Complex Activities

Complex Activities

This core theory provides the foundation for representing and reasoning about complex activities and the relationship between occurrences of an activity and occurrences of its subactivities. Occurrences of complex activities correspond to sets of occurrences of subactivities; in particular, these sets are subtrees of the occurrence tree.

The basic ontological commitments of the Complex Activities Theory are based on the following intuitions:

Intuition 1:

An activity tree consists of all possible sequences of atomic subactivity occurrences beginning from a root subactivity occurrence.

In a sense, activity trees are a microcosm of the occurrence tree, in which we consider all of the ways in which the world unfolds in the context of an occurrence of the complex activity.

Any activity tree is actually isomorphic to multiple copies of a minimal activity tree arising from the fact that other external activities may be occurring during the complex activity.

Intuition 2:

Different subactivities may occur on different branches of the activity tree i.e. different occurrences of an activity may have different subactivity occurrences or different orderings on the same subactivity occurrences.

In this sense, branches of the activity tree characterize the nondeterminism that arises from different ordering constraints or iteration.

Intuition 3:

An activity will in general have multiple activity trees within an occurrence tree, and not all activity trees for an activity need be isomorphic. Different activity trees for the same activity can have different subactivity occurrences.

Following this intuition, the Complex Activities Theory does not constrain which subactivities occur. For example, conditional activities are characterized by cases in which the state that holds prior to the activity occurrence determines which subactivities occur. In fact, an activity may have subactivities that do not occur; the only constraint is that any subactivity occurrence must correspond to a subtree of the activity tree that characterizes the occurrence of the activity.

Intuition 4:

Not every occurrence of a subactivity is a subactivity occurrence. There may be other external activities that occur during an occurrence of an activity.

This theory does not force the existence of complex activities; there may be subtrees of the occurrence tree that contain occurrences of subactivities, yet not be activity trees. This allows for the existence of activity attempts, intended effects, and temporal constraints; subtrees that do not satisfy the desired constraints will simply not correspond to activity trees for the activity.


Informal Semantics for Complex Activities

(min_precedes ?s1 ?s2 ?a) is TRUE in an interpretation of the Complex Activity Theory if and only if ?s1 and ?s2 are subactivity occurrences in the activity tree for ?a, and ?s1 precedes ?s2 in the subtree. Any occurrence of an activity ?a corresponds to an activity tree (which is a subtree of the occurrence tree). The activity occurrences within this subtree are the subactivity occurrences of the occurrence of ?a.

(root ?s ?a) is TRUE in an interpretation of the Complex Activity Theory if and only if the activity occurrence ?s is the root of an activity tree for ?a.

(subtree ?a1 ?a2) ?occ2) is TRUE in an interpretation of the Complex Activity Theory if and only if every atomic subactivity occurrence in the activity tree for ?a1 is an element of the activity tree for ?a2.

(do ?a ?s1 ?s2) is TRUE in an interpretation of the Complex Activity Theory if and only if ?s1 is the root of an activity tree and ?s2 is a leaf of the same activity tree such that both activity occurrences are elements of the same branch of the activity tree.

(leaf ?s ?a) is TRUE in an interpretation of the Complex Activity Theory if and only if the activity occurrence ?s is the leaf of an activity tree for ?a.

(next_subocc ?s1 ?s2 ?a) is TRUE in an interpretation of the Complex Activity Theory if and only if ?s1 precedes ?s2 in the tree and there does not exist a subactivity occurrence that is between them in the tree.


Axioms of Complex Activities


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

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