Supertypes and Subtypes

1
Chapter 21

• Supertypes and Subtypes

2
Generalization

• Focuses on those object types whose abstractions
  are more generic than other object types.
• Presents an option of how we understand our
  environment
• Allows us to specify super-object types
  (supertypes) and sub-object types (subtypes)

3
Sets that include sets

• The lt symbol specifies that one object type is
  more general than another. (Also shown as a
  symbol.)
• Generalization implies (includes) their
  intensions (and their subintensions) and
  extensions (and their subextensions).
• Extension(Billed) lt Extension(Transaction)

U
4
Supersets and Subsets

• A superset refers to a set that includes all the
  members of one ore more sets.
• A subset refers to a set whose members are all
  included in another set.

Transactions subset
Activities superset
Trans
In progress
Completed
Sched.
Pay
Billed
5
Supertypes and Subtypes

• A supertype refers to an object type whose
• set includes all the members of one or more sets
• definition that is more general than another
• A subtype refers to an object type whose
• set memberships are all included in another set
• definition is more specialized than another

6
Generalization Hierarchies

• a.k.a. directed acrylic graphs (DAG)
• a.k.a. lattices

Activity
Transaction
Completed
Provider
Case
. . .
7
Type (Set) Partitions

• A type partition divides a type into disjoint
  subtypes (non-overlapping subsets).
• Multiple partitions exist when an object type (or
  set) can be partitioned into multiple themes.

Transactions
Transactions
In progress
Civil
Completed
Criminal
Deleted
Contract
Billed
Wills
8
Type (Set) Partitions (contd)

• A complete partition is a partition that contains
  a full list of subtypes of a specific subtype.
• An incomplete partition is a partition that
  contains a partial list of its subtypes.

Incomplete
Complete
Case
Criminal
In Progress
Civil
Completed
Transaction