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Conceptual Graphs

Conceptual Graphs. (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation ) Presented by Matt Selway. Conceptual Graphs basics. ~(Ex)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) ^ ~( Ey )(Bus(y) ^ Instrument(x, y))).

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Conceptual Graphs

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

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

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

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

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

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

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

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

  9. Conceptual Graphsnotations • 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)))

  10. Conceptual Graphsnotations • 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)))) ) ) )

  11. Conceptual Graphsreasoning • Basic Rules • Copy <-> Simplify • Restrict <-> Unrestrict • Join <-> Detach • Possible Effects • Equivalence (copy, simplify) • Specialisation (restrict, join) • Generalisation (unrestrict, detach)

  12. Conceptual Graphsreasoning Copy Simplify

  13. Conceptual Graphsreasoning Restrict Unrestrict

  14. Conceptual Graphsreasoning Join Detach

  15. Conceptual Graphsreasoning Maximal Join

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

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