Transcript The Logical Structure of Knowledge

The Logical Structure
of Knowledge
Two Statements
Olga is pretty and Fred is a liar
Something is providing a True to the AND - let’s represent that
with a structure
True
AND
Olga is pretty
Fred is a liar
Falsify One Statement
False
Unknowable
AND
Olga is pretty
Fred is a liar
We show that Fred is not a liar, it works the right way - the
other statement becomes Unknowable
Logical Connection
We give the something that is providing a True to the AND a
name
Knowledge
True
AND
Olga is pretty
Fred is a liar
Now we can change the logical state of Knowledge whenever we like
Statements Down the Page
We change the statements so they run down the page, with an
implicit AND
Olga is pretty
Knowledge
AND
True
Fred is a liar
Now we can have thousands of statements, all ANDed together. If
one is False, then the rest are Unknowable
Uncertain Knowledge
What happens if we are unsure about the state of Knowledge.
If we show that each statement is true, then we can assume
Knowledge is True
True
Knowledge
AND
Olga is pretty
Fred is a liar
This is a closed world assumption - there may be other things
involved
Open World
If we don’t want Knowledge to be True if all the statements are
true, we can add an Unknowable
True
Knowledge
AND
Olga is pretty
Fred is a liar
Unknowable
Now we can make the statements True by setting Knowledge True,
but not the reverse
Logical Implication
If Olga is pretty then Fred is a liar
If we have an implication, we control the implication in the
same way
Knowledge
True
AND
True
Olga is pretty
IMPLIES
Fred is a liar
Modus Tollens
If Olga is pretty then Fred is a liar
We are not sure about the antecedent, but the consequent is
false
Knowledge
True
AND
False
Olga is pretty
False
IMPLIES
Fred is a liar
We have the antecedent falsified
Invalid
If Olga is pretty then Fred is a liar
The antecedent is true, the consequent is false
Knowledge
False
AND
True
Olga is pretty
False
IMPLIES
Fred is a liar
We have the knowledge falsified
Numbers
R = E/I
Knowledge
AND
True
Fred is a liar
Numbers fit right in - we control the equality logically,
or get a True out of it
We can handle a large subset of technical knowledge
with just numbers and logic
Building Large Structures
We can combine
small logical
structures into
larger structures
without concern
for how they will
later be used
IF a + b = c THEN d + e = f
Stitching
We can stitch the different worlds together with undirected thread,
so a change goes anywhere it needs to
Isn’t It Static?
Not necessarily - we can have while and for loops, fetch and store
- we can still build processes, we just make them out of logical
components which switch logical states, not sequential
procedures
Isn’t this just like microcircuits? Not quite - the logical states can
flow in either direction along the “wires”, and some operators can
change the connections
Not Enough
We now have all of propositional logic and numbers, but
it is not enough
He can go
He may go
Something different is happening here - we have
to handle the existence of the relation, and its
logical validity. They are linked somehow,
because certain logical states are incompatible
He can’t go
He went
Possibility of Relation
ToGo
True
Existence
Relation
He
He can go
Logic
Probability of Relation
ToGo
True
Existence
0.75 True
Relation
MAY
True
Logic
He
He may go
If we don’t know about the existence state, it can’t be less
than the logical state
Relation Error
ToGo
True
False
Existence
Relation
Logic
He
He can’t go
He went
Leaving time out of it, we now have an error that needs to be
resolved, possibly by falsifying the state that “said” he
couldn’t go
Building from Components
If we build up from undirected logical components, we can
represent things like
Tenant hereby leases, on the terms and conditions set forth below, for a period commencing on the
Commencement Date, that portion of 27th Floor of the Office Building containing approximately
8,000 square feet of rentable area and designated as Suite 2703 (the ”Interim Space") and expiring
on the earlier to occur of the date Tenant's Work (as defined in Exhibit D attached hereto) is
"substantially complete" (hereinafter defined) and August 31, 2009.
or
Gene ABCA1
The membrane-associated protein encoded by this gene is a member of the
superfamily of ATP-binding cassette (ABC) transporters. ABC proteins transport
various molecules across extra- and intracellular membranes. ABC genes are
divided into seven distinct subfamilies (ABC1, MDR/TAP, MRP, ALD, OABP,
GCN20, White). This protein is a member of the ABC1 subfamily. With cholesterol
as its substrate, this protein functions as a cholesteral efflux pump in the cellular
lipid removal pathway. Mutations in this gene have been associated with Tangier's
disease and familial high-density lipoprotein deficiency.
Automatic
Unlike the simple statements at the start of this presentation,
building structures to represent text has to be done automatically,
as there are dozens of interacting and synergistic processes
involved, processes which change their own structure in the
process of building structure (the dictionary for example)
The Structure of Knowledge
If we agree there is a structure, we can argue about the details
A structure gives us a way to link knowledge together, to
eliminate the segmentation and specialisation, the narrowness
of viewpoint, that causes so many problems