1. The Logical Structure of Knowledge

2. 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 prettyFred is a liar AND True

3. Falsify One Statement We show that Fred is not a liar, it works the right way - the other statement becomes Unknowable Olga is prettyFred is a liar AND False Unknowable

4. Logical Connection We give the something that is providing a True to the AND a name Olga is prettyFred is a liar AND True Knowledge Now we can change the logical state of Knowledge whenever we like

5. 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 AND True Knowledge Now we can have thousands of statements, all ANDed together. If one is False, then the rest are Unknowable

6. 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 AND True Knowledge This is a closed world assumption - there may be other things involved

7. 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 AND True Knowledge Unknowable Now we can make the statements True by setting Knowledge True, but not the reverse

8. 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 IMPLIES Olga is pretty True

9. 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 IMPLIES Olga is pretty False We have the antecedent falsified

10. 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 IMPLIES Olga is pretty False We have the knowledge falsified False

11. Numbers R = E/I Fred is a liar AND 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

12. 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

13. Stitching We can stitch the different worlds together with undirected thread, so a change goes anywhere it needs to

14. 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

15. 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

16. Possibility of Relation Relation ToGo He LogicExistence True He can go

17. 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

18. Relation Error Relation ToGo He LogicExistence True He can’t go He 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

19. 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 27 th 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

20. 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)

21. 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