Store:FLen01

Introduction

We have come this far because, as colleagues, are very often faced with responsibilities and decisions that are very difficult to take and issues such as conscience, intelligence and humility come into play. In such a situation, however, we are faced with two equally difficult obstacles to manage that of one $KB$ (Knowledge Basis), as we discussed in the chapter ‘Logic of probabilistic language’, limited in the time that we codify in $KB_{t}$ and one $KB$ limited in the specific context ($KB_{c}$). These two parameters of epistemology characterize the scientific age in which we live. Also, both $KB_{t}$ that the $KB_{c}$ are dependent variables of our phylogeny, and, in particular of our conceptual plasticity and attitude to change.

«I'm not following you»
(I'll give you a practical example)

• How much research has been produced on the topic 'Fuzzy logic'?

Pubmed responds with 2862 articles in the last 10 years, so that we can say that ours is current and is sufficiently updated. However, if we wanted to focus attention on a specific topic like ‘Temporomandibular Disorders’, the database will respond with as many as 2,235 articles. Hence, if we wanted to check another topic like ‘Orofacial Pain’, Pubmed gives us 1,986 articles. This means that the $KB_{t}$ for these three topics in the last 10 years it has been sufficiently updated.

If, now, we wanted to verify the interconnection between the topics, we will notice that $KB_{c}$ in the contexts will be the following:

1. $KB_{c}=$ 'Temporomandibular disorders AND Orofacial Pain'$\rightarrow$ 9 articles in the last 10 years
2. $KB_{c}=$ 'Temporomandibular disorders AND Orofacial Pain AND Fuzzy logic' 0 articles in the last 10 years

The example means that the $KB_{t}$ is relatively up-to-date individually for the three topics while it decreases dramatically when the topics between contexts are merged and specifically to 9 articles for Point 1 and even to 0 articles for Point 2. So, the $KB_{t}$ is a time dependent variable while the $KB_{c}$ is a cognitive variable dependent on our aptitude for the progress of science, as already mentioned—among other things—in the chapter ‘Introduction’.

«you almost convinced me»
(Wait and see)

We ended the previous chapter by asserting that the logic of a classical language and subsequently probabilistic logic have helped us a lot in the progress of medical science and diagnostics but implicitly carry within themselves the limits of their own logic of language, which limits the vision of the biological universe. We also verified that with the logic of a classical language—so to speak, Aristotelian—the logical syntax that is derived from it in the diagnostics of our Mary Poppins limits, in fact, the clinical conclusion.

$\{a\in x\mid \forall {\text{x}}\;A({\text{x}})\rightarrow {B}({\text{x}})\vdash A(a)\rightarrow B(a)\}$ (see chapter Classical Language's Logic),

argues that: "every normal patient $\forall {\text{x}}$ which is positive on the radiographic examination of the TMJ $\mathrm {\mathcal {A}} ({\text{x}})$ has TMDs$\rightarrow \mathrm {\mathcal {B}} ({\text{x}})$, as a direct consequence $\vdash$ Mary Poppins being positive (and also being a "normal" patient) on the TMJ x-ray $A(a)$ then Mary Poppins is also affected by TMDs $\rightarrow {\mathcal {B}}(a)$

The limitation of the logical path that has been followed has led us to undertake an alternative path, in which the bivalence or binary nature of classical language logic is avoided and a probabilistic model is followed. The dentist colleague, in fact, changed the vocabulary and preferred a conclusion like:

$P(D|Deg.TMJ\cap TMDs)=0.95$

and which is, that our Mary Poppins is 95% affected by TMDs since she has a degeneration of the temporomandibular joint supported by the positivity of the data $D=\{\delta _{1},\dots \delta _{4}\}$ in a population sample $n$. However, we also found that in the process of constructing probabilistic logic (Analysandum $=\{P(D),a\}$) which allowed us to formulate the aforementioned differential diagnostic conclusions and choose the most plausible one, there is a crucial element to the whole Analysand$=\{\pi ,a,KB\}$ represented by the term $KB$ which indicates, specifically, a 'Knowledge Base' of the context on which the logic of probabilistic language is built.

We therefore concluded that perhaps the dentist colleague should have become aware of his own 'Subjective Uncertainty' (affected by TMDs or _nOP?) and 'Objective Uncertainty' (probably more affected by TMDs or _nOP?).

• Why have we come to these critical conclusions?

For a widely shared form of the representation of reality, supported by the testimony of authoritative figures who confirm its criticality. This has given rise to a vision of reality which, at first glance, would seem unsuitable for medical language; in fact, expressions such as ‘about 2’ or ‘moderately’ can arouse legitimate perplexity and seem an anachronistic return to pre-scientific concepts. On the contrary, however, the use of fuzzy numbers or assertions allows scientific data to be treated in contexts in which one cannot speak of ‘probability’ but only of ‘possibility’.

«Probability or Possibility?»