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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