# A Brief Roadmap into Uncertain Knowledge Representation via Probabilistic Description Logics
## 2 The Many Faces of Uncertainty
Hence, when we say that a medical test has 95% diagnostic specificity--in lay terms, if the test is positive, then there is a 95% chance that the individual is in fact positive for the disorder under scrutiny--what we are saying is that 95 out of every 100 positive tests are correct (and the remaining 5 are wrong). Hence, if we randomly take one of these tests, it has a 95% chance of being a correct one. Note that one can only be so specific about the probability if the whole population is known. In contrast, subjective probabilities consider unique instances which are characterised by different possibilities. The prototypical example in this direction is the weather forecast. When a meteorological model predicts a 40% chance of rain tomorrow, it cannot be read as a statistical statement saying that rain will be present in 40 out of 100 _tomorrows_. Instead, it studies different scenarios based on possible parameters such as wind speed and direction, temperature and humidity to verify in which of those scenarios rain is present (In reality, the values provided by actual weather forecasts are more complex, as they also take into account the area of the region under consideration [16]. For the sake of the example, we do not delve deeper into these details). [PERSON]'s classification, however, is not fully satisfied in the context of knowledge representation, particularly in the context of incomplete domain knowledge and expert knowledge. We use these two cases to exemplify the limitations of each of the two types of probabilities. As previously mentioned, statistical probabilities are derived as proportional observations of an event within a given population. The term _statistical_ hence refers to a very basic analysis of data. The name is unfortunate, as it also evokes the use of more advanced statistical analyses, which are _not_ foreseen in these logics. The most basic example is the presence of incomplete knowledge. While it is pretty straightforward to determine the exact proportion of students in a given classroom who are left-handed, the same cannot be said about, e.g., COVID-19 patients who have pulmonary scars. To know this latter proportion, it is necessary to precisely identify who has been infected with the disease, and make a pulmonary plaque on all those subjects. Both of these tasks induce high economic, social, and human costs which one might not be willing to cover. Instead, it is possible to approximate this knowledge using a statistical analysis of the available data on publicly known infected individuals, and the results from hospital analyses of people suspected of having lung issues arising from it. Alternatively, one can also _sample_ the population to estimate these proportions. Both ideas are intended to fill the gap left by the incomplete knowledge of exactly how many people fall into each of the categories of interest. The cost, however, is that there are (uncertain) margins of error that one needs to take into account. Let us consider now subjective probabilities, which aim to represent beliefs about the likelihood of specific events. A common use of subjective probabilities is for modelling expert knowledge, where a (human) expert may--perhaps based on past observations--assign a probability to an event. In these cases, the numerical values underlying probabilities (and their algebraic manipulations) become more of a hindrance than an advantage. Indeed, there is no-one capable of discerning a probability of 95% from one of 95.5% nor, for that matter, 60% from 70%. Importantly, even subtle differences may cause huge mismatches over a derivation process; they may even lead to inconsistency in the collected knowledge. In these cases, it is perhaps more useful to represent _comparative_ statements, of the form _X is more likely than Y_. However, this requires the development of new reasoning techniques, especially in the presence of mixed statements. Moreover, it comes at the price of losing precision.