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

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

Representation)

Presented by Matt Selway

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Conceptual Graphsbasics

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

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Conceptual Graphsbasics

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

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Conceptual Graphsbasics

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

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Conceptual Graphsbasics

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

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Conceptual Graphsbasics

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

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Conceptual Graphsbasics

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

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Conceptual Graphsbasics

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

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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)))

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Conceptual Graphs notations

• 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)))) ) ) )

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Conceptual Graphsreasoning

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

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

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Conceptual Graphsreasoning

Copy Simplify

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Conceptual Graphsreasoning

Restrict Unrestrict

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Conceptual Graphsreasoning

Join Detach

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Conceptual Graphsreasoning

Maximal Join

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Conceptual Graphsproof procedure

Proof of ((p -> r) ^ (q -> s)) -> ((p ^ q) -> (r ^ s)) in 7 steps(Sowa 2008)