the logical structure of knowledge. two statements olga is pretty and fred is a liar something is...
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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
Olga is pretty Fred is a liar
AND
True
Falsify One Statement
We show that Fred is not a liar, it works the right way - the other statement becomes Unknowable
Olga is pretty Fred is a liar
AND
FalseUnknowable
Logical Connection
We give the something that is providing a True to the AND a name
Olga is pretty Fred is a liar
AND
True
Knowledge
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
Fred is a liar
AN
DTrue
Knowledge
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
Olga is pretty
Fred is a liar
AN
DTrue
Knowledge
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
Olga is pretty
Fred is a liar
AN
DTrue
Knowledge
Unknowable
Now we can make the statements True by setting Knowledge True, but not the reverse
Logical Implication
If we have an implication, we control the implication in the same way
If Olga is pretty then Fred is a liar
Fred is a liar
AND
True
Knowledge
IMPLIESOlga is pretty
True
Modus Tollens
We are not sure about the antecedent, but the consequent is false
If Olga is pretty then Fred is a liar
Fred is a liar
AND
True
Knowledge
IMPLIESOlga is prettyFalseFalse
We have the antecedent falsified
Invalid
The antecedent is true, the consequent is false
If Olga is pretty then Fred is a liar
Fred is a liar
AND
True
Knowledge
IMPLIESOlga is prettyFalse
We have the knowledge falsified
False
Numbers
R = E/I
Fred is a liar
AN
D
True
Knowledge
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
Probability of Relation
Relation
ToGo
He
LogicExistence
True
He may go
MAY
0.75 TrueTrue
If we don’t know about the existence state, it can’t be less than the logical state
Relation Error
Relation
ToGo
He
LogicExistence
True
He can’t goHe went
False
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
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.
If we build up from undirected logical components, we can represent things like
or
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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)
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