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

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

Possibility of Relation

Relation

ToGo

He

LogicExistenceTrue

He can go

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

Gene ABCA1The membrane-associated protein encoded by this gene is a member of thesuperfamily of ATP-binding cassette (ABC) transporters. ABC proteins transportvarious molecules across extra- and intracellular membranes. ABC genes aredivided into seven distinct subfamilies (ABC1, MDR/TAP, MRP, ALD, OABP,GCN20, White). This protein is a member of the ABC1 subfamily. With cholesterolas its substrate, this protein functions as a cholesteral efflux pump in the cellularlipid removal pathway. Mutations in this gene have been associated with Tangier'sdisease 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