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The model in usual case is constituted of rather complex coupled systems of non-linear equations. For example the inpidual pressure-flow relations for the discrete paths are generally non-linear but nevertheless depend on key design parameters of the flow path (e.g. size of window opening, speed of a ventilation fan, or height of a monitor window). In most practical situations, however, it will not be possible to establish this relationship formally as the combined system of equations will be hopelessly complex. Consequently, it will be necessary to establish the relation numerically by systematically varying key design parameters over a range of reasonable values and solving for the system response (i.e. for a given building and ambient and operating conditions). Whether formally or numerically derived, one may establish the relation between system response and the key design parameters for a given design problem and for a given boundary condition vector: { } ( ) { } { } ( ) { } { } ( ) { } f f f RH m T f RH f m f T = = = , , && where T, m & and RH are surface temperature, air mass flow rate and relative humidity vectors while f is the vector of key design parameters. This relationship could be very complex, because of the non-linearity and the instability of t he system whose behaviour can drastically change with varying design parameters or boundary conditions. By combining the system response results developed in terms of the key design parameters, with a comfort metric (i.e. considering for a given zone ‘i’ the dry bulb temperature and air velocity along with the spatial average of the mean radiant temperature) we may establish the relation between the T, m & , RH and the design parameters. As we can readily deduce, the mathematical model embodies in general a system of coupled equations, which it is not possible to explicitly solve in terms of design parameters. So we can use this model (as well as a microscopic numerical model) only to predict the behaviour of a well-defined system and nothing we can say about the strategy to be adopted in order to modify that behaviour in a required way. 4. EXPLICIT CAUSAL MODELING OF PHYSICAL BEHAVIOUR Our efforts was aimed to support the decision making, with particular attention to the preliminary stage of design when the student is involved in complex inferences which integrate prediction and diagnosis in order to guide its trial and error activity. Numerical analysis approaches are directed instead only to predictive analysis while diagnosing numerical data (obtained through simulations or testing physical models) is essential to take corrective actions. Bayesian Networks (also known as Belief networks or causal diagrams) we have employed in VENTPad, were developed to model distributed processing in reading comprehension, where both semantical expectations and perceptual evidence must be combined to form a coherent interpretation. The ability to co-ordinate bi-directional inferences filled a void in expert systems technology of the early 1980’s, and Bayesian networks have emerged as a general representation scheme for uncertain knowledge. Bayesian networks are directed acyclic graphs in which the nodes represent variables of interest and the links represent informational or causal dependencies among the variables. The strength of a dependency is represented by conditional probabilities that are attached to each cluster of parents-child nodes in the network. For variables without parents (as the boundary condition variables), the probabilities are unconditional distributions. With these data, a Bayesian network allows one to calculate the joint distribution over all variables1 from which all probabilistic queries, involved in reasoning, can be answered coherently using probability calculus. They can be used t o model the causal mechanisms that operate in real systems rather than, as in many other knowledge representation schemes (e.g., rule-based systems and neural networks), the reasoning process. This model is obtained by representing the causal dependencies among the system variables as probabilistic functions (i.e., the probability that variable C assumes the value z when A assumes the value x and B assumes the value y is equal to 0,85, written P(C=z|A=x,B=y)=0.85, means that there’s a high probability that the state (x,y) forces C to assume the value z). Bayesian networks effectively allow a number of integrated logical and quantitative inferences about the behaviour of physical systems and their application could be an interesting connection tool between logical and analytical procedures in preliminary design aiding. The inference process based on bayesian networks is described in large body of literature and is best summarised in (Pearl 1988). Anyway I refer to following basic works for key concepts and terminology related to these issues (Pearl 1988, 1996; Shachter 1990; Jensen 1996; Spirtes et al. 1993). Bayesian networks have been applied to problems in medical diagnosis (Heckerman et al. 1992; Spiegelhalter, et al. 1989), map learning (Dean 1990), language understanding (Charniak and Goldman 1989a, 1989b). In architecture design and construction early applications are related to reliability analysis of innovative building products (Naticchia 1999a) and to diagnosis of building failures (Naticchia 1999b). 4.1 CAUSAL MODEL OF NATURAL VENTILATION As an example, it is useful to think of the ventilation model from a causal point of view, as a network that links the key parameters – namely the ‘design space’ - to the physical variables (i.e. Ti and im & ). The comfort criteria also define a causal network along with the variables.