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== Abstract ==
[[File:Spasmo_emimasticatorio_JJ.jpg|alt=|left|250x250px]]
The text deals with the logic of probabilistic language applied to the medical field, highlighting how uncertainty is an intrinsic part of scientific practice. Through probabilistic and statistical concepts, efforts are made to manage and understand the uncertainties associated with medical theory and practice.
The role of probability in the relationship between theory and observation is emphasized, distinguishing between subjective uncertainty and randomness. Subjective uncertainty concerns individuals' state of knowledge and belief, while randomness refers to the lack of a certain connection between cause and effect.
In the medical approach, the importance of understanding and distinguishing between subjective and objective probability is discussed. Subjective probability reflects individual belief, while objective probability is based on data and empirical evidence.
The concept of probabilistic-causal analysis is then further explored, which seeks to quantify the relationship between events and random processes in clinical diagnosis. A detailed exposition is presented on how conditional probabilities can be interpreted and how causal relevance partitioning can be used to formulate a differential diagnosis.
Finally, the theme of interdisciplinarity in scientific research is addressed, highlighting the importance of an interdisciplinary approach to tackling complex problems. Fuzzy logic is also mentioned as a possible tool for managing uncertainty in medical contexts.


{{ArtBy|
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| autore3 = Flavio Frisardi
| autore3 = Flavio Frisardi
}}
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'''Abstract:''' This chapter introduces the concept of probabilistic language and its critical role in medical diagnosis, particularly in cases of diagnostic uncertainty such as that of Mary Poppins, who suffers from Orofacial Pain. Medical diagnoses often rely on deterministic logic, but this is not always sufficient in complex clinical cases where uncertainty plays a significant role. The chapter distinguishes between subjective and objective uncertainties, showing how probabilistic methods help manage these uncertainties. It explains how clinicians apply subjective probability to their beliefs about a diagnosis, while objective probability deals with the statistical likelihood of conditions based on available data.


By analyzing Mary Poppins' case, the chapter emphasizes how probability theory enhances clinical reasoning, particularly when the causal relationships between symptoms and diseases are unclear. Using examples such as Temporomandibular Disorders (TMD) and Orofacial Pain (OP), the chapter demonstrates how probabilistic-causal analysis assists in determining the causal relevance of various clinical signs and symptoms.
The chapter introduces mathematical formalism to quantify the uncertainty in medical diagnosis, highlighting how partitioning patient data into subsets based on causal relevance improves differential diagnosis. Finally, it explores the limits of probabilistic reasoning in medical language and suggests the need for a more flexible linguistic approach, such as fuzzy logic, to address the inherent uncertainties in medical practice. This prepares the reader for the following chapter on fuzzy logic, offering a broader perspective on managing diagnostic uncertainty.
== Introduction to the Probabilistic Language ==
== Introduction to the Probabilistic Language ==
Every scientific idea—whether in medicine, architecture, engineering, chemistry, or any other field—when implemented, is prone to small errors and uncertainties. Mathematics, through the lens of probability theory and statistical inference, aids in precisely managing and thereby mitigating these uncertainties. It must always be considered that in all practical scenarios, "the outcomes also depend on many other external factors to the theory," be they initial and environmental conditions, experimental errors, or others.
Every scientific idea—whether in medicine, architecture, engineering, chemistry, or any other field—when implemented, is prone to small errors and uncertainties. Mathematics, through the lens of probability theory and statistical inference, aids in precisely managing and thereby mitigating these uncertainties. It must always be considered that in all practical scenarios, "the outcomes also depend on many other external factors to the theory," be they initial and environmental conditions, experimental errors, or others.
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<center>
<center>
===Second Clinical Approach===
<big>'''Second Clinical Approach'''</big>
 
''(hover over the images)''
''(hover over the images)''
<gallery widths="350" heights="282" perrow="2" mode="slideshow">
<gallery widths="350" heights="282" perrow="2" mode="slideshow">
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File:Atm1 sclerodermia.jpg|'''<!--85-->Figure 3:''' Computed Tomography of the TMJ
File:Atm1 sclerodermia.jpg|'''<!--85-->Figure 3:''' Computed Tomography of the TMJ
File:Spasmo emimasticatorio assiografia.jpg|'''<!--87-->Figure 4:''' Axiography of the patient showing a flattening of the chewing pattern on the right condyle
File:Spasmo emimasticatorio assiografia.jpg|'''<!--87-->Figure 4:''' Axiography of the patient showing a flattening of the chewing pattern on the right condyle
File:EMG2.jpg|'''<!--89-->Figure 5:''' EMG Interferential Pattern. Overlapping upper traces corresponding to the right masseter, lower to the left masseter.  
File:EMG2.jpg|'''<!--89-->Figure 5:''' EMG Interferential Pattern. Overlapping upper traces corresponding to the right masseter, lower to the left masseter.
</gallery>
</gallery>
</center>
</center>
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In order to take advantage of the information provided by this dataset, the concept of partition of causal relevance is introduced:
In order to take advantage of the information provided by this dataset, the concept of partition of causal relevance is introduced:
====The partition of causal relevance====
==== The partition of causal relevance====


:Always be <math>n</math> the number of people we have to conduct the analyses upon, if we divide (based on certain conditions as explained below) this group into <math>k</math> subsets <math>C_i</math> with <math>i=1,2,\dots,k</math>, a cluster is created that is called a "partition set" <math>\pi</math>:
:Always be <math>n</math> the number of people we have to conduct the analyses upon, if we divide (based on certain conditions as explained below) this group into <math>k</math> subsets <math>C_i</math> with <math>i=1,2,\dots,k</math>, a cluster is created that is called a "partition set" <math>\pi</math>:
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|<math>P(D| noDeg.TMJ  \cap noTMDs)=0.001  \qquad \qquad \;</math>
|<math>P(D| noDeg.TMJ  \cap noTMDs)=0.001  \qquad \qquad \;</math>
|
|
|where
|where  
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====Clinical situations====
====Clinical situations====
These conditional probabilities demonstrate that each of the partition's four subclasses is causally relevant to patient data <math>D=\{\delta_1,.....\delta_n\}</math> in the population sample <math>PO</math>. Given the aforementioned partition of the reference class, we have the following clinical situations:
These conditional probabilities demonstrate that each of the partition's four subclasses is causally relevant to patient data <math>D=\{\delta_1,.....\delta_n\}</math> in the population sample <math>PO</math>. Given the aforementioned partition of the reference class, we have the following clinical situations:  
*Mary Poppins <math>\in</math> degeneration of the temporomandibular joint <math>\cap</math>  Temporomandibular Disorders
*Mary Poppins <math>\in</math> degeneration of the temporomandibular joint <math>\cap</math>  Temporomandibular Disorders  


*Mary Poppins <math>\in</math> degeneration of the temporomandibular joint <math>\cap</math> no Temporomandibular Disorders
*Mary Poppins <math>\in</math> degeneration of the temporomandibular joint <math>\cap</math> no Temporomandibular Disorders  


*Mary Poppins <math>\in</math> no degeneration of the temporomandibular joint <math>\cap</math> Temporomandibular Disorders
*Mary Poppins <math>\in</math> no degeneration of the temporomandibular joint <math>\cap</math> Temporomandibular Disorders  


*Mary Poppins <math>\in</math> no degeneration of the temporomandibular joint <math>\cap</math> no Temporomandibular Disorders
*Mary Poppins <math>\in</math> no degeneration of the temporomandibular joint <math>\cap</math> no Temporomandibular Disorders
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----
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==Final considerations==
==Final considerations ==
We took a long and tortuous path to better understand the complexity encountered by the colleague struggling with the very heavy ethical responsibility of making a diagnosis. However, this task becomes even more complex when we need to be detailed and careful in making a differential diagnosis.
We took a long and tortuous path to better understand the complexity encountered by the colleague struggling with the very heavy ethical responsibility of making a diagnosis. However, this task becomes even more complex when we need to be detailed and careful in making a differential diagnosis.


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  | LCCN =  
  | LCCN =  
  | OCLC =  
  | OCLC =  
  }}</ref> for an implementation in the analysis and reconstruction of how 'knowledge' is built in different disciplines, demands an answer to the following question from the dentist:{{q4|...<!--145-->is there another world or context, parallel to yours, in which in addition to the D data there are further data unknown to you?|}}
  }}</ref> for an implementation in the analysis and reconstruction of how 'knowledge' is built in different disciplines, demands an answer to the following question from the dentist:
 
{{q4|...is there another world or context, parallel to yours, in which in addition to the D data there are further data unknown to you?|}}


and increase the dose: submit Mary Poppins to the following trigeminal electrophysiological tests, label them as we did previously for the set data <math>D=\{\delta_1,\dots\delta_n\}</math> generating another set containing a number <math>m</math> of unknown data (not belonging to the purely dental branch) <math>C=\{\gamma_1,\dots\gamma_m\}</math> thereby creating an entirely new set that we will call <math>S_{unknow}= D+C=\{\delta_1,\dots,\delta_n,\gamma_1,\dots,\gamma_m\}</math> (called <math>S_{unknown}</math> precisely due to the presence of data unknown to the dental context).
and increase the dose: submit Mary Poppins to the following trigeminal electrophysiological tests, label them as we did previously for the set data <math>D=\{\delta_1,\dots\delta_n\}</math> generating another set containing a number <math>m</math> of unknown data (not belonging to the purely dental branch) <math>C=\{\gamma_1,\dots\gamma_m\}</math> thereby creating an entirely new set that we will call <math>S_{unknow}= D+C=\{\delta_1,\dots,\delta_n,\gamma_1,\dots,\gamma_m\}</math> (called <math>S_{unknown}</math> precisely due to the presence of data unknown to the dental context).
Gianni
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