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{{:Store:LPLen04}}
==Probabilistic-Causal Analysis==
From these premises, it is evident that clinical diagnosis employs the so-called hypothetical-deductive method, known as DN<ref name=":1">{{Cite book
| autore = Sarkar S
| titolo = Nagel on Reduction
| url = https://pubmed.ncbi.nlm.nih.gov/26386529/
| volume =
| opera = Stud Hist Philos Sci
| anno = 2015
| editore =
| città =
| ISBN =
| PMID = 26386529
| PMCID =
| DOI = 10.1016/j.shpsa.2015.05.006
| oaf = <!-- qualsiasi valore -->
| LCCN =
| OCLC =
}}</ref> ([[wikipedia:Deductive-nomological_model|deductive-nomological model]]<ref>''<!--52-->DN model of scientific explanation'', <!--53-->also known as ''<!--54-->Hempel's model'', ''Hempel–Oppenheim model'', ''Popper–Hempel model'', <!--55-->or ''<!--56-->covering law model''</ref>). However, this is not realistic, as the medical knowledge used in clinical decision-making rarely contains causal deterministic laws that allow for causal explanations and, consequently, the formulation of clinical diagnoses, among other things in the specialist context. Let us re-examine the case of Mary Poppins, this time adopting a probabilistic-causal approach.


{{:Store:LPLen05}}
Consider a number <math>n</math> of individuals, including those who report Orofacial Pain, who generally have bone degeneration of the Temporomandibular Joint. However, there might also be other apparently unrelated causes. We must mathematically translate the 'relevance' of these causal uncertainties in determining a diagnosis.
----
 
===The casual relevance===
To do this we consider the degree of causal relevance <math>(cr)</math> of an event <math>E_1</math> with respect to an event <math>E_2</math> where:
*<math>E_1</math> = patients with bone degeneration of the temporomandibular joint.
 
*<math>E_2</math> = patients reporting orofacial pain.
 
*<math>E_3</math> = patients without bone degeneration of the temporomandibular joint.
 
We will use the conditional probability <math>P(A \mid B)</math>, that is the probability that the <math>A</math> event occurs only after the event <math>B</math> has already occurred.
 
With these premises the causal relevance <math>cr</math> of the sample <math>n</math> of patients is:
 
<math>cr=P(E_2 \mid E_1)- P(E_2 \mid E_3)</math>
 
where
:<math>P(E_2 \mid E_1)</math> indicates the probability that some people (among <math>n</math> taken into consideration) suffer from Orofacial Pain caused by bone degeneration of the Temporomandibular Joint,
 
while
:<math>P(E_2 \mid E_3)</math> indicates the probability that other people (always among <math>n</math> taken into consideration) suffer from Orofacial Pain conditioned by something other than bone degeneration of the Temporomandibular Joint.
 
Since all probability suggest that <math>P(A \mid B)</math> is a value between <math>0 </math> and <math>1 </math>, the parameter <math>(cr)</math> will be a number that is between <math>-1 </math> and <math>1 </math>.
 
The meanings that we can give to this number are as follows:
*we have the extreme cases (which in reality never occur) which are:
 
:*<math>cr=1</math> indicating that the only cause of orofacial pain is bone degeneration of the TMJ,
:*<math>cr=-1</math> which indicates that the cause of orofacial pain is never bone degeneration of the TMJ but is something else,
:*<math>cr=0</math> indicating that the probability that orofacial pain is caused by bone degeneration of the TMJ or otherwise is exactly the same,
 
*and the intermediate cases (which are the realistic ones)
 
:*<math>cr>0</math> indicating that the cause of orofacial pain is more likely to be bone degeneration of the TMJ,
:*<math>cr<0</math> which indicates that the cause of orofacial pain is more likely not bone degeneration of the TMJ.
 
 
 
<center>
===Second Clinical Approach===
''(hover over the images)''
<gallery widths="350" heights="282" perrow="2" mode="slideshow">
File:Spasmo emimasticatorio.jpg|'''<!--81-->Figure 1:''' Patient reporting "Orofacial pain in the right hemilateral"
File:Spasmo emimasticatorio ATM.jpg|'''<!--83-->Figure 2:''' Patient's TMJ Stratigraphy showing signs of condylar flattening and osteophyte
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:EMG2.jpg|'''<!--89-->Figure 5:''' EMG Interferential Pattern. Overlapping upper traces corresponding to the right masseter, lower to the left masseter.
</gallery>
</center>
 
So be it then <math>P(D)</math> the probability of finding, in the sample of our <math>n</math> people, individuals who present the elements belonging to the aforementioned set <math>D=\{\delta_1,\delta_2,...,\delta_n\}</math>
 
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====
 
: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>:
 
:<math>\pi = \{C_1, C_2,\dots,C_k \}  \qquad \qquad \text{with} \qquad \qquad C_i \subset n , </math>
 
where with the symbolism <math>C_i \subset n </math> it indicates that the subclass <math>C_i</math> is contained in <math>n</math>.
 
The partition <math>\pi</math>, in order for it to be defined as a partition of causal relevance, must have these properties:
#For each subclass <math>C_i</math> the condition must apply <math>rc=P(D \mid C_i)- P(D )\neq 0, </math> ie the probability of finding in the subgroup <math>C_i</math> a person who has the symptoms, clinical signs and elements belonging to the set <math>D=\{\delta_1,\delta_2,...,\delta_n\}</math>. A causally relevant partition of this type is said to be '''homogeneous'''.
#Each subset <math>C_i</math> must be 'elementary', i.e. it must not be further divided into other subsets, because if these existed they would have no causal relevance.
 
Now let us assume, for example, that the population sample <math>n</math>, to which our good patient Mary Poppins belongs, is a category of subjects aged 20 to 70. We also assume that in this population we have those who present the elements belonging to the data set <math>D=\{\delta_1,.....\delta_n\}</math> which correspond to the laboratory tests mentioned above and precisa in '[[The logic of the classical language|The logic of classical language]]'.
 
Let us suppose that in a sample of 10,000 subjects from 20 to 70 we will have an incidence of 30 subjects <math>p(D)=0.003</math> showing clinical signs <math>\delta_1</math> and <math>\delta_4
</math>. We preferred to use these reports for the demonstration of the probabilistic process because in the literature the data regarding clinical signs and symptoms for Temporomandibular Disorders have too wide a variation as well as too high an incidence in our opinion.<ref name=":2">{{Cite book
| autore = Pantoja LLQ
| autore2 = De Toledo IP
| autore3 = Pupo YM
| autore4 = Porporatti AL
| autore5 = De Luca Canto G
| autore6 = Zwir LF
| autore7 = Guerra ENS
| titolo = Prevalence of degenerative joint disease of the temporomandibular joint: a systematic review
| url = https://pubmed.ncbi.nlm.nih.gov/30311063/
| volume =
| opera = Clin Oral Investig
| anno = 2019
| editore =
| città =
| ISBN =
| PMID = 30311063
| PMCID =
| DOI = 10.1007/s00784-018-2664-y
| oaf = <!-- qualsiasi valore -->
| LCCN =
| OCLC =
}}</ref><ref name=":3">{{Cite book
| autore = De Toledo IP
| autore2 = Stefani FM
| autore3 = Porporatti AL
| autore4 = Mezzomo LA
| autore5 = Peres MA
| autore6 = Flores-Mir C
| autore7 = De Luca Canto G
| titolo = Prevalence of otologic signs and symptoms in adult patients with temporomandibular disorders: a systematic review and meta-analysis
| url = https://www.ncbi.nlm.nih.gov/pubmed/27511214
| volume =
| opera = Clin Oral Investig
| anno = 2017
| editore =
| città =
| ISBN =
| PMID = 27511214
| PMCID =
| DOI = 10.1007/s00784-016-1926-9
| oaf = <!-- qualsiasi valore -->
| LCCN =
| OCLC =
}}</ref><ref name=":4">{{Cite book
| autore = Bonotto D
| autore2 = Penteado CA
| autore3 = Namba EL
| autore4 = Cunali PA
| autore5 = Rached RN
| autore6 = Azevedo-Alanis LR
| titolo = Prevalence of temporomandibular disorders in rugby players
| url = https://www.ncbi.nlm.nih.gov/pubmed/31355769
| volume =
| opera = Gen Dent
| anno =
| editore =
| città =
| ISBN =
| PMID = 31355769
| PMCID =
| DOI =
| oaf = <!-- qualsiasi valore -->
| LCCN =
| OCLC =
}}</ref><ref name=":5">{{Cite book
| autore = da Silva CG
| autore2 = Pachêco-Pereira C
| autore3 = Porporatti AL
| autore4 = Savi MG
| autore5 = Peres MA
| autore6 = Flores-Mir C
| autore7 = De Luca Canto G
| titolo = Prevalence of clinical signs of intra-articular temporomandibular disorders in children and adolescents: A systematic review and meta-analysis
| url = https://www.ncbi.nlm.nih.gov/pubmed/26552334
| volume =
| opera = Am Dent Assoc
| anno = 2016
| editore =
| città =
| ISBN =
| PMID =
| PMCID = 26552334
| DOI = 10.1016/j.adaj.2015.07.017
| oaf = <!-- qualsiasi valore -->
| LCCN =
| OCLC =
}}</ref><ref name=":6">{{Cite book
| autore = Gauer RL
| autore2 = Semidey MJ
| titolo = Diagnosis and treatment of temporomandibular disorders
| url = https://www.aafp.org/afp/2015/0315/afp20150315p378.pdf
| volume =
| opera = Am Fam Physician
| anno = 2015
| editore =
| città =
| ISBN =
| PMID = 25822556
| PMCID =
| DOI =
| oaf = <!-- qualsiasi valore -->
| LCCN =
| OCLC =
}}</ref><ref name=":7">{{Cite book
| autore = Kohlmann T
| titolo = Epidemiology of orofacial pain
| url = https://www.ncbi.nlm.nih.gov/pubmed/12235497
| volume =
| opera = Schmerz
| anno = 2002
| editore =
| città =
| ISBN =
| PMID = 12235497
| PMCID =
| DOI = 10.1007/s004820200000
| oaf = <!-- qualsiasi valore -->
| LCCN =
| OCLC =
}}</ref>
 
An example of a partition with presumed probability in which TMJ degeneration (Deg.TMJ) occurs in conjunction with Temporomandibular Disorders (TMDs) would be the following:
{|
|+
|<math>P(D| Deg.TMJ  \cap TMDs)=0.95  \qquad \qquad \; </math>
|
|where
|
|
|<math>\C_1 \equiv Deg.TMJ  \cap TMDs</math>
|-
|<math>P(D| Deg.TMJ \cap noTMDs)=0.3  \qquad \qquad  \quad </math>
|
|where
|
|
|<math>C_2\equiv  Deg.TMJ  \cap noTMDs</math>
|-
|<math>P(D| no Deg.TMJ  \cap TMDs)=0.199  \qquad \qquad \; </math>
|
|where
|
|
|<math>C_3\equiv  no Deg.TMJ  \cap TMDs</math>
|-
|<math>P(D| noDeg.TMJ  \cap noTMDs)=0.001  \qquad \qquad \;</math>
|
|where
|
|
|<math> C_4\equiv noDeg.TMJ  \cap noTMDs</math>
|}
 
*{{q2|<!--107-->A homogeneous partition provides what we are used to calling Differential Diagnosis.|}}
 
====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> 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> no Temporomandibular Disorders
 
To arrive at the final diagnosis above, we conducted a probabilistic-causal analysis of Mary Poppins' health status whose initial data were <math>D=\{\delta_1,.....\delta_n\}</math>.
 
In general, we can refer to a logical process in which we examine the following elements:
*an individual: <math>a</math>
*its initial data set <math>D=\{\delta_1,.....\delta_n\}</math>
*a population sample <math>n</math> to which it belongs,
*a base probability <math>P(D)=0,003</math>
 
At this point we should introduce too specialized arguments that would take the reader off the topic but that have an high epistemic importance for which we will try to extract the most described logical thread of the Analysandum/Analysans concept.
 
The probabilistic-causal analysis of <math>D=\{\delta_1,.....\delta_n\}</math> is then a couple of the following logical forms (Analysandum / Analysans<ref>{{Cite book
| autore = Westmeyer H
| titolo = The diagnostic process as a statistical-causal analysis
| url = https://psycnet.apa.org/record/1976-01749-001
| volume =
| opera = APA
| anno = 1975
| editore =
| città =
| ISBN =
| PMID =
| PMCID =
| DOI = 10.1007/BF00139821
| oaf = CC BY<!-- qualsiasi valore -->
| LCCN =
| OCLC =
}}</ref>):
*'''Analysandum''' <math>  = \{P(D),a\}</math>: is a logical form that contains two parameters: ''probability'' <math>P(D)</math> to select a person who has the symptoms and elements belonging to the set <math>D=\{\delta_1,\delta_2,...,\delta_n\}</math>, and the ''generic individual'' <math>a</math> who is prone to those symptoms.
 
*'''Analysan <math>= \{\pi,a,KB\}</math>''': is a logical form that contains three parameters: the ''partition'' <math>\pi</math>, the ''generic individual'' <math>a</math> belonging to the population sample <math>n</math> and ''<math>KB</math> (Knowledge Base)'' which includes a set of <math>n>1</math> statements of conditioned probability.
 
For example, it can be concluded that the definitive diagnosis is the following:
 
<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|...<!--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?|}}
 
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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