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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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Conceptual Graphs

(Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation)

Presented by Matt Selway


Conceptual Graphsbasics

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


Conceptual Graphsbasics

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


Conceptual Graphsbasics

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


Conceptual Graphsbasics

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


Conceptual Graphsbasics

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


Conceptual Graphsbasics

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


Conceptual Graphsbasics

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


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)))


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)))) ) ) )


Conceptual Graphsreasoning

  • Basic Rules

    • Copy <-> Simplify

    • Restrict <-> Unrestrict

    • Join <-> Detach

  • Possible Effects

    • Equivalence (copy, simplify)

    • Specialisation (restrict, join)

    • Generalisation (unrestrict, detach)


Conceptual Graphsreasoning

Copy

Simplify


Conceptual Graphsreasoning

Restrict

Unrestrict


Conceptual Graphsreasoning

Join

Detach


Conceptual Graphsreasoning

Maximal Join


Conceptual Graphsproof procedure

Proof of ((p -> r) ^ (q -> s)) -> ((p ^ q) -> (r ^ s)) in 7 steps

(Sowa 2008)


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