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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|
{{ArtBy|
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| autore3 = Flavio Frisardi
| autore3 = Flavio Frisardi
}}
}}
'''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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<math>P(D| Deg.TMJ  \cap TMDs)=0.95</math> - this means that our Mary Poppins is 95% affected by TMDs, since she has a degeneration of the Temporomandibular Joint in addition to the positive data <math>D=\{\delta_1,.....\delta_n\}</math>
<math>P(D| Deg.TMJ  \cap TMDs)=0.95</math> - this means that our Mary Poppins is 95% affected by TMDs, since she has a degeneration of the Temporomandibular Joint in addition to the positive data <math>D=\{\delta_1,.....\delta_n\}</math>


----
==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.


Here, we enter a delicate topic, that is connected with the epistemological contents and that first of all was reported in the "[[Introduction]]". We are talking about:
*'''Interdisciplinarity''': <br>''In science policy, it is generally recognized that science-based problem solving requires interdisciplinary research ('''IDR'''), as proposed by the EU project called Horizon 2020<ref>European Union, ''[https://ec.europa.eu/programmes/horizon2020/en/h2020-section/societal-challenges Horizon 2020]''</ref>. In a recent study, the authors focus on the question why researchers have cognitive and epistemic difficulties in conducting IDR. It is believed that the loss of philosophical interest in the epistemology of interdisciplinary research is caused by a philosophical paradigm of science called "Physics Paradigm of Science", which prevents recognition of important IDR changes in both the philosophy of science and research.<br>The proposed alternative philosophical paradigm, called 'Engineering Paradigm of Science', makes alternative philosophical assumptions about aspects such as the purpose of science, the character of knowledge, the epistemic and pragmatic criteria for the acceptance of knowledge and the role of technological tools. Consequently, scientific researchers need so-called metacognitive scaffolds to assist them in the analysis and reconstruction of how 'knowledge' is constructed in different disciplines.<br>In interdisciplinary research, metacognitive scaffolds help interdisciplinary communication analyse and articulate how the discipline builds knowledge<ref name=":0">{{cita libro
| autore = Boon M
| autore2 = Van Baalen S
| titolo = Epistemology for interdisciplinary research - shifting philosophical paradigms of science
| url = https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6383598/
| volume =
| opera = Eur J Philos Sci
| anno = 2019
| editore =
| città =
| ISBN =
| LCCN =
| DOI = 10.1007/s13194-018-0242-4
| OCLC =
}} 9(1):16.</ref><ref>{{cita libro
| autore = Boon M
| titolo = An engineering paradigm in the biomedical sciences: Knowledge as epistemic tool
| url = https://www.ncbi.nlm.nih.gov/pubmed/28389261
| volume =
| opera = Prog Biophys Mol Biol
| anno = 2017
| editore =
| città =
| ISBN =
| LCCN =
| DOI = 10.1016/j.pbiomolbio.2017.04.001
| OCLC =
}}</ref>''


This concept is linked to the previously discussed topic in which the colleague should be aware of his own 'Subjective Uncertainty' (due to a classic logic language 'sick or healthy') and of 'Objective Uncertainty' (due to a probabilistic logic language 'probably sick or probably healthy'). It is not complicated to prove this assertion: the uncertainty we are talking about derives from the fact that the elements, assertions, data, classes and subclasses mentioned and that build the apparatus of the logic of probabilistic's language: Analysandum <math>  = \{P(D),a\}</math> and Analysan '''<math>= \{\pi,a,KB\}</math>''' are elements that exist in a specific world, and in this case in a dental context in which the element <math>KB</math> of the process indisputably indicates a "basic knowledge" only in a specific dental context.


This conclusion confirmed by the dentist was the following:


<math>P(D| Deg.TMJ  \cap TMDs)=0.95</math>


----
or better: it is my 95% belief that Mary Poppins is affected by TMDs since she has a degeneration of the temporomandibular joint in addition to the positivity of the data <math>D=\{\delta_1,\dots\delta_n\}</math>But something strange happens because out of nowhere, a researcher, who uses 'metacognitive scaffolds'<ref>{{Cite book
| autore = Boon M
| autore2 = Van Baalen S
| titolo = Epistemology for interdisciplinary research - shifting philosophical paradigms of science
| url = https://pubmed.ncbi.nlm.nih.gov/30873248/
| volume =
| opera = Eur J Philos Sci
| anno = 2019
| editore =
| città =
| ISBN =
| PMID = 30873248
| PMCID = PMC6383598
| DOI = 10.1007/s13194-018-0242-4
| oaf = CC BY<!-- qualsiasi valore -->
| LCCN =
| 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|...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).
 
<math>\delta_1=</math> Positive radiological report of the TMJ in Figure 2
 
<math>\delta_2=</math> Positive CT report of the TMJ in Figure 3
 
<math>\delta_3=</math> Positive axiographic report of the condylar traces in Figure 4
 
<math>\delta_4=</math> Asymmetric EMG interference pattern in Figure 5
 
<math>{\gamma _{1}}=</math> Jaw jerk in Figure 6
 
<math>{\displaystyle \gamma _{2}}=</math> Mechanical Silent Period in Figure 7
 
<math>{\displaystyle \gamma _{3}}=</math> CT right masseter muscle in Figure 8
 
<center>
===Third Clinical Approach===
''(hover over the images)''
<center><gallery widths="350" heights="282" perrow="2" mode="slideshow">
File:Spasmo emimasticatorio.jpg|'''Figure 1:''' Patient reporting "Orofacial pain in the right hemilateral)
File:Spasmo emimasticatorio ATM.jpg|'''<!--159-->Figure 2:''' <!--160-->Patient's TMJ Stratigraphy showing signs of condylar flattening and osteophyte
File:Atm1 sclerodermia.jpg|'''<!--161-->Figure 3:''' <!--162-->Computed Tomography of the TMJ
File:Spasmo emimasticatorio assiografia.jpg|'''<!--163-->Figure 4:''' <!--164-->Axiography of the patient showing a flattening of the chewing pattern on the right condyle
File:EMG2.jpg|'''<!--165-->Figure 5:''' <!--166-->EMG Interferential Pattern. Overlapping upper traces corresponding to the right masseter, lower to the left masseter.
File:Spasmo emimasticatorio JJ.jpg|'''<!--167-->Figure 6:''' <!--168-->Jaw jerk electrophysiologically detected on the right (upper traces) and left (lower traces) masseters
File:Spasmo emimasticatorio SP.jpg|'''Figure 7:''' Mechanical silent period detected electrophysiologically on the right (upper overlapping traces) and left (lower overlapping traces) masseters
File:Spasmo emimasticatorio TC.jpg|'''Figure 8:''' Axial CT of the facial massif in which there is a marked hypertrophy of the right masseter
</gallery>
</center>
</center>
</center>
 
In this way it has been shown that, inevitably,
{{q2|the logic of medical language is more or less based on data that derive from a specific world or context or rather, a specialistic context in which the perimeter that delimits this knowledge does not allow us to project ourselves into parallel contexts}}
 
By exploring this perimeter line of the specialist context, we will create an area close to it which we will call the 'fuzzy zone' or 'fuzzy logic' which we will discuss in the next chapter.
 
{{q4|... from what it seems not even with a probabilistic language logic we will be able to define an exact diagnosis.|in fact, for this reason we should also consider [[Fuzzy logic language|Fuzzy Logic Language]] }}
 
 
 
{{bib}}


{{apm}}


[[Category:Articles about logic of language]]


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