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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

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

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

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

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

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

- Extended CGIF
[If: [Person: John] [Go *x] [City: Boston] (Agent ?x John) (Destination ?x Boston)

[Then: [Bus *y] (Instrument ?x ?y) ]]

- First Order Logic

- 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)))) ) ) )

- Basic Rules
- Copy <-> Simplify
- Restrict <-> Unrestrict
- Join <-> Detach

- Possible Effects
- Equivalence (copy, simplify)
- Specialisation (restrict, join)
- Generalisation (unrestrict, detach)

Copy

Simplify

Restrict

Unrestrict

Join

Detach

Maximal Join

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

(Sowa 2008)