Progression of Decomposed Local-Effect Action Theories
  In many tasks related to reasoning about consequences of a logical theory, it
is desirable to decompose the theory into a number of weakly-related or
independent components. However, a theory may represent knowledge that is
subject to change, as a result of executing actions that have effects on some
of the initial properties mentioned in the theory. Having once computed a
decomposition of a theory, it is advantageous to know whether a decomposition
has to be computed again in the newly-changed theory (obtained from taking into
account changes resulting from execution of an action). In the paper, we
address this problem in the scope of the situation calculus, where a change of
an initial theory is related to the notion of progression. Progression provides
a form of forward reasoning; it relies on forgetting values of those
properties, which are subject to change, and computing new values for them. We
consider decomposability and inseparability, two component properties known
from the literature, and contribute by 1) studying the conditions when these
properties are preserved and 2) when they are lost wrt progression and the
related operation of forgetting. To show the latter, we demonstrate the
boundaries using a number of negative examples. To show the former, we identify
cases when these properties are preserved under forgetting and progression of
initial theories in local-effect basic action theories of the situation
calculus. Our paper contributes to bridging two different communities in
Knowledge Representation, namely research on modularity and research on
reasoning about actions.
