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2. The Ramication Problem
2.1 Indirect Eects of Actions
An invaluable advantage of action laws is that they allow to describe actions
by their eects rather than by an exhaustive state transition table. How-
ever, the sole use of action laws quickly becomes unmanageable in complex
domains, too. For action laws as they stand are supposed to be complete
in that they specify the entire eect of an action. Yet although there are
good reasons to assume that an action causes only a small number of
direct
changes, these in turn may initiate a long chain of
indirect
eects. Recall the
action of toggling a switch, which, in the rst place, causes nothing but a
change of the switch's position. However, the switch may be part of an elec-
tric circuit so that, say, some light bulb is turned o as a side eect, which
in turn may cause someone to hurt himself in a suddenly darkened room
by running against a chair that, as a consequence, falls into a television set
whose implosion activates the re alarm and so on and so forth.
1
Let us state the problem more precisely. Suppose we perform the action
of toggling the switch in the simple electric circuit depicted in Fig. 2.1. In the
rst place, the action changes nothing but the position of the switch, which
thus is the
direct
eect. Obviously, however, a now closed switch means that
the light goes on.
2
This is an
indirect
eect of our action. This additional
eect is a consequence of the general relation between the position of the
switch and the state of the bulb, namely, light is on if and only if the switch
is in the upper position. This relation is formally described by the fluent
formula
(
s
1
). Fluent formulas of this kind, which are supposed
light
up
1
A crucial question in this context concerns the distinction between indirect
eects occurring during a single world's state transition step and those which
deserve separate state transitions (also called \delayed" eects). E.g., the above
may not only be described as \the re alarm is activated in the successor state
after having closed the switch," but also as, say, \the chair is falling in the
successor state (and presumably hits the television set during the next state
transition)." As a reasonable, albeit informal, guidance we suggest a single state
transition should summarize what happens until some agent has the possibility
to intervene by acting again (stopping the chair from falling, for instance). See
also Section 2.7 for a discussion on indirect vs. delayed eects.
2
We tacitly assume that battery and bulb are in working order; more to this in
Chapter 4.
