
D
If the existence of the object has no effect, then
ignore the object.
If there were an OtherEffects connection, the
inference could not be made.
Handling Classes
May Exist
Gene_1
Genes
Does Exist
M
E
M
B
E
R
Gene_1
Gene_2
Genes
Gene_3
Gene_4
Does Exist
Does Not
Exist
M
E
M
B
E
R
Gene_2
Gene_3
Gene_4
Attributes Controlling Existence
Gene_1
Genes
ATTRIBUTES
Att_1
Att_2
M
E
M
B
E
R
Gene_2
Gene_3
Gene_4
Does Not
Exist (In General)
Finding Attributes
MEMBERS
MEMBERS
MEMBERS
MEMBERS
G1
16
“q1.3“
Attributes are found by exciting the structure. Existence can
be controlled to vary attributes under different conditions
- parts of the structure temporarily cease to exist
Dynamically Created Sets
• Diseases specific to the liver
• Diseases common to liver and kidney
• Commonality between chromosomes 10 and 21
These are not really sets, just areas of the
structure that are activated into existence, while
other areas are either not activated, or activated
out of existence - the control structures to do
this are generated from the question
Activate To Search
Other
Cause
The structure represents everything in the text
An existence pulse travels through the structure
Extent of Activation
Up to now we have been assuming all the structure
we have built is to be active, and switching off
selected areas using logical control.
This method is not effective for huge structures instead, we need to control the area of activation.
The huge structures will mostly be about objects,
whose existence or nonexistence or irrelevance for
current analysis we will need to control
Mouldable Search Space
Other
Cause
Knowledge
Space
Search
Space
Other
Cause
You decide what to include and what to ignore, by
examining what is currently being ignored
Legal Existence
Legal text is full of references to existence
• Tenant can use the entire Premises
• Landlord shall be able to determine
• Any Transfer shall, at the option of Landlord,
constitute a Default
• specific consent from Landlord shall not be required
• Under these circumstances, Section 9 is void
Structures that represent such text need to
be able to modify and control existence
from afar - to treat existence as having a
value like anything else
Logic of Existence
The logic of existence handles the existence or
nonexistence of objects.
It can be freely intermixed with propositional logic,
amplifying the efficacy of Bayesian values in the
process.
Separate control and propagation of existence is
necessary to prevent smearing - the confusion
between propositional logic and existence logic.
Its ability to excite a structure and return information
about the connections in it opens up areas of
analysis closed to numbers and Boolean logic.