The logic of Existence

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The Logic of Existence
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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
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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
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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
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Existence in a Database
Cost
Length
Cost gt 20
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,
doesnt exist
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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
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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 gt 0.3 then
Antibody is present
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Existence Web
Does Not Exist
Leg
Exist
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
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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.
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The EXISTS Operator
False
DoesNotExist
EXISTS
MayExist 0.5
UKE 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.
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Operators Handling Existence
A
PLUS
X
B
C
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
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The Cause Operator
Relation Object
Logical Control
Existence Control
CAUSE
Mutation
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
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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
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Relation Operator
Fred cant 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)
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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.

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Multiple Causes and Effects
A N D
Mutation1
CAUSE
O R
Disease
CAUSE
Mutation2
CAUSE
Mutation3
Other Causes
Logic operators now handle existence
interchangeably with logic - they combine causes
and effects around variables.
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No Effect - No Existence
Disease_1
CAUSE
A N D
Mutation1
CAUSE
Disease_2
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.
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Handling Classes
May Exist
MEMBER
Gene_1
MEMBER
Gene_1
Gene_2
Gene_2
Genes
Genes
Gene_3
Gene_3
Does Exist
Does Not Exist
Gene_4
Gene_4
Does Exist
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Attributes Controlling Existence
MEMBER
Gene_1
Gene_2
Genes
Gene_3
Gene_4
ATTRIBUTES
Does Not Exist (In General)
Att_2
Att_1
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Finding Attributes
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
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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
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Activate To Search
The structure represents everything in the
text An existence pulse travels through the
structure
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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
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Mouldable Search Space
You decide what to include and what to ignore, by
examining what is currently being ignored
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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
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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.