Conceptual graphs
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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

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)


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