conceptual graphs
DESCRIPTION
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))). - PowerPoint PPT PresentationTRANSCRIPT
1
Conceptual Graphs(Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge
Representation)
Presented by Matt Selway
2
Conceptual Graphsbasics
~(Ex)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) ^ ~(Ey)(Bus(y) ^ Instrument(x, y)))
3
Conceptual Graphsbasics
~(Ex)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) ^ ~(Ey)(Bus(y) ^ Instrument(x, y)))
4
Conceptual Graphsbasics
~(Ex)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) ^ ~(Ey)(Bus(y) ^ Instrument(x, y)))
5
Conceptual Graphsbasics
~(Ex)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) ^ ~(Ey)(Bus(y) ^ Instrument(x, y)))
6
Conceptual Graphsbasics
~(Ex)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) ^ ~(Ey)(Bus(y) ^ Instrument(x, y)))
7
Conceptual Graphsbasics
(Ax)(Ay)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) -> Bus(y) ^ Instrument(x, y))
8
Conceptual Graphsbasics
(Ax)(Ay)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) -> Bus(y) ^ Instrument(x, y))
9
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)))
10
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)))) ) ) )
11
Conceptual Graphsreasoning
• Basic Rules– Copy <-> Simplify– Restrict <-> Unrestrict– Join <-> Detach
• Possible Effects– Equivalence (copy, simplify)– Specialisation (restrict, join)– Generalisation (unrestrict, detach)
12
Conceptual Graphsreasoning
Copy Simplify
13
Conceptual Graphsreasoning
Restrict Unrestrict
14
Conceptual Graphsreasoning
Join Detach
15
Conceptual Graphsreasoning
Maximal Join
16
Conceptual Graphsproof procedure
Proof of ((p -> r) ^ (q -> s)) -> ((p ^ q) -> (r ^ s)) in 7 steps(Sowa 2008)