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theory is causality-oriented and follows the idea of successively generating
indirect eects, starting with preliminary successors and continuing until an
acceptable state is obtained. Minimality of changes is not required. This
general approach was used in [48] to extend the so-called Temporal Action
Logic [23]. The approach [10] builds on the action calculus called Linear
Connection Method (see below). It introduces resource-sensitive implications
which are syntactically identical to the action descriptions used therein. These
additional implications are applied with higher priority and have certain flu-
ent literals marked which must have previously occurred as eects in order for
the implication to apply. The resulting calculus can be viewed as realization
of causal relationships as means to address the Ramication Problem.
In [21], a least xpoint semantics is used to model chains of indirect eects.
The article also contains the proposal to extend the Ramication Problem
to indirect eects which derive from constraints that connect the states in
dierent situations.
An approach which is considerably dierent from all methods discussed
so far yet still related is based on networks representing probabilistic causal
theories [81]. These networks describe, in the rst place, static dependencies
among their components. As argued in [82, 83], however, the truth-values
of one or more nodes may be reset dynamically and, then, the values of all
depending nodes need to be adjusted according to standard (Bayesian) rules
of probability. This can be regarded as generating indirect eects. If prob-
ability values are restricted to the binary 0/1-case, then a network whose
nodes are fluent names resembles our concept of influence information. For
instance, Fig. 2.13a) depicts a network suitable for our electric circuit with
the relay and light detector. In view of a general solution to the Rami-
cation Problem, some restrictions of causal networks are worth mentioning.
First, we note that the resulting value of a node, after having xed the di-
rect eects, must not be computed until all new values of its predecessors
have been determined. Consequently, the proposition
in the net-
work of Fig. 2.13a) necessarily remains false after toggling switch
detect
s
1
in the
state depicted in Fig. 2.8; hence, the non-minimal successor state where a
light flash has been detected cannot be obtained. Second, recall the domain
with the trapdoor, Example 2.10.1. Since fluent
changing pos-
trap-open
sibly aects
), the adequate
network is the one depicted in Fig. 2.13b). This, however, does not allow to
distinguish between the two situations where either
trap-open
becomes true
with
(
), depending on
(
alive
turkey
at-trap
turkey
) being true, or it happens to be the other way round.
Hence, the distinction between context and triggering eect is not supported
by causal networks. Finally, networks representing causal theories are based
on acyclic graphs, which means that cyclic dependencies, like the one given
by our switches of Fig. 2.5, which are being connected by a spring, cannot be
represented (c.f. Fig. 2.13c)).
The Fluent Calculus paradigm we used for an axiomatization of our ac-
tion theory emerged from the urge to solve the fundamental so-called Frame
(
at-trap
turkey
