Conceptual Graphs:

1. Conceptual Graphs: Combing logic and semantic net

2. Motivations • Semantic networks & frame systems have trouble handling • negation, the fact that something is not true • disjunction • quantification, the fact that something is true for all objects • Conceptual graphs can handle them naturally.

3. Objectives • Examples of conceptual graphs • Conceptual graph syntax • Individual (article: the) and generic (article: a) concepts • Conceptual graph operations: how to produce new conceptual graphs from old ones • Conceptual graphs and logic

4. A bird flies bird(B), flies(B). Examples of conceptual graphs • A dog has a color of brown • dog(D), brown(B), color(D,B). • A child has as parents, a father and a mother. • child(C), father(F), mother(M), parents(C,F,M). A relation of arity n is represented by a node having n arcs.

5. Mary gave John the book • Concepts represented as boxes • Some concepts have a type and referent field • type : individual • Relations are represented as ovals. • Directed arcs connection concepts and conceptual relations • Unlike, semantic net, arcs are NOT labeled. Nodes represents concepts or relations

6. Specific individuals Conceptual graph indicating that the dog named Emma is brown. Conceptual graph indicating that a particular (but unnamed) dog is brown. The marker # followed by a number indicates an individual in the domain of discourse. Conceptual graph indicating that a particular dog named Emma is brown.

7. Conceptual graph of a person with three names Her name was McGill, and she called herself Lil, but everyone knew her as Nancy.

8. The dog scratches its ear with its paw The marker * followed by a variable name indicates a particular unspecified individual, i.e., a fixed constant value. This is the same dog *Xas the one earlier.

9. isa hierarchy Lattice: partial order The concept fido is ambiguous.

10. universal type v is the common supertype of s and u. t is the common subtype of s and u. absurd type Type Hierarchy: Example s and u are not comparable.

11. eats animal eats dog barks dog Operations to create new graphs copy: an exact copy restrict: nodes replaced by a node representing their specialization. dog is a specialized animal join: combines the two with the substitutions. simplify: removes duplicate relations eats dog barks

12. Example: Simplification

13. Example: Restriction

14. Inheritance in conceptual graphs

15. Relations between propositions • Tom believes that Jane likes pizza. • believesis a relation between an object and an entire proposition

16. barks dog bites barks dog: emma bites Logical quantifiers dog(emma)  barks(emma)  bites(emma)  X (dog(X)  barks(X)  bites(X)) barks  X (dog(X)  barks(X)  bites(X)) dog: X bites

17. Negation • All dogs are non-pink. xy ¬(dog(x)color(x,y)pink(y)) • There are no pink dog ¬(xy(dog(x)color(x,y)pink(y)))

18. neg proposition barks dog:fido neg proposition barks dog More negations fido does not bark ¬(dog(fido)  bark(fido)) dog(fido) → ¬ bark(fido) bark(fido) → ¬ dog(fido) dogs do not bark  X ¬(dog(X)  bark(X))

19. Conceptual graphs vs predicate logic • Any conceptual graph can be reformulated into predicate logic • But conceptual graphs support additional operations (ex. join, restrict…) • Restriction can be used to implement inheritance • Criticism • no sound inference rules • no formal semantics

20. Conclusion • Conceptual graph expresses meaning in a form that is logically precise, humanly readable, and computationally tractable. • Unlike semantic net, it can naturally express logical negation and existential and universal quantifications. • We have now added another tool in our arsenal of knowledge representation.