Although the given description of diagnostic problem solving carries much of the flavor of the process of diagnosis, it is still an imprecise description and in fact, several formal theories have been proposed to capture the concept of diagnosis more precisely. In doing so, however, researchers became aware that there are actually various conceptual models of diagnosis, determined by the kind of knowledge involved. Hence, diagnosis concerns the interpretation of observed findings in the context of knowledge from a problem domain. A good starting point for describing diagnosis at a conceptual level is the various types of knowledge that play a role in diagnostic applications. The knowledge embodied in a diagnostic system may be based on one or more of the following descriptions:

1. A description of the normal structure and functional behavior of a system.
2. A description of abnormal functional behavior of a system; abnormal structure is usually not taken into account.
3. An enumeration of defects and collections of observable findings for every possible defect concerned, without the availability of explicit knowledge concerning the (abnormal) functional behavior of the system.
4. An enumeration of findings for the normal situation.

These types of knowledge may coexist in real-life diagnostic systems, but it is customary to emphasize their distinction in conceptual and formal theories of diagnosis. Similar classifications of types of knowledge appear in the literature on diagnosis, although often no clear distinction is made between the conceptual, formal and implementation aspects of diagnostic systems.

An observed finding that has been gathered in diagnosing a problem is often said to be either a normal finding, i.e. a finding that matches the normal situation, or an abnormal finding, i.e. a finding that does not match the normal situation. Based on the four types of knowledge mentioned above, and the two sorts of findings, three different conceptual models of diagnosis are usually distinguished; they will be called:

1. Deviation-from-Normal-Structure-and-Behavior Diagnosis, abbreviated to DNSB diagnosis;
2. Matching-Abnormal-Behavior diagnosis, abbreviated to MAB diagnosis; and
3. Abnormality Classification diagnosis, abbreviated to AC diagnosis.

For diagnosis based on knowledge concerning normal structure and behavior (DNSB), little or no explicit knowledge is available about the relationships between defects of the system, on the one hand, and findings to be observed when certain defects are present, on the other hand. Hence, DNSB diagnosis typically employs knowledge of the first and fourth types mentioned above. From a practical point of view, the primary motivation for investigating this approach to diagnosis is that in many domains little knowledge concerning abnormality is available, which is certainly true for new human-developed artifacts. DNSB diagnosis is frequently erroneously called model-based diagnosis in the literature, as if it were the only instance of model-based diagnosis. As far as known, DNSB diagnosis-like approaches have been used in medical applications on a limited scale; because more work is needed in which DNSB diagnosis has been applied to solve practical problems.

For diagnosis based on knowledge of abnormal behavior (MAB), diagnostic problem solving amounts to simulating the abnormal behavior using an explicit model of that behavior. Hence, in MAB diagnosis the use of knowledge of abnormal behavior (the second type mentioned above) is emphasized. By assuming the presence of certain defects, some observable abnormal findings can be predicted. It can be investigated which of these assumed defects account for the observed findings by matching the predicted abnormal findings with those observed. Based on the type of reasoning employed to formalize MAB diagnosis, i.e. reasoning from effects to causes instead of from causes to effects, this theory of diagnosis is also referred to as abductive diagnosis.

Where DNSB and MAB diagnosis employ a model of normal or abnormal structure and behavior for the purpose of diagnosis, the third conceptual model of diagnosis uses neither. The knowledge employed in this conceptual model of diagnosis consists of the enumeration of more or less typical evidence that can be observed, i.e. observable findings, when a particular defect or defect category is present (the third type of knowledge mentioned above). For example, sneezing is a finding that may be typically observed in a disorder like common cold. This form of knowledge has been referred to as empirical associations, diagnostic problem solving amounts to establishing which of the elements in a finite set of defects have associated findings that account for as many of the findings observed as possible.

The enumeration of findings for the normal situation (knowledge of the fourth type mentioned above) is sometimes also used in AC diagnosis, together with knowledge of the third type; then observed findings are classified in terms of present and absent defects. The main goal of AC diagnosis, however, remains the classification of observed findings in terms of abnormality. AC diagnosis is often referred to as heuristic classification in the literature, although this term is broader, since it also includes a reasoning strategy. The MYCIN system, is the classical system in which this conceptual approach to diagnosis has been adopted. AC diagnosis can be characterized in terms of logical deduction in a straightforward way. It is referred to this formalization of AC diagnosis as hypothetico-deductive diagnosis.