Description Logic in AI ( Assignment )

What do you recall about the description language DL

discussed in this course?

The syntactic elements are punctuations, positive integers, concept-forming operators, connectives, concepts, roles and constants.

Constants are also known as individuals or objects.

Operators AND, ALL, EXISTS and FILLS are used for describing concepts.

Connectives "⊑", "≐" and "→" are used for making statements about the domain

Allows variable free notation for writing concept descriptions (expressions).

What can you say about Description Logics?

Description Logics uses variable free notation to express FOL statements.

Description Logics is not a single language but a collection of languages.

DL

is a member of Description Logics.

Description Logics is a decidable fragment of FOL.

Description Logics is used to describe concepts and classify concepts.

Mark the properties of DL

knowledge base.

It is always consistent because DL

is a decidable fragment of FOL.

It describes concepts and subsumption between concepts.

It is a collection of DL

statements.

It describes individuals.

It describes relationships between roles.

A DL

knowledge base has an interpretation domain, what is true about that domain?

Its elements are individuals and concepts.

It is a superset of all individuals from all concepts in the knowledge base.

It contains only individuals.

It forms the nonlogical part of DL

language.

It forms the logical part of DL

language.

Choose the correct statements about DL

concepts.

A concept describes a class of individuals.

Thing is a super-concept which subsumes all other concepts.

Thing is an atomic concept.

Thing is neither atomic nor derived.

DL

concepts correspond to unary predicates in FOL.

What can you say about a taxonomy in a DL

knowledge base?

It is a network of nodes. Each node is either a concept or a domain individual.

Thing is the topmost node.

It is a concept–subconcept (class–subclass) hierarchy.

It is a subsumption hierarchy.

It is produced by the classification algorithm.

[EXISTS 4 :OwnsCar] is a concept.

It describes a class of individuals each of whom owns atleast 4 distinct cars.

It describes a class of individuals each of whom are linked to 4 distinct objects via the OwnsCar role.

The constant 4 in the concept description is an element of the domain.

If the concept has 10 individuals then the size of OwnsCar relation is atleast 400.

If the concept is non empty then the size of OwnsCar relation is atleast 4.

[ALL :Friend Rich] is a concept.

It includes individuals who do not have any friends.

It includes individuals who have rich friends.

It includes individuals each of who’s friends are all rich.

It excludes rich individuals who are their own friends.

It enforces a global type restriction on Friend relation.

[FILLS :EnrolledIn krr] is a concept.

It includes individuals who are enrolled in krr.

It includes individuals who are enrolled ONLY in krr.

If this concept has 10 individuals then the size of EnrolledIn relation is atleast 10.

There is no relationship between the number of individuals in this concept and the size of EnrolledIn relation.

Given a KB and two normalized concepts d and e of length n and m respectively, what can you say about "d⊑e

" subsumption test?

Running time of Structure Matching is O (n × m).

Structure Matching always terminates with a YES if KB ⊨ d ⊑ e.

Running time of Structure Matching is O (n + m).

Occasionally, Structure-Matching runs forever when KB ⊭ d ⊑ e.

Which of the following are true about “B ⊑

A”?

A subsumes B

A is the subsumer and B is the subsumee

A is the most specific subsumer and B is the most general subsumee

All members of B also belong to A

B is a subconcept of A

Which of the following statements are true about “B ≐

A”?

A subsumes B

B subsumes A

All members of B also belong to A

A is the most specific subsumer and B is the most general subsumee

All members of A also belong to B

B is the most specific subsumer and A is the most general subsumee

Given the KB = {c → A, c → B, c → D}, where c is a constant and A, B, D are concepts, pick the correct statements:

c is a member of A

c satisfies all the conditions that A satisfies.

A, B and D are equivalent.

c → [AND A B D]

There are no roles and all subsumptions are as in figure 1, now, tell us about KB14.

Author is an atomic concept.

Here: i, j, k, m, n, o are domain constants.

The individual k can be FULLY described in DL

The individuals i, j, m, n, and o can be FULLY described in DL

(Think)

Professor is not an atomic concept because it subsumes Dean.

Which of these statements (English and DL

) are entailed by KB14?

Only professors can be deans.

Author ⊑ WellRead

Some authors are bridge players.

[AND Dean Author] ⊑ BridgePlayer

Authors are bridge players.

The most specific subsumers of [AND Dean Author] are:

BridgePlayer

Dean

Author

[AND WellRead Professor]

WellRead

The most general subsumee of BridgePlayer is:

[AND Professor Author]

[AND WellRead Professor]

Author

[AND Dean Author]

None of the above.

The most specific DL

concept and the node that describe “k” is:

Node 5

[AND Author Dean]

Thing

Node 8

None of the above

Node 9

[AND Professor Author]

Thing

Node 8

None of the above

Which of these statements describe the edge between node 5 and 2 in the taxonomy?

It is an inferred edge.

[AND Professor WellRead] ⊑ BridgePlayer

BridgePlayer ≐ [AND Professor WellRead]

[AND Dean Author] ⊑ BridgePlayer

It is an asserted edge.