The process of constructing models of the world is essential if an agent is to act in an intelligent way. One area of particular interest is in constructing causal models, which, for example, can allow the agent to plan what actions to take to achieve a particular goal. One of the problems in forming models is what to include in the model and what not to. P.P. Nayak proposes a systematic way of constructing adequate causal models using a minimal causal explanation.

Initially Nayak asks the following questions which cast the problem as one of search:

What is a model, and what is the space of possible models? (What is the search space?)

What is an adequate model? (What is the goal criterion?)

How do we search the space of possible modes for adequate models? (What is the search strategy?)

To which he answers that a model is constructed of model fragments, which are equations that partially describe a single device phenomena (as the domain of this technique is explaining physical systems, such as a temperature gage or a block and tackle) which can be collected together into a library. An adequate model is a model that describes some system as a causal chain or ordering of causality and is parsimonious or minimal in that it describes only enough detail to capture the system and contains no extraneous information (for example, a temperature gage based on the a thermistor might include a description of the electromagnetic field surrounding the thermistor, but this would be more detail than necessary to describe the workings of device as a temperature gage). The explanation of the value of a parsimonious system description that Nayak provides is an appeal to Occam's Razor in that a simpler model explains fewer aspects of the system and approximation descriptions are simpler than exhaustive descriptions.

The final component of the problem, finding an adequate model, is a daunting one as Nayak explains, because the search space for possible system models is an exponentially large one, and in fact is NP-complete. Nayak presents a number of cases where he proves that this is the case. But like the SAT problem with respect to HORN-SAT, Nayak proposes a set of modifications to make the search of the causal model space tractable. This is achieved by imposing certain constraints on the construction of the problem space which he calls causal approximations. Causal approximations allow a search to be conducted in polynomial time by forcing the model to be refined in a monotonically decreasing method. This monotonicity is derived from the decomposition of the model fragments into mutually contradictory sets (i.e. only one member of a set of model fragments can be used in a model) which a partial order of approximation level (i.e. x is more approximate than y) can be imposed upon. Another important characteristic of causal approximation monotonicity is that once a model has been found to be inadequate, no additional simplification of that model will be adequate, thus trimming the search space. Model fragments interrelate by the variables or parameters to their equations which can either be local or shared. This allows a chain of causality to be constructed by forcing each fragment to interrelate with other fragments with one parameter (which seems simplistic, but Nayak indicates that this is the case for a wide range of systems). The search proceeds by attempting to simplify the most accurate model as much as possible.

One of the problems with this system is that there does not appear to be a clear statement of where the search should start. Nayak indicates that selecting this starting point is one of the components of the NP-Hardness of this problem, but does not adequately explain how this is overcome (with the possible nod of his head to domain dependence of the problems).

Another problem is based on the fact that the specification of model fragments and the sets that they belong to are problem domain dependent, which means that an outside agency (i.e. the user) must define them and set the search going. This is adequate, in my opinion, for testing this knowledge representation system, but it does seem to require to much input by the user. It begs the question of theory formation and learning in general, which is where the system causal approximation, as it is a technique for constructing abstractions, could really shine.