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In this chapter, we will discuss the logic of language coupled with mathematical probability. We have seen that [[The logic of classical language|classical logic]] alone is insufficient to determine accurate diagnoses; hence, a conceptual and formal overview is given on why probability can be very useful. Providing illustrations of instances of clinical cases, we will see how the logic of probabilistic language is able to provide us a differential diagnosis in a ‘good enough’ way.  
<translate><!--T:1--> In this chapter, we will discuss the logic of language coupled with mathematical probability</translate>. <translate><!--T:2--> We have seen that [[The logic of classical language|classical logic]] alone is insufficient to determine accurate diagnoses</translate>; <translate><!--T:3--> hence, a conceptual and formal overview is given on why probability can be very useful</translate>. <translate><!--T:4--> Providing illustrations of instances of clinical cases, we will see how the logic of probabilistic language is able to provide us a differential diagnosis in a ‘good enough’ way</translate>.  


The conclusion is that it is possible to demonstrate that, even with the addition of probabilistic reasoning alone, it is not possible to determine exact diagnoses, so other enrichments are being sought for our language.   
<translate><!--T:5--> The conclusion is that it is possible to demonstrate that, even with the addition of probabilistic reasoning alone, it is not possible to determine exact diagnoses, so other enrichments are being sought for our language</translate>.   


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==<!--6-->Probabilistic language logic in medicine==


<!--7-->every scientific idea (whether in medicine, architecture, engineering, chemistry, or any other subject), when put into practice, is subject to small errors and uncertainties. <!--8-->Mathematics - through probability theory and statistical inference - helps to precisely control and thereby contain these uncertainties. <!--9-->It always has to be considered that in all practical cases "the outcomes also depend on many other factors external to the theory", whether they be initial and environmental conditions, experimental errors, or something else.  
<translate><!--T:7--> every scientific idea (whether in medicine, architecture, engineering, chemistry, or any other subject), when put into practice, is subject to small errors and uncertainties</translate>. <translate><!--T:8--> Mathematics - through probability theory and statistical inference - helps to precisely control and thereby contain these uncertainties</translate>. <translate><!--T:9--> It always has to be considered that in all practical cases "the outcomes also depend on many other factors external to the theory", whether they be initial and environmental conditions, experimental errors, or something else</translate>.  


<!--10-->All the uncertainties about these factors make the theory–observation relationship a probabilistic one. <!--11-->In the medical approach, there are two types of uncertainty that weigh the most on diagnoses: subjective uncertainty and casuality.<ref>{{Cite book  
<translate><!--T:10--> All the uncertainties about these factors make the theory–observation relationship a probabilistic one</translate>. <translate><!--T:11--> In the medical approach, there are two types of uncertainty that weigh the most on diagnoses: subjective uncertainty and casuality</translate>.<ref>{{Cite book  
  | autore = Vázquez-Delgado E
  | autore = Vázquez-Delgado E
  | autore2 = Cascos-Romero J
  | autore2 = Cascos-Romero J
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  }}</ref>
  }}</ref>


<!--12-->It becomes essential, therefore, in this scenario to distinguish between these two uncertainties and to show that the concept of probability has different meanings in these two contexts.  
<translate><!--T:12--> It becomes essential, therefore, in this scenario to distinguish between these two uncertainties and to show that the concept of probability has different meanings in these two contexts</translate>.  


<!--13-->We will try to expose these concepts by linking each crucial step to the clinical approach that has been reported in the previous chapters and in particular the approach in the dental and neurological context in contending for the primacy of the diagnosis for our dear Mary Poppins.
<translate><!--T:13--> We will try to expose these concepts by linking each crucial step to the clinical approach that has been reported in the previous chapters and in particular the approach in the dental and neurological context in contending for the primacy of the diagnosis for our dear Mary Poppins</translate>.


==<!--14-->Subjective uncertainty and casuality==
==<translate><!--T:14--> Subjective uncertainty and casuality</translate>==
<!--15-->Let us imagine asking Mary Poppins which of the two medical colleagues — the dentist or the neurologist — is right.  
<translate><!--T:15--> Let us imagine asking Mary Poppins which of the two medical colleagues — the dentist or the neurologist — is right</translate>.  


<!--16-->The question would create a kind of agitation based on inner uncertainty; therefore, the notions of certainty and uncertainty refer to subjective epistemic states of human beings and not to states of the external world, because there is no certainty or uncertainty in that world. In this sense, as we have mentioned, there are an inner world and a world outside ourselves that both do not respond to canons of uncertainty, yet of probability.  
<translate><!--T:16--> The question would create a kind of agitation based on inner uncertainty; therefore, the notions of certainty and uncertainty refer to subjective epistemic states of human beings and not to states of the external world, because there is no certainty or uncertainty in that world. In this sense, as we have mentioned, there are an inner world and a world outside ourselves that both do not respond to canons of uncertainty, yet of probability.</translate>


<!--17-->Mary Poppins may be subjectively certain or uncertain as to whether she is suffering from TMDs or a neuropathic or neuromuscular form of OP: this because "uncertainty" is a subjective, epistemic state below the threshold of knowledge and belief; hence the term.  
<translate><!--T:17--> Mary Poppins may be subjectively certain or uncertain as to whether she is suffering from TMDs or a neuropathic or neuromuscular form of OP: this because "uncertainty" is a subjective, epistemic state below the threshold of knowledge and belief; hence the term</translate>.  


====<!--18-->Subjective uncertainty====
====<translate><!--T:18--> Subjective uncertainty</translate>====
<!--19-->Without a doubt the term ‘subjective’ scares many, especially those who intend to practice science by pursuing the healthy ideal of ‘objectivity’, as this term is perceived by common sense. It is, therefore, appropriate to make some clarifications on the use of this term in this context:   
<translate><!--T:19--> Without a doubt the term ‘subjective’ scares many, especially those who intend to practice science by pursuing the healthy ideal of ‘objectivity’, as this term is perceived by common sense. It is, therefore, appropriate to make some clarifications on the use of this term in this context</translate>:   


*‘<!--20-->Subjective’ <!--21-->indicates that the probability assessment depends on the information status of the individual who performs it.
*‘<translate><!--T:20--> Subjective</translate>’ <translate><!--T:21--> indicates that the probability assessment depends on the information status of the individual who performs it</translate>.


*‘<!--22-->Subjective’ <!--23-->does not mean arbitrary.
*‘<translate><!--T:22--> Subjective</translate>’ <translate><!--T:23--> does not mean arbitrary</translate>.


<!--24-->The so-called ‘objectivity’, as perceived by those outside scientific research, is defined when a community of rational beings shares the same state of information. But even in this case, one should speak more properly of ‘intersubjectivity’ (i.e. the sharing, by a group, of subjective opinions).  
<translate><!--T:24--> The so-called ‘objectivity’, as perceived by those outside scientific research, is defined when a community of rational beings shares the same state of information. But even in this case, one should speak more properly of ‘intersubjectivity’ (i.e. the sharing, by a group, of subjective opinions). </translate>


<!--25-->In clinical cases — precisely because patients rarely possess advanced notions of medicine — subjective uncertainty must be considered. Living with uncertainty requires us to use a probabilistic approach.
<translate><!--T:25--> In clinical cases — precisely because patients rarely possess advanced notions of medicine — subjective uncertainty must be considered. Living with uncertainty requires us to use a probabilistic approach</translate>.


======<!--26-->Casuality======
======<translate><!--T:26--> Casuality</translate>======


<!--27-->The casuality indicates the lack of a certain connection between cause and effect. The uncertainty of a close union between the source and the phenomenon is among the most adverse problems in determining a diagnosis.  
<translate><!--T:27--> The casuality indicates the lack of a certain connection between cause and effect. The uncertainty of a close union between the source and the phenomenon is among the most adverse problems in determining a diagnosis.</translate>


<!--28-->In a clinical case a phenomenon <math>A(x)</math> (such as for example a malocclusion, a crossbite, an openbite, etc ...) is randomly associated with another phenomenon <math>B(x)</math> (such as TMJ bone degeneration); <!--29-->when there are exceptions for which the logical proposition <math>A(x) \rightarrow B(x)</math> it's not always true (but it is most of the time), we will say that the relation <math>A(x) \rightarrow B(x)</math> is not always true but it is probable.
<translate><!--T:28--> In a clinical case a phenomenon <math>A(x)</math> (such as for example a malocclusion, a crossbite, an openbite, etc ...) is randomly associated with another phenomenon <math>B(x)</math> (such as TMJ bone degeneration)</translate>; <translate><!--T:29--> when there are exceptions for which the logical proposition <math>A(x) \rightarrow B(x)</math> it's not always true (but it is most of the time), we will say that the relation <math>A(x) \rightarrow B(x)</math> is not always true but it is probable</translate>.


{{q2|<!--30-->We are moving from a deterministic condition to a stochastic one.|}}
{{q2|<translate><!--T:30--> We are moving from a deterministic condition to a stochastic one</translate>.|}}


==<!--31-->Subjective and objective probability==
==<translate><!--T:31--> Subjective and objective probability</translate>==


<!--32-->In this chapter, some topics already treated in the fantastic book by Kazem Sadegh-Zadeh<ref>{{cita libro
<translate><!--T:32--> In this chapter, some topics already treated in the fantastic book by Kazem Sadegh-Zadeh</translate><ref>{{cita libro
|autore=Sadegh-Zadeh Kazem
|autore=Sadegh-Zadeh Kazem
|titolo=Handbook of Analytic Philosophy of Medicine
|titolo=Handbook of Analytic Philosophy of Medicine
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|DOI=10.1007/978-94-007-2260-6
|DOI=10.1007/978-94-007-2260-6
|OCLC=
|OCLC=
}}.</ref>, <!--33-->who tackles the problem of the logic of medical language, are taken up again and we reshape their content by referring them to our clinical case of Mary Poppins, to keep our understanding closer to dental contexts.
}}.</ref>, <translate><!--T:33--> who tackles the problem of the logic of medical language, are taken up again and we reshape their content by referring them to our clinical case of Mary Poppins, to keep our understanding closer to dental contexts</translate>.


<!--34-->Random and subjectively uncertain events are said to be probable; consequently, casuality and uncertainty are treated as qualitative, comparative or quantitative probabilities.
<translate><!--T:34--> Random and subjectively uncertain events are said to be probable; consequently, casuality and uncertainty are treated as qualitative, comparative or quantitative probabilities.</translate>


<!--35-->To clarify this concept, let us go back to the example of Mary Poppins. A doctor, having heard her symptoms will be able to say that:
<translate><!--T:35--> To clarify this concept, let us go back to the example of Mary Poppins. A doctor, having heard her symptoms will be able to say that:</translate>


#<!--36-->Mary Poppins is probably suffering from TMDs (<!--37-->qualitative term).
#<translate><!--T:36--> Mary Poppins is probably suffering from TMDs</translate> (<translate><!--T:37--> qualitative term</translate>).
#<!--38-->Mary Poppins is more likely to have TMDs than neuropathic OP (<!--39-->comparative term: <!--40-->number of diagnosed cases of TMDs versus <sub>n</sub>OP.
#<translate><!--T:38--> Mary Poppins is more likely to have TMDs than neuropathic OP</translate> (<translate><!--T:39--> comparative term</translate>: <translate><!--T:40--> number of diagnosed cases of TMDs versus <sub>n</sub>OP</translate>.
#<!--41-->The probability that Mary Poppins has TMDs is 0.15 (<!--42-->quantitative term, relative to the population).
#<translate><!--T:41--> The probability that Mary Poppins has TMDs is 0.15</translate> (<translate><!--T:42--> quantitative term, relative to the population</translate>).


===<!--43-->Subjective probability===
===<translate><!--T:43--> Subjective probability</translate>===


<!--44-->In a context of human subjective uncertainty, the probabilistic, qualitative, comparative and/or quantitative data can be interpreted as a measure of subjective uncertainty by the clinician, in order to make the 'states of conviction' numerically representable.
<translate><!--T:44--> In a context of human subjective uncertainty, the probabilistic, qualitative, comparative and/or quantitative data can be interpreted as a measure of subjective uncertainty by the clinician, in order to make the 'states of conviction' numerically representable</translate>.


<!--45-->For example, saying that "the probability that Mary Poppins is affected by TMDs is 0.15 of the cases" is the same as saying "in the measure of 15%, I believe that Mary Poppins is affected by TMDs"; which means that the degree of conviction is the degree of subjective probability.
<translate><!--T:45--> For example, saying that "the probability that Mary Poppins is affected by TMDs is 0.15 of the cases" is the same as saying "in the measure of 15%, I believe that Mary Poppins is affected by TMDs"; which means that the degree of conviction is the degree of subjective probability.</translate>


===<!--46-->Objective probability===
===<translate><!--T:46--> Objective probability</translate>===


<!--47-->On the other hand, events and random processes cannot be described by deterministic processes in the form 'if A then B'. Statistics are used to quantify the frequency of association between A and B and to represent the relationships between them as a degree of probability that introduces the degree of objective probability.  
<translate><!--T:47--> On the other hand, events and random processes cannot be described by deterministic processes in the form 'if A then B'. Statistics are used to quantify the frequency of association between A and B and to represent the relationships between them as a degree of probability that introduces the degree of objective probability. </translate>


<!--48-->In the wake of the growing probabilization of uncertainty and randomness in medicine since the eighteenth century, the term "probability" has become a respected element of medical language, methodology and epistemology.
<translate><!--T:48--> In the wake of the growing probabilization of uncertainty and randomness in medicine since the eighteenth century, the term "probability" has become a respected element of medical language, methodology and epistemology.</translate>


<!--49-->Unfortunately, the two types of probability, the subjective probability and the objective one, are not accurately differentiated in medicine, and the same happens in other disciplines too. The fundamental fact remains that the most important meaning that probability theory has generated in medicine, particularly in the concepts of probability in aetiology, epidemiology, diagnostics and therapy, is its contribution to our understanding and representation of biological casuality.
<translate><!--T:49--> Unfortunately, the two types of probability, the subjective probability and the objective one, are not accurately differentiated in medicine, and the same happens in other disciplines too. The fundamental fact remains that the most important meaning that probability theory has generated in medicine, particularly in the concepts of probability in aetiology, epidemiology, diagnostics and therapy, is its contribution to our understanding and representation of biological casuality.</translate>


==<!--50-->Probabilistic-causal analysis==
==<translate><!--T:50--> Probabilistic-causal analysis</translate>==
<!--51-->From these premises it is clear that the clinical diagnosis is made using the so-called hypothetical-deductive method referred to as DN<ref name=":1">{{Cite book  
<translate><!--T:51--> From these premises it is clear that the clinical diagnosis is made using the so-called hypothetical-deductive method referred to as DN</translate><ref name=":1">{{Cite book  
  | autore = Sarkar S
  | autore = Sarkar S
  | titolo = Nagel on Reduction
  | titolo = Nagel on Reduction
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  | LCCN =  
  | LCCN =  
  | OCLC =  
  | OCLC =  
  }}</ref> ([https://en.wikipedia.org/wiki/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>). <!--57-->But this is not realistic, since the medical knowledge used in clinical decision-making hardly contains causal deterministic laws to allow causal explanations and, hence, to formulate clinical diagnoses, among other things in the specialist context. Let us try to analyse again the case of our Mary Poppins, this time trying a probabilistic-causal approach.
  }}</ref> ([https://en.wikipedia.org/wiki/Deductive-nomological_model deductive-nomological model]<ref>''<translate><!--T:52--> DN model of scientific explanation</translate>'', <translate><!--T:53--> also known as</translate> ''<translate><!--T:54--> Hempel's model</translate>'', ''Hempel–Oppenheim model'', ''Popper–Hempel model'', <translate><!--T:55--> or</translate> ''<translate><!--T:56--> covering law model</translate>''</ref>). <translate><!--T:57--> But this is not realistic, since the medical knowledge used in clinical decision-making hardly contains causal deterministic laws to allow causal explanations and, hence, to formulate clinical diagnoses, among other things in the specialist context. Let us try to analyse again the case of our Mary Poppins, this time trying a probabilistic-causal approach.</translate>


<!--58-->Let us consider a number <math>n</math> of individuals including people who report Orofacial Pain who generally have bone degeneration of the Temporomandibular Joint. However, there may also be other apparently unrelated causes. We must mathematically translate the 'relevance' that these causal uncertainties have in determining a diagnosis.
<translate><!--T:58--> Let us consider a number <math>n</math> of individuals including people who report Orofacial Pain who generally have bone degeneration of the Temporomandibular Joint. However, there may also be other apparently unrelated causes. We must mathematically translate the 'relevance' that these causal uncertainties have in determining a diagnosis.</translate>


===<!--59-->The casual relevance===
===<translate><!--T:59--> The casual relevance</translate>===
<!--60-->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:
<translate><!--T:60--> 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:</translate>


*<math>E_1</math> = <!--61-->patients with bone degeneration of the temporomandibular joint.
*<math>E_1</math> = <translate><!--T:61--> patients with bone degeneration of the temporomandibular joint</translate>.


*<math>E_2</math> = <!--62-->patients reporting orofacial pain.
*<math>E_2</math> = <translate><!--T:62--> patients reporting orofacial pain</translate>.


*<math>E_3</math> = <!--63-->patients without bone degeneration of the temporomandibular joint.
*<math>E_3</math> = <translate><!--T:63--> patients without bone degeneration of the temporomandibular joint</translate>.


<!--64-->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.
<translate><!--T:64--> 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</translate>.


<!--65-->With these premises the causal relevance <math>cr</math> of the sample <math>n</math> of patients is:
<translate><!--T:65--> With these premises the causal relevance <math>cr</math> of the sample <math>n</math> of patients is:</translate>


<math>cr=P(E_2 \mid E_1)- P(E_2 \mid E_3)</math>
<math>cr=P(E_2 \mid E_1)- P(E_2 \mid E_3)</math>


<!--66-->where  
<translate><!--T:66--> where</translate>


:<math>P(E_2 \mid E_1)</math> <!--67-->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,
:<math>P(E_2 \mid E_1)</math> <translate><!--T:67--> 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</translate>,


<!--68-->while  
<translate><!--T:68--> while</translate>


:<math>P(E_2 \mid E_3)</math> <!--69-->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.
:<math>P(E_2 \mid E_3)</math> <translate><!--T:69--> 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</translate>.


<!--70-->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>.
<translate><!--T:70--> 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></translate>.


<!--71-->The meanings that we can give to this number are as follows:  
<translate><!--T:71--> The meanings that we can give to this number are as follows: </translate>


*<!--72-->we have the extreme cases (which in reality never occur) which are:
*<translate><!--T:72--> we have the extreme cases (which in reality never occur) which are:</translate>


:*<math>cr=1</math> <!--73-->indicating that the only cause of orofacial pain is bone degeneration of the TMJ,
:*<math>cr=1</math> <translate><!--T:73--> indicating that the only cause of orofacial pain is bone degeneration of the TMJ</translate>,
:*<math>cr=-1</math> <!--74-->which indicates that the cause of orofacial pain is never bone degeneration of the TMJ but is something else,
:*<math>cr=-1</math> <translate><!--T:74--> which indicates that the cause of orofacial pain is never bone degeneration of the TMJ but is something else</translate>,
:*<math>cr=0</math> <!--75-->indicating that the probability that orofacial pain is caused by bone degeneration of the TMJ or otherwise is exactly the same,
:*<math>cr=0</math> <translate><!--T:75--> indicating that the probability that orofacial pain is caused by bone degeneration of the TMJ or otherwise is exactly the same</translate>,


*<!--76-->and the intermediate cases (which are the realistic ones)
*<translate><!--T:76--> and the intermediate cases (which are the realistic ones)</translate>


:*<math>cr>0</math> <!--77-->indicating that the cause of orofacial pain is more likely to be bone degeneration of the TMJ,
:*<math>cr>0</math> <translate><!--T:77--> indicating that the cause of orofacial pain is more likely to be bone degeneration of the TMJ</translate>,
:*<math>cr<0</math> <!--78-->which indicates that the cause of orofacial pain is more likely not bone degeneration of the TMJ.
:*<math>cr<0</math> <translate><!--T:78--> which indicates that the cause of orofacial pain is more likely not bone degeneration of the TMJ</translate>.






<center>
<center>
===<!--79-->Second Clinical Approach===
===<translate><!--T:79--> Second Clinical Approach</translate>===
''(<!--80-->hover over the images)''
''(<translate><!--T:80--> hover over the images</translate>)''




<gallery widths="350" heights="282" perrow="2" mode="slideshow">
<gallery widths="350" heights="282" perrow="2" mode="slideshow">
File:Spasmo emimasticatorio.jpg|'''<!--81-->Figure 1:''' <!--82-->Patient reporting "Orofacial pain in the right hemilateral"
File:Spasmo emimasticatorio.jpg|'''<translate><!--T:81--> Figure</translate> 1:''' <translate><!--T:82--> Patient reporting "Orofacial pain in the right hemilateral"</translate>
File:Spasmo emimasticatorio ATM.jpg|'''<!--83-->Figure 2:''' <!--84-->Patient's TMJ Stratigraphy showing signs of condylar flattening and osteophyte
File:Spasmo emimasticatorio ATM.jpg|'''<translate><!--T:83--> Figure</translate> 2:''' <translate><!--T:84--> Patient's TMJ Stratigraphy showing signs of condylar flattening and osteophyte</translate>
File:Atm1 sclerodermia.jpg|'''<!--85-->Figure 3:''' <!--86-->Computed Tomography of the TMJ
File:Atm1 sclerodermia.jpg|'''<translate><!--T:85--> Figure</translate> 3:''' <translate><!--T:86--> Computed Tomography of the TMJ</translate>
File:Spasmo emimasticatorio assiografia.jpg|'''<!--87-->Figure 4:''' <!--88-->Axiography of the patient showing a flattening of the chewing pattern on the right condyle
File:Spasmo emimasticatorio assiografia.jpg|'''<translate><!--T:87--> Figure</translate> 4:''' <translate><!--T:88--> Axiography of the patient showing a flattening of the chewing pattern on the right condyle</translate>
File:EMG2.jpg|'''<!--89-->Figure 5:''' <!--90-->EMG Interferential Pattern. Overlapping upper traces corresponding to the right masseter, lower to the left masseter.
File:EMG2.jpg|'''<translate><!--T:89--> Figure</translate> 5:''' <translate><!--T:90--> EMG Interferential Pattern. Overlapping upper traces corresponding to the right masseter, lower to the left masseter</translate>.
</gallery>
</gallery>
</center>
</center>
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<br /><!--91-->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>
<br /><translate><!--T:91--> 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></translate>


<!--92-->In order to take advantage of the information provided by this dataset, the concept of partition of causal relevance is introduced:
<translate><!--T:92--> In order to take advantage of the information provided by this dataset, the concept of partition of causal relevance is introduced</translate>:


====<!--93-->The partition of causal relevance====
====<translate><!--T:93--> The partition of causal relevance</translate>====


:<!--94-->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>:
:<translate><!--T:94--> 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></translate>:


:<math>\pi = \{C_1, C_2,\dots,C_k \}  \qquad \qquad \text{with} \qquad \qquad C_i \subset n , </math>
:<math>\pi = \{C_1, C_2,\dots,C_k \}  \qquad \qquad \text{with} \qquad \qquad C_i \subset n , </math>


<!--95-->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>.
<translate><!--T:95--> 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></translate>.


<!--96-->The partition <math>\pi</math>, in order for it to be defined as a partition of causal relevance, must have these properties:
<translate><!--T:96--> The partition <math>\pi</math>, in order for it to be defined as a partition of causal relevance, must have these properties</translate>:


#<!--97-->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'''.
#<translate><!--T:97--> 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'''</translate>.
#<!--98-->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.
#<translate><!--T:98--> 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</translate>.


<!--99-->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 classical language]]'.
<translate><!--T:99--> 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 classical language]]'</translate>.


<!--100-->
<translate><!--T:100-->
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
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>. <!--101-->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  
</math></translate>. <translate><!--T:101--> 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</translate>.<ref name=":2">{{Cite book  
  | autore = Pantoja LLQ
  | autore = Pantoja LLQ
  | autore2 = De Toledo IP
  | autore2 = De Toledo IP
Line 354: Line 347:




<!--102-->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:
<translate><!--T:102--> 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</translate>:
{|
{|
|+
|+
|<math>P(D| Deg.TMJ  \cap TMDs)=0.95  \qquad \qquad \; </math>
|<math>P(D| Deg.TMJ  \cap TMDs)=0.95  \qquad \qquad \; </math>
|
|
|<!--103-->where
|<translate><!--T:103--> where</translate>
|
|
|
|
Line 366: Line 359:
|<math>P(D| Deg.TMJ \cap noTMDs)=0.3  \qquad \qquad  \quad </math>
|<math>P(D| Deg.TMJ \cap noTMDs)=0.3  \qquad \qquad  \quad </math>
|
|
|<!--104-->where
|<translate><!--T:104--> where</translate>
|
|
|
|
Line 373: Line 366:
|<math>P(D| no Deg.TMJ  \cap TMDs)=0.199  \qquad \qquad \; </math>
|<math>P(D| no Deg.TMJ  \cap TMDs)=0.199  \qquad \qquad \; </math>
|
|
|<!--105-->where
|<translate><!--T:105--> where</translate>
|
|
|
|
Line 380: Line 373:
|<math>P(D| noDeg.TMJ  \cap noTMDs)=0.001  \qquad \qquad \;</math>
|<math>P(D| noDeg.TMJ  \cap noTMDs)=0.001  \qquad \qquad \;</math>
|
|
|<!--106-->where
|<translate><!--T:106--> where</translate>
|
|
|
|
Line 387: Line 380:


*
*
{{q2|<!--107-->A homogeneous partition provides what we are used to calling Differential Diagnosis.|}}
{{q2|<translate><!--T:107--> A homogeneous partition provides what we are used to calling Differential Diagnosis</translate>.|}}




====<!--108-->Clinical situations====
====<translate><!--T:108--> Clinical situations</translate>====
<!--109-->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>. <!--110-->Given the aforementioned partition of the reference class, we have the following clinical situations:
<translate><!--T:109--> 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></translate>. <translate><!--T:110--> Given the aforementioned partition of the reference class, we have the following clinical situations</translate>:


*<!--111-->Mary Poppins <math>\in</math> degeneration of the temporomandibular joint <math>\cap</math>  Temporomandibular Disorders
*<translate><!--T:111--> Mary Poppins <math>\in</math> degeneration of the temporomandibular joint <math>\cap</math>  Temporomandibular Disorders</translate>


*<!--112-->Mary Poppins <math>\in</math> degeneration of the temporomandibular joint <math>\cap</math> no Temporomandibular Disorders
*<translate><!--T:112--> Mary Poppins <math>\in</math> degeneration of the temporomandibular joint <math>\cap</math> no Temporomandibular Disorders</translate>


*<!--113-->Mary Poppins <math>\in</math> no degeneration of the temporomandibular joint <math>\cap</math> Temporomandibular Disorders
*<translate><!--T:113--> Mary Poppins <math>\in</math> no degeneration of the temporomandibular joint <math>\cap</math> Temporomandibular Disorders</translate>


*<!--114-->Mary Poppins <math>\in</math> no degeneration of the temporomandibular joint <math>\cap</math> no Temporomandibular Disorders
*<translate><!--T:114--> Mary Poppins <math>\in</math> no degeneration of the temporomandibular joint <math>\cap</math> no Temporomandibular Disorders</translate>


<!--115-->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>.  
<translate><!--T:115--> 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></translate>.  


<!--116-->In general, we can refer to a logical process in which we examine the following elements:
<translate><!--T:116--> In general, we can refer to a logical process in which we examine the following elements</translate>:


*<!--117-->an individual: <math>a</math>
*<translate><!--T:117--> an individual</translate>: <math>a</math>
*<!--118-->its initial data set <math>D=\{\delta_1,.....\delta_n\}</math>
*<translate><!--T:118--> its initial data set</translate> <math>D=\{\delta_1,.....\delta_n\}</math>
*<!--119-->a population sample <math>n</math> <!--120-->to which it belongs,
*<translate><!--T:119--> a population sample</translate> <math>n</math> <translate><!--T:120--> to which it belongs</translate>,
*<!--121-->a base probability <math>P(D)=0,003</math>
*<translate><!--T:121--> a base probability</translate> <math>P(D)=0,003</math>


<!--122-->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.
<translate><!--T:122--> 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</translate>.


<!--123-->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  
<translate><!--T:123--> The probabilistic-causal analysis of <math>D=\{\delta_1,.....\delta_n\}</math> is then a couple of the following logical forms (Analysandum / Analysans</translate><ref>{{Cite book  
  | autore = Westmeyer H
  | autore = Westmeyer H
  | titolo = The diagnostic process as a statistical-causal analysis
  | titolo = The diagnostic process as a statistical-causal analysis
Line 430: Line 423:
  }}</ref>):
  }}</ref>):


*'''<!--124-->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.'''
*'''<translate><!--T:124--> 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</translate>.'''


*'''<!--125-->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.'''
*'''<translate><!--T:125--> 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</translate>.'''


<!--126-->For example, it can be concluded that the definitive diagnosis is the following:
<translate><!--T:126--> For example, it can be concluded that the definitive diagnosis is the following</translate>:


<math>P(D| Deg.TMJ  \cap TMDs)=0.95</math> - <!--127-->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> - <translate><!--T:127--> 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</translate> <math>D=\{\delta_1,.....\delta_n\}</math>


==Final considerations==
==Final considerations==
<!--128-->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.  
<translate><!--T:128--> 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</translate>.  


<!--129-->Here, we enter a delicate topic, that is connected with the epistemological contents and that first of all was reported in the "[[Introduction]]". <!--130-->We are talking about:
<translate><!--T:129--> Here, we enter a delicate topic, that is connected with the epistemological contents and that first of all was reported in the "[[Introduction]]"</translate>. <translate><!--T:130--> We are talking about</translate>:


*'''<!--131-->Interdisciplinarity''': <br>''<!--132-->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>. <!--133-->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><!--134-->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><!--135-->In interdisciplinary research, metacognitive scaffolds help interdisciplinary communication analyse and articulate how the discipline builds knowledge<ref name=":0">{{cita libro  
*'''<translate><!--T:131--> Interdisciplinarity</translate>''': <br>''<translate><!--T:132--> 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</translate><ref>European Union, ''[https://ec.europa.eu/programmes/horizon2020/en/h2020-section/societal-challenges Horizon 2020]''</ref>. <translate><!--T:133--> 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</translate>.<br><translate><!--T:134--> 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</translate>.<br><translate><!--T:135--> In interdisciplinary research, metacognitive scaffolds help interdisciplinary communication analyse and articulate how the discipline builds knowledge</translate><ref name=":0">{{cita libro  
  | autore = Boon M
  | autore = Boon M
  | autore2 = Van Baalen S
  | autore2 = Van Baalen S
Line 472: Line 465:
  }}</ref>''
  }}</ref>''


<!--136-->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'). <!--137-->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> <!--138-->and Analysan <math>  = \{P(D),a\}</math> <!--139-->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.
<translate><!--T:136--> 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')</translate>. <translate><!--T:137--> 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</translate>: Analysandum <math>  = \{P(D),a\}</math> <translate><!--T:138--> and</translate> Analysan <math>  = \{P(D),a\}</math> <translate><!--T:139--> 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</translate>.


<!--140-->This conclusion confirmed by the dentist was the following:   
<translate><!--T:140--> This conclusion confirmed by the dentist was the following</translate>:   


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


<!--141-->or better: <!--142-->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>
<translate><!--T:141--> or better</translate>: <translate><!--T:142--> 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></translate>


<!--143-->But something strange happens because out of nowhere, a researcher, who uses 'metacognitive scaffolds'<ref>{{Cite book  
<translate><!--T:143--> But something strange happens because out of nowhere, a researcher, who uses 'metacognitive scaffolds'</translate><ref>{{Cite book  
  | autore = Boon M
  | autore = Boon M
  | autore2 = Van Baalen S
  | autore2 = Van Baalen S
Line 497: Line 490:
  | LCCN =  
  | LCCN =  
  | OCLC =  
  | OCLC =  
  }}</ref> <!--144-->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:
  }}</ref> <translate><!--T:144--> 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</translate>:


{{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?|}}
{{q4|...<translate><!--T: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?</translate>|}}


<!--146-->and increase the dose: <!--147-->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).
<translate><!--T:146--> and increase the dose</translate>: <translate><!--T:147--> 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)</translate>.


<math>\delta_1=</math> <!--148-->Positive radiological report of the TMJ in Figure 2
<math>\delta_1=</math> <translate><!--T:148--> Positive radiological report of the TMJ in Figure 2</translate>


<math>\delta_2=</math> <!--149-->Positive CT report of the TMJ in Figure 3
<math>\delta_2=</math> <translate><!--T:149--> Positive CT report of the TMJ in Figure 3</translate>


<math>\delta_3=</math> <!--150-->Positive axiographic report of the condylar traces in Figure 4
<math>\delta_3=</math> <translate><!--T:150--> Positive axiographic report of the condylar traces in Figure 4</translate>


<math>\delta_4=</math> <!--151-->Asymmetric EMG interference pattern in Figure 5
<math>\delta_4=</math> <translate><!--T:151--> Asymmetric EMG interference pattern in Figure 5</translate>


<math>{\gamma _{1}}=</math> <!--152-->Jaw jerk in Figure 6
<math>{\gamma _{1}}=</math> <translate><!--T:152--> Jaw jerk in Figure 6</translate>


<math>{\displaystyle \gamma _{2}}=</math> <!--153-->Mechanical Silent Period in Figure 7
<math>{\displaystyle \gamma _{2}}=</math> <translate><!--T:153--> Mechanical Silent Period in Figure 7</translate>


<math>{\displaystyle \gamma _{3}}=</math> <!--154-->CT right masseter muscle in Figure 8
<math>{\displaystyle \gamma _{3}}=</math> <translate><!--T:154--> CT right masseter muscle in Figure 8</translate>




<center>
<center>
===<!--155-->Third Clinical Approach===
===<translate><!--T:155--> Third Clinical Approach</translate>===
''(<!--156-->hover over the images)''
''(<translate><!--T:156--> hover over the images</translate>)''
<center>
<center>
<gallery widths="350" heights="282" perrow="2" mode="slideshow">
<gallery widths="350" heights="282" perrow="2" mode="slideshow">
File:Spasmo emimasticatorio.jpg|'''<!--157-->Figure 1:''' <!--158-->Patient reporting "Orofacial pain in the right hemilateral)
File:Spasmo emimasticatorio.jpg|'''<translate><!--T:157--> Figure</translate> 1:''' <translate><!--T:158--> Patient reporting "Orofacial pain in the right hemilateral)</translate>
File:Spasmo emimasticatorio ATM.jpg|'''<!--159-->Figure 2:''' <!--160-->Patient's TMJ Stratigraphy showing signs of condylar flattening and osteophyte
File:Spasmo emimasticatorio ATM.jpg|'''<translate><!--T:159--> Figure</translate> 2:''' <translate><!--T:160--> Patient's TMJ Stratigraphy showing signs of condylar flattening and osteophyte</translate>
File:Atm1 sclerodermia.jpg|'''<!--161-->Figure 3:''' <!--162-->Computed Tomography of the TMJ
File:Atm1 sclerodermia.jpg|'''<translate><!--T:161--> Figure</translate> 3:''' <translate><!--T:162--> Computed Tomography of the TMJ</translate>
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:Spasmo emimasticatorio assiografia.jpg|'''<translate><!--T:163--> Figure</translate> 4:''' <translate><!--T:164--> Axiography of the patient showing a flattening of the chewing pattern on the right condyle</translate>
File:EMG2.jpg|'''<!--165-->Figure 5:''' <!--166-->EMG Interferential Pattern. Overlapping upper traces corresponding to the right masseter, lower to the left masseter.
File:EMG2.jpg|'''<translate><!--T:165--> Figure</translate> 5:''' <translate><!--T:166--> EMG Interferential Pattern. Overlapping upper traces corresponding to the right masseter, lower to the left masseter</translate>.
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 JJ.jpg|'''<translate><!--T:167--> Figure</translate> 6:''' <translate><!--T:168--> Jaw jerk electrophysiologically detected on the right (upper traces) and left (lower traces) masseters</translate>
File:Spasmo emimasticatorio SP.jpg|'''<!--169-->Figure 7:''' <!--170-->Mechanical silent period detected electrophysiologically on the right (upper overlapping traces) and left (lower overlapping traces) masseters
File:Spasmo emimasticatorio SP.jpg|'''<translate><!--T:169--> Figure</translate> 7:''' <translate><!--T:170--> Mechanical silent period detected electrophysiologically on the right (upper overlapping traces) and left (lower overlapping traces) masseters</translate>
File:Spasmo emimasticatorio TC.jpg|'''<!--171-->Figure 8:''' <!--172-->Axial CT of the facial massif in which there is a marked hypertrophy of the right masseter
File:Spasmo emimasticatorio TC.jpg|'''<translate><!--T:171--> Figure</translate> 8:''' <translate><!--T:172--> Axial CT of the facial massif in which there is a marked hypertrophy of the right masseter</translate>
</gallery>
</gallery>
</center>
</center>




<!--173-->In this way it has been shown that, inevitably,  
<translate><!--T:173--> In this way it has been shown that, inevitably</translate>,  
{{q2|<!--174-->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}}
{{q2|<translate><!--T:174--> 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</translate>}}




<!--175-->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.
<translate><!--T:175--> 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</translate>.




{{q4|... <!--176-->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]] }}
{{q4|... <translate><!--T:176--> 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]]</translate> }}


{{Btnav|The logic of classical language|<!--177-->Fuzzy logic language}}
{{Btnav|The logic of classical language|<translate><!--T:177--> Fuzzy logic language</translate>}}


{{bib}}
{{bib}}
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