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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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Presentation on theme: "Conceptual Graphs (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation) Presented by Matt Selway 1."— Presentation transcript:

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

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

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

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

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

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

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

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

9 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

10 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

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

12 Conceptual Graphs reasoning 12 CopySimplify

13 Conceptual Graphs reasoning 13 RestrictUnrestrict

14 Conceptual Graphs reasoning 14 JoinDetach

15 Conceptual Graphs reasoning 15 Maximal Join

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


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