Conceptual Graphs (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation)...
-
Upload
andrew-sare -
Category
Documents
-
view
218 -
download
1
Transcript of Conceptual Graphs (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation)...
![Page 1: Conceptual Graphs (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation) Presented by Matt Selway 1.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649cbf5503460f949852cd/html5/thumbnails/1.jpg)
1
Conceptual Graphs(Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge
Representation)
Presented by Matt Selway
![Page 2: Conceptual Graphs (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation) Presented by Matt Selway 1.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649cbf5503460f949852cd/html5/thumbnails/2.jpg)
2
Conceptual Graphsbasics
~(Ex)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) ^ ~(Ey)(Bus(y) ^ Instrument(x, y)))
![Page 3: Conceptual Graphs (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation) Presented by Matt Selway 1.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649cbf5503460f949852cd/html5/thumbnails/3.jpg)
3
Conceptual Graphsbasics
~(Ex)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) ^ ~(Ey)(Bus(y) ^ Instrument(x, y)))
![Page 4: Conceptual Graphs (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation) Presented by Matt Selway 1.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649cbf5503460f949852cd/html5/thumbnails/4.jpg)
4
Conceptual Graphsbasics
~(Ex)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) ^ ~(Ey)(Bus(y) ^ Instrument(x, y)))
![Page 5: Conceptual Graphs (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation) Presented by Matt Selway 1.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649cbf5503460f949852cd/html5/thumbnails/5.jpg)
5
Conceptual Graphsbasics
~(Ex)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) ^ ~(Ey)(Bus(y) ^ Instrument(x, y)))
![Page 6: Conceptual Graphs (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation) Presented by Matt Selway 1.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649cbf5503460f949852cd/html5/thumbnails/6.jpg)
6
Conceptual Graphsbasics
~(Ex)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) ^ ~(Ey)(Bus(y) ^ Instrument(x, y)))
![Page 7: Conceptual Graphs (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation) Presented by Matt Selway 1.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649cbf5503460f949852cd/html5/thumbnails/7.jpg)
7
Conceptual Graphsbasics
(Ax)(Ay)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) -> Bus(y) ^ Instrument(x, y))
![Page 8: Conceptual Graphs (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation) Presented by Matt Selway 1.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649cbf5503460f949852cd/html5/thumbnails/8.jpg)
8
Conceptual Graphsbasics
(Ax)(Ay)(Person(John) ^ City(Boston) ^ Go(x) ^ Agent(x, John) ^ Destination(x, Boston) -> Bus(y) ^ Instrument(x, y))
![Page 9: Conceptual Graphs (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation) Presented by Matt Selway 1.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649cbf5503460f949852cd/html5/thumbnails/9.jpg)
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)))
![Page 10: Conceptual Graphs (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation) Presented by Matt Selway 1.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649cbf5503460f949852cd/html5/thumbnails/10.jpg)
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)))) ) ) )
![Page 11: Conceptual Graphs (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation) Presented by Matt Selway 1.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649cbf5503460f949852cd/html5/thumbnails/11.jpg)
11
Conceptual Graphsreasoning
• Basic Rules– Copy <-> Simplify– Restrict <-> Unrestrict– Join <-> Detach
• Possible Effects– Equivalence (copy, simplify)– Specialisation (restrict, join)– Generalisation (unrestrict, detach)
![Page 12: Conceptual Graphs (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation) Presented by Matt Selway 1.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649cbf5503460f949852cd/html5/thumbnails/12.jpg)
12
Conceptual Graphsreasoning
Copy Simplify
![Page 13: Conceptual Graphs (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation) Presented by Matt Selway 1.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649cbf5503460f949852cd/html5/thumbnails/13.jpg)
13
Conceptual Graphsreasoning
Restrict Unrestrict
![Page 14: Conceptual Graphs (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation) Presented by Matt Selway 1.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649cbf5503460f949852cd/html5/thumbnails/14.jpg)
14
Conceptual Graphsreasoning
Join Detach
![Page 15: Conceptual Graphs (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation) Presented by Matt Selway 1.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649cbf5503460f949852cd/html5/thumbnails/15.jpg)
15
Conceptual Graphsreasoning
Maximal Join
![Page 16: Conceptual Graphs (Sowa, JF 2008, ‘Conceptual Graphs’, in Handbook of Knowledge Representation) Presented by Matt Selway 1.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649cbf5503460f949852cd/html5/thumbnails/16.jpg)
16
Conceptual Graphsproof procedure
Proof of ((p -> r) ^ (q -> s)) -> ((p ^ q) -> (r ^ s)) in 7 steps(Sowa 2008)