The paper concerns a significant problem in the diagnostics of industrial processes, which is the need to achieve high fault distinguishability. High distinguishability results in the generation of precise diagnoses that enable making appropriate security decisions. In the known approaches, the efforts to obtain high distinguishability are focused on the selection of an appropriate set of generated residuals. The paper presents a new method of diagnostic reasoning using the notation of faults/diagnostic signals’ relations in the form of a Fault Isolation System (FIS), which enables the use of multivalent diagnostic signals. In addition, the proposed method uses knowledge (usually incomplete) about the sequence of symptoms. Reasoning was carried out on the basis of simple, physically possible signatures, resulting from the FIS. Assumptions and a diagnostic algorithm are given. The reasoning algorithm works in a step-by-step manner, after observing further symptoms. In each reasoning step, two diagnoses are generated in parallel. A more accurate, but less certain diagnosis is formulated on the basis of the value of all diagnostic signals, and the diagnosis is less accurate, but more reliable, solely on the basis of symptoms. An example of using the method for diagnosing a set of connected liquid tanks is given. The method was compared with other reasoning methods based on columns (signatures) and, also, with row-based reasoning methods. It is shown that the proposed method allows the increase of the distinguishability of faults compared to other methods. The distinguishability grows with the knowledge of elementary symptom sequences. It is also noted that the proposed approach makes possible diagnosing not only faults, but also cyber attacks.