Relationships among activity occurrences that are elements of the same activity tree

Are the activity occurrences isomorphic to permutations of each other?

The set of atomic subactivity occurrences in an activity occurrence is isomorphic to a permutation of the atomic subactivity occurrences in every other activity occurrence in the same activity tree.

The set of atomic subactivity occurrences in an activity occurrence is isomorphic to a permutation of the atomic subactivity occurrences in some other activity occurrence in the same activity tree.

The set of activity occurrences that are in the same activity tree is isomorphic to the union of occurrences that are permutations of other occurrences, and occurences that are not permutations of any other occurrences.

None of the activity occurrences in the same activity tree are isomorphic to permutations of each other.

Relationships among activity occurrences that are elements of the same activity tree

Does there exist an activity occurrence whose atomic subactivity occurrences are the combination of the atomic subactivity occurrences in other activity occurrences in the same activity tree?

There exists an activity occurrence whose set of atomic subactivity occurrences is a combination of the atomic subactivity occurrence of every other activity occurrence in the same activity tree.

There exists multiple activity occurrences in the same activity tree whose set of atomic subactivity occurrences is a combination of the atomic subactivity occurrence in other activity occurrence in the same activity tree.

The set of activity occurrences that are in the same activity tree is the union of those whose atomic subactivity occurrences are part of a combination and those that are not combined with any other occurrences in the same tree.

None of the occurrences in the same activity tree are combinations of any others.

Uniform Branch Structure

Are there any constraints on the set of minimal activity trees for the complex activity?

There are no constraints on the set of minimal activity trees for the complex activity; all minimal activity trees are isomorphic.

There are constraints on the set of minimal activity trees for the complex activity; there exist multiple nonisomorphic minimal activity trees, but if the roots of the activity trees are occurrence equivalent, then the trees are isomorphic.

There are constraints on the set of minimal activity trees for the complex activity; there exist multiple nonisomorphic minimal activity trees, regardless of the root occurrences of the activity trees.

Constraints on Variation based on State

Are the constraints on the set of minimal activity trees for the complex activity based only on the state prior to the occurrences of the activity?

The branch structure of an occurrence of the complex activity depends only on fluents that hold prior to the activity occurrence.

The branch structure of some (but not all) occurrences of the complex activity depend only on fluents that hold prior to the activity occurrence.

There is no relationship between the branch structure of occurrences of the complex activity and the fluents that hold prior to the activity occurrences.

Time-based Constraints on Complex Activity Occurrences

Are the constraints on the branch structure of occurrences of the complex activity based on the time at which the activity occurrence begins?

The branch structure of any occurrence of the activity depends only on the time at which the activity occurrence begins.

The branch structure of some (but not all) occurrences of the activity depend only on the time at which the activity occurrence begins.

There is no relationship between the branch structure of occurrences of the complex activity and the time at which the activity occurrence begins.

Constraints on the Branch Structure of Activity Occurrences based on State and Time

Are the constraints on the branch structure of occurrences of the complex activity based both on the state prior to the activity occurrence and the time at which the activity occurrence begins?

The branch structure of any occurrence of the activity depends only on the conjunction of the fluents that hold prior to the activity occurrence and the time at which the activity occurrence begins.

The branch structure of some (but not all) occurrences of the activity depend only on the conjunction of the fluents that hold prior to the activity occurrence and the time at which the activity occurrence begins.

There is no relationship between the branch structure of occurrences of the activity, the fluents that hold prior to occurrences of the activity, or the time at which the activity occurrence begins.

Unconstrained Complex Activity Occurrences

Are there any constraints on the occurrence of the complex activity?

There are no constraints on the occurrences of the complex activity; the activity occurs whenever it is possible.

There are constraints on the occurrences of the complex activity; there are circumstances under which the activity is possible yet does not occur, but there are activities such that all occurrences are roots of activity trees for the complex activity.

There are constraints on the occurrences of the complex activity; there are circumstances under which the activity is possible yet does not occur.

Constraints on Complex Activity Occurrences based on State

Are the constraints on the occurrence of the complex activity based only on the state prior to the activity occurrence?

Any occurrence of the activity depends only on fluents that hold prior to the activity occurrence.

Some (but not all) occurrences of the activity depend only on fluents that hold prior to the activity occurrence.

There is no relationship between occurrences of the activity and the fluents that hold prior to occurrences of the activity.

Time-based Constraints on Complex Activity Occurrences

Are the constraints on the occurrence of the complex activity based on the time at which the activity occurrence begins?

Any occurrence of the activity depends only on the time at which the activity occurrence begins.

Some (but not all) occurrences of the activity depend only on the time at which the activity occurrence begins.

time at which the activity occurrence begins.

Constraints on Complex Activity Occurrences based on State and Time

Are the constraints on the occurrence of the complex activity based both on the state prior to the activity occurrence and the time at which the activity occurrence begins?

Any occurrence of the activity depends only on the conjunction of the fluents that hold prior to the activity occurrence and the time at which the activity occurrence begins.

Some (but not all) occurrences of the activity depend only on the conjunction of the fluents that hold prior to the activity occurrence and the time at which the activity occurrence begins.

There is no relationship between occurrences of the activity, the fluents that hold prior to occurrences of the activity, or the time at which the activity occurrence begins.