The last decades have witnessed a considerable development of knowledge-based systems in medicine aiming at providing support for physicians in the decision-making process.

The Computer-Assisted DIAGnostic (CADIAG) systems, developed at the Medical University of Vienna, are reasonably successful examples along this line. CADIAG-1 deals with Boolean (yes/no) relationships, formulated as IF-THEN rules, between symptoms, signs, test results and clinical findings on the one hand and diagnoses on the other hand.

Mathematical logic plays an important role in these systems. A simple and elegant formalization of the IF-THEN rules of CADIAG-1 into a decidable fragment of first-order classical logic led to the detection of 17 inconsistencies in the knowledge base (see here).

However, the information available to physicians about their patients and in general about medical relationships, is not sharp. Therefore computer systems for medical decision making cannot be accurate when based on formal systems whose objects can only be either absolutely true or absolutely false (as in classical logic). To process vague information, the successor systems CADIAG-2 and CADIAG-4 were based on fuzzy set theory ("fuzzy logic", in Zadeh's terminology). Fuzzy IF-THEN rules are evaluated using Zadeh's min/max functions. This design, however, faces some difficulties which will be addressed by the proposed project. Indeed the results of inferences do not take into account the possibility of several independent rules confirming the same diagnosis with an equal weight. Moreover, not being based on formal logics, the resulting systems do not lend themselves to rigorous checking (e.g. consistency) and it is not clear whether their inferential mechanism can be exported to other medical areas (the effect of "non portability" of the fuzzy operations was already experienced with MYCIN -the forefather of all expert systems--and its extension eMYCIN). Using the potential of our theoretical research in t-norm based logics (that have been recognized to be the logical counterpart of many inferential mechanisms of "fuzzy logic") we aim to solve the above drawbacks.

In particular, we will use symbolic logic to
(i) perform a formal consistency check of the rules of CADIAG-2 and CADIAG-4,
(ii) formally justify the choice of the operators (t-norms) and the way of combining the rules of the systems and
(iii) compute satisfactory results in the presence of incomplete information.
The potential of fuzzy description logics to describe medical ontologies in these systems will be also explored.