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Assignment of DL and Inheritance in AI


1. What do you recall about the description language 𝓐𝓛𝓒 ?

2. Identify the expressions that define or denote a concept in 𝓐𝓛𝓒.

3. Between 𝓓𝓛 and 𝓐𝓛𝓒 :

4. ∀Owns.Car is a concept that:

5. The negation normal form (NNF) of ¬[(∀R.¬C) ⊔ ∃R.C] is:

6. In 𝓐𝓛𝓒, to show KB ⊨ α we apply tableau on KB ⋃ {¬α}. As 𝓐𝓛𝓒 tableau executes:

7. An 𝓐𝓛𝓒 knowledge base and its interpretation-domain with six individuals is shown below.
KB7: {
Dean ⊑ Professor,
Author ⊑ WellRead,
(Professor ⊓ WellRead) ⊑ BridgePlayer
What is true about the individuals shown in KB7?

8. From figure 1 and KB7, pick the most specific descriptions of individuals.

9. An 𝓐𝓛𝓒 knowledge base KB9 has one role (Owns), three atomic concepts (Vehicle, Van, Car),
and seven concept definitions of the form Name ≡ Description.
The graph below shows a concept-hierarchy (with transitive edges removed) for KB9,
the nodes denote Name, Description pairs taken from Name ≡ Description statements,
and edges denote subsumption between Descriptions.
KB9: {
⊤ is top concept,
Vehicle ⊑ ⊤,
Car ⊑ Vehicle,
Van ⊑ Vehicle,
Owner ≡ ∃Owns.⊤,
CarOwner1 ≡ ∃Owns.Car,
CarOwner2 ≡ ∀Owns.Car,
CarOwner3 ≡ Owner ⊓ ∀Owns.Car,
VehicleOwner1 ≡ ∃Owns.Vehicle,
VehicleOwner2 ≡ ∀Owns.Vehicle,
VehicleOwner3 ≡ Owner ⊓ ∀Owns.Vehicle
Now, build this graph and determine the node names, for example,
node 1 is ⟨Owner, ∃Owns.⊤⟩, it corresponds to Owner ≡ ∃Owns.⊤.
Question: identify the nodes in the above graph.

10. What is true about the graph in question 9?

11. What is the difference between hierarchies created by frames and that created by DL?

12. Which of the following statements are true about “Inheritance networks”?

13. While choosing an extension (i.e. reasoning over paths in an inheritance network)
what happens when a node has more than one parent node?

14. A negative path in an inheritance hierarchy

15. A path in an inheritance hierarchy can support a conclusion of the form

16. An inheritance hierarchy with a conclusion node C w.r.t. a node A

17. The shortest path heuristic in defeasible reasoning

18. A credulous extension of a (possibly ambiguous) inheritance hierarchy with respect to a node A

19. Given the following inheritance hierarchy, what can be said about the individual 'a'
based on the criteria of there being an admissible path to support the conclusion?

20. Looking at the inheritance hierarchy in question 19, what can be said about the individual 'b'
based on the criteria of there being an admissible path to support the conclusion?

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