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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

Conceptual Graphs

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

Presented by Matt Selway


Conceptual graphs basics
Conceptual Graphsbasics

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


Conceptual graphs basics1
Conceptual Graphsbasics

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


Conceptual graphs basics2
Conceptual Graphsbasics

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


Conceptual graphs basics3
Conceptual Graphsbasics

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


Conceptual graphs basics4
Conceptual Graphsbasics

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


Conceptual graphs basics5
Conceptual Graphsbasics

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


Conceptual graphs basics6
Conceptual Graphsbasics

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


Conceptual graphs notations
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 graphs notations1
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 graphs reasoning
Conceptual Graphsreasoning

  • Basic Rules

    • Copy <-> Simplify

    • Restrict <-> Unrestrict

    • Join <-> Detach

  • Possible Effects

    • Equivalence (copy, simplify)

    • Specialisation (restrict, join)

    • Generalisation (unrestrict, detach)


Conceptual graphs reasoning1
Conceptual Graphsreasoning

Copy

Simplify


Conceptual graphs reasoning2
Conceptual Graphsreasoning

Restrict

Unrestrict


Conceptual graphs reasoning3
Conceptual Graphsreasoning

Join

Detach


Conceptual graphs reasoning4
Conceptual Graphsreasoning

Maximal Join


Conceptual graphs proof procedure
Conceptual Graphsproof procedure

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

(Sowa 2008)