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4.2 Model-Based Diagnosis with LYDIA Model-Based Fault Diagnosis
Thus, {A, B} and {B, C} are conflict sets. Then, finding the minimal conflicts can be achieved by
applying an algorithm for the Hitting Set problem. This also results in the sets {B} and {A, C}.
This method is used in [11], and is based upon the extraction of conflicts and candidates from a
lattice in order to produce the diagnoses. Results using this method yield exactly the same results,
as when writing the propositional model to DNF-form.
In summary, MBD of combinational systems means solving a model for h using propositional
logic. The next section describes the MBD implementation that is used in this thesis. It uses the
first method, writing the model to DNF-form, for solving the model for h.
4.2 Model-Based Diagnosis with LYDIA
This section introduces the system modeling language LYDIA (Language for sYstem DIAgnosis),
and the corresponding LYDIA toolkit. Other diagnostic systems are GDE by de Kleer and Williams
[11], Sherlock by de Kleer and Williams [12], and Livingston by Williams and Nayak [30]. See
[28] for a comprehensive introduction to LYDIA. The LYDIA toolkit consists of tools enabling the
diagnosis of systems; the diagnostic engine. The language LYDIA is able to describe structure and
behavior of a wide range of phenomena. It is compositional, which means that it can be used to build
up a system from previously defined constituents. These constituents can be hardware components,
processes and even software subsystems. The following is - like in the previous section - split up
into the two artifacts MBD requires: the modeling language LYDIA and the diagnostic engine that
operates on a LYDIA model.
LYDIA Language
Lydia is a declarative language. Each LYDIA statement is a proposition. All statements are true, and
apply concurrently. Recall the example of the 3 inverters, as shown in Figure 4.1. Its propositional
system of equations of 4.2 can easily be translated to LYDIA. The behavioral rule for one inverter (in
proposition logic: h ⇒ (i ⇔ ¬o)) is defined in LYDIA as follows:
system inverter(bool i, h, o) {
//declaration health variable
attribute health(h) = true;
attribute probability(h) = h ? 0.99 : 0.01;
}
//behavioral rule
h => (i = !o); // If healthy, output equals inverse of the input
Then, 3 of such inverters can be connected by the following structural description:
#include inverter.sys
// Include the definition of one inverter
system inverters3 (
bool w,
//input
bool hA, hB, hC, //healths
bool y, z
//outputs
) {
// Declaration internal variable
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