Complex Activity Occurrences
# Complex Activity Occurrences

Within the Complex Activity Theory,
complex activity occurrences correspond to activity trees, and
consequently occurrences of complex activities are not elements of the
legal occurrence tree. The axioms of the Activity Occurrences core theory
ensure that complex activity occurrences correspond to branches of activity trees.
Each complex activity occurrence has a unique atomic root occurrence and each finite
complex activity occurrence has a unique atomic leaf occurrence.
A subactivity occurrence corresponds to a sub-branch of the branch corresponding
to the complex activity occurrence.

## Informal Semantics for Activity Occurrences

`(subactivity_occurrence ?occ1 ?occ2)`
is TRUE in an interpretation of the Activity Occurrence Theory if and only if the branch corresponding to the activity occurrence ?occ1 is a subset of the branch corresponding to activity occurrence ?occ2.

`(root_occ ?occ1 ?occ2)`
is TRUE in an interpretation of the Activity Occurrence Theory if and only if activity occurrence ?occ1 is the root occurrence in the branch of the activity tree for ?a corresponding to the activity occurrence ?occ2.

`(leaf_occ ?occ1 ?occ2)`
is TRUE in an interpretation of the Activity Occurrence Theory if and only if activity occurrence ?occ1 is the leaf occurrence in the branch of the activity tree for ?a corresponding to the activity occurrence ?occ2.

` (iso_occ ?occ1 ?occ2 ?a)`
is TRUE in an interpretation of the Activity Occurrence Theory if and only if both ?occ1 and ?occ2 are occurrences of an atomic activity that contain a common subactivity.

`(same_grove ?occ1 ?occ2)`
is TRUE in an interpretation of the Activity Occurrence Theory if and only if activity occurrences ?occ1 and ?occ2 of ?a correspond to branches in the same activity tree for ?a.

`(mono ?s1 ?s2 ?a)`
is TRUE in an interpretation of the Activity Occurrence Theory if and only if
there is a one-to-one mapping between branches of an activity tree for ?a that
maps the atomic subactivity occurrence ?s1 to the atomic subactivity occurrence
?s2.

`(hom ?s1 ?s2 ?a)`
is TRUE in an interpretation of the Activity Occurrence Theory if and only if
there is a mapping between branches of an activity tree for ?a that
maps the atomic subactivity occurrence ?s1 to the atomic subactivity occurrence
?s2.

Last Updated: Wednesday, 15-December-2003 11:42:40

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