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Conceptual Graphs (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation) Presented by Matt Selway 1

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Conceptual Graphs basics ~(Ex)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) ^ ~(Ey)(Bus(y) ^ Instrument(x, y))) 2

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Conceptual Graphs basics ~(Ex)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) ^ ~(Ey)(Bus(y) ^ Instrument(x, y))) 3

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Conceptual Graphs basics ~(Ex)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) ^ ~(Ey)(Bus(y) ^ Instrument(x, y))) 4

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Conceptual Graphs basics ~(Ex)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) ^ ~(Ey)(Bus(y) ^ Instrument(x, y))) 5

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Conceptual Graphs basics ~(Ex)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) ^ ~(Ey)(Bus(y) ^ Instrument(x, y))) 6

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Conceptual Graphs basics (Ax)(Ay)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) -> Bus(y) ^ Instrument(x, y)) 7

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Conceptual Graphs basics (Ax)(Ay)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) -> Bus(y) ^ Instrument(x, y)) 8

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Conceptual Graphs notations Extended CGIF [If: [Person: John] [Go *x] [City: Boston] (Agent ?x John) (Destination ?x Boston) [Then: [Bus *y] (Instrument ?x ?y) ]] First Order Logic ~(Ex)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) ^ ~(Ey)(Bus(y) ^ Instrument(x, y))) 9

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Conceptual Graphs notations Extended CGIF -> CLIF (exists ((x Go)) (if (and (Person John) (City Boston) (Agent x John) (Destination x Boston) ) (exists ((y Bus)) (Instrument x y) ) ) ) Extended CGIF -> Core CGIF ~[ [*x] (Person John) (Go ?x) (City Boston) (Agent ?x John) (Destinination ?x Boston) ~[ [*y] (Bus ?y) (Instrument ?x ?y) ]] Core CGIF -> CLIF (not (exists (x) (and (Person John) (Go x) (City Boston) (Agent x John) (Destination x Boston) (not (exists (y) (and (Bus y) (Instrument x y)))) ) ) ) 10

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Conceptual Graphs reasoning Basic Rules – Copy Simplify – Restrict Unrestrict – Join Detach Possible Effects – Equivalence (copy, simplify) – Specialisation (restrict, join) – Generalisation (unrestrict, detach) 11

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Conceptual Graphs reasoning 12 CopySimplify

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Conceptual Graphs reasoning 13 RestrictUnrestrict

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Conceptual Graphs reasoning 14 JoinDetach

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Conceptual Graphs reasoning 15 Maximal Join

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Conceptual Graphs proof procedure Proof of ((p -> r) ^ (q -> s)) -> ((p ^ q) -> (r ^ s)) in 7 steps (Sowa 2008) 16

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To write another equivalent equation, multiply each side by 0.5. 4x – 12y = 8 To write one equivalent equation, multiply each side by 2. SOLUTION Write.

To write another equivalent equation, multiply each side by 0.5. 4x – 12y = 8 To write one equivalent equation, multiply each side by 2. SOLUTION Write.

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