Atomic Activity Theory
# Atomic Activity Theory

The core theory of Atomic Activities provides axioms for intuitions about the
concurrent aggregation of primitive activities.
Although the Subactivity Theory can represent arbitrary composition of activities,
the composition of atomic activities is restricted to concurrency;
to represent complex, or nonatomic, activities requires the Complex Activity Theory.

The basic ontological commitments of the Atomic Activity Theory are based on the
following intuitions:

** Intuition 1:**

*
Concurrency is represented by the occurrence of one concurrent activity
rather than multiple concurrent occurrences.
*

Since concurrent activities may have preconditions and effects that are not
the conjunction of the preconditions and effects of their activities,
this core theory takes the following approach:

** Intuition 2:**

*
Every concurrent activity is equivalent to the composition of a set of
primitive activities.
*

Atomic activities are either primitive or concurrent (in which case they
have proper subactivities).
The Atomic Activities core theory introduces the function `conc` that
maps any two atomic activities to the activity that is their concurrent composition.
Essentially, what we call an atomic activity corresponds to some set of primitive
activities.

## Informal Semantics for the Atomic Activity Theory

`(atomic ?a)` is TRUE in an interpretation of the Atomic Activity
Theory if and only if either ?a is primitive or it is the concurrent superposition
of a set of primitive activities.

`(= ?a (conc ?a1 ?a2))` is TRUE in an interpretation of the
Atomic Activity Theory if and only if
?a3 is the atomic activity that is the concurrent superposition of the two atomic
activities ?a1 and ?a2.

`(primitive ?a)` is TRUE in an interpretation of the Atomic Activity
if and only if ?a has no proper subactivities.

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

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