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Documents, reports and clinical evidence can be used to make the neurologist's assertion incompatible and the dentist's diagnostic conclusion compatible. To do this we must present some logical rules that describe the compatibility or incompatibility of the logic of classical language:

Documents, reports and clinical evidence can be used to make the neurologist's assertion incompatible and the dentist's diagnostic conclusion compatible. To do this we must present some logical rules that describe the compatibility or incompatibility of the logic of classical language:

#A set of sentences <math>\Im</math>, and a number <math>n\geq1</math> of other phrases or statements <math>(a_1,a_2,.....a_n)</math>they are logically compatible if and only if the union between them <math>\Im\cup\{a_1,a_2.....a_n\}</math>   it is coherent.

#A set of sentences <math>\Im</math>, and a number <math>n\geq1</math> of other phrases or statements <math>(\delta_1,\delta_2,.....\delta_n \ )</math>they are logically compatible if and only if the union between them <math>\Im\cup\{\delta_1,\delta_2.....\delta_n\}</math>   it is coherent.

#A set of sentences <math>\Im</math>, and a number <math>n\geq1</math> of other phrases or statements <math>(a_1,a_2,.....a_n)</math> they are logically incompatible if and only if the union between them <math>\Im\cup\{a_1,a_2.....a_n\}</math>it is incoherent.

#A set of sentences <math>\Im</math>, and a number <math>n\geq1</math> of other phrases or statements <math>(\delta_1,\delta_2,.....\delta_n \ )</math> they are logically incompatible if and only if the union between them <math>\Im\cup\{\delta_1,\delta_2.....\delta_n\}</math>it is incoherent.

Let us try to follow the reasoning with practical examples:

Let us try to follow the reasoning with practical examples:

At this point, however, the thesis must be confirmed with further clinical and laboratory tests and in fact the colleague make a series of assertions that must pass the compatibility filter as described above, namely:l

At this point, however, the thesis must be confirmed with further clinical and laboratory tests and in fact the colleague make a series of assertions that must pass the compatibility filter as described above, namely:l

<math>a_1=</math> '''Bone remodelling:''' The flattening of the axiographic traces highlighted in figure 5 indicates the joint remodelling of the right TMJ of Mary Poppins, a report that can be correlated to a series of researches and articles that confirm how malocclusion can be associated with morphological changes in the temporomandibular joints , particularly when combined with the age as the presence of a chronic malocclusion can worsen the picture of bone remodelling.<ref>{{cite book  

<math>\delta_1=</math> '''Bone remodelling:''' The flattening of the axiographic traces highlighted in figure 5 indicates the joint remodelling of the right TMJ of Mary Poppins, a report that can be correlated to a series of researches and articles that confirm how malocclusion can be associated with morphological changes in the temporomandibular joints , particularly when combined with the age as the presence of a chronic malocclusion can worsen the picture of bone remodelling.<ref>{{cite book  

  | autore = Solberg WK

  | autore = Solberg WK

  | autore2 = Bibb CA

  | autore2 = Bibb CA

  }}</ref> These scientific references determine compatibility of the assertion.

  }}</ref> These scientific references determine compatibility of the assertion.

<math>a_2=</math> '''Sensitivity and specificity of the axiographic measurement:''' A study conducted to verify the sensitivity and specificity of the data collected from a group of patients affected by temporomandibular joint disorders with an ARCUSdigma axiographic system ([https://www.kavo.com/de-de/ KaVo Dental GmbH, Biberach / Ris]) confirmed a sensitivity of the 84.21% and 92.86% sensitivity for the right and left TMJs respectively and a specificity of 93.75% and 95.65%.<ref>{{cite book  

<math>\delta_2=</math> '''Sensitivity and specificity of the axiographic measurement:''' A study conducted to verify the sensitivity and specificity of the data collected from a group of patients affected by temporomandibular joint disorders with an ARCUSdigma axiographic system ([https://www.kavo.com/de-de/ KaVo Dental GmbH, Biberach / Ris]) confirmed a sensitivity of the 84.21% and 92.86% sensitivity for the right and left TMJs respectively and a specificity of 93.75% and 95.65%.<ref>{{cite book  

  | autore = Kobs G

  | autore = Kobs G

  | autore2 = Didziulyte A

  | autore2 = Didziulyte A

  }}</ref>

  }}</ref>

<math>a_2=</math> '''Alteration of condylar paths:''' Urbano Santana-Mora and coll.<ref>{{cite book  

<math>\delta_3=</math> '''Alteration of condylar paths:''' Urbano Santana-Mora and coll.<ref>{{cite book  

  | autore = López-Cedrún J

  | autore = López-Cedrún J

  | autore2 = Santana-Mora U

  | autore2 = Santana-Mora U

  }}</ref> evaluated 24 adult patients suffering from severe chronic unilateral pain diagnosed as Temporomandibular Disorders (TMDs). The following functional and dynamic factors were evaluated: (1) masticatory function; (2) remodelling of the TMJ or condylar pathway (CP); and (3) lateral movement of the jaw or lateral guide (LG). The CPs were assessed using conventional axiography and LG was assessed by using kinesiograph tracing ([https://www.myotronics.com/ Myotronics Inc., Kent, WA, US]) Seventeen (71%) of the 24 (100%) patients consistently showed a side of habitual chewing side. The mean and standard deviation of the CP angles was 47.90 <math>\pm</math> 9.24) degrees. The average of LG angles was 42.95<math>\pm</math>11.78 degrees. Data collection emerged from the conception of a new TMD paradigm in which the affected side could be the usual chewing side, the side where the mandibular lateral kinematic angle was flatter. This parameter may also be compatible with the dental claim.

  }}</ref> evaluated 24 adult patients suffering from severe chronic unilateral pain diagnosed as Temporomandibular Disorders (TMDs). The following functional and dynamic factors were evaluated: (1) masticatory function; (2) remodelling of the TMJ or condylar pathway (CP); and (3) lateral movement of the jaw or lateral guide (LG). The CPs were assessed using conventional axiography and LG was assessed by using kinesiograph tracing ([https://www.myotronics.com/ Myotronics Inc., Kent, WA, US]) Seventeen (71%) of the 24 (100%) patients consistently showed a side of habitual chewing side. The mean and standard deviation of the CP angles was 47.90 <math>\pm</math> 9.24) degrees. The average of LG angles was 42.95<math>\pm</math>11.78 degrees. Data collection emerged from the conception of a new TMD paradigm in which the affected side could be the usual chewing side, the side where the mandibular lateral kinematic angle was flatter. This parameter may also be compatible with the dental claim.

<math>a_2=</math> '''EMG Intereference pattern:''' M.O. Mazzetto and coll.<ref>{{cite book  

<math>\delta_4=</math> '''EMG Intereference pattern:''' M.O. Mazzetto and coll.<ref>{{cite book  

  | autore = Oliveira Mazzetto M

  | autore = Oliveira Mazzetto M

  | autore2 = Almeida Rodrigues C

  | autore2 = Almeida Rodrigues C

  }}</ref> showed that the electromyographic activity of the anterior temporal muscles and the masseter was positively correlated with the "Craniomandibular index" 'indiced (CMI) with a <math>P=0,01</math> and suggesting that the use of CMI to quantify the severity of TMDs and EMG to assess the masticatory muscle function, may be an important diagnostic and therapeutic elements. These scientific references determine compatibility of the assertion.

  }}</ref> showed that the electromyographic activity of the anterior temporal muscles and the masseter was positively correlated with the "Craniomandibular index" 'indiced (CMI) with a <math>P=0,01</math> and suggesting that the use of CMI to quantify the severity of TMDs and EMG to assess the masticatory muscle function, may be an important diagnostic and therapeutic elements. These scientific references determine compatibility of the assertion.

<math>a_n=</math>  Obviously the dentist colleague could go on making his statements indefinitely.

<math>\delta_n=</math>  Obviously the dentist colleague could go on making his statements indefinitely.

Well, all of ''these statements seem coherent'' with the sentence <math>\Im</math> initially described, whereby the dentist colleague feels justified in saying that the set of sentences <math>\Im</math>, and a number <math>n\geq1</math> of other assertions or clinical data <math>(a_1,a_2,.....a_n)</math>are logically compatible as the union between them <math>\Im\cup\{a_1,a_2.....a_n\}</math> it is coherent.

Well, all of ''these statements seem coherent'' with the sentence <math>\Im</math> initially described, whereby the dentist colleague feels justified in saying that the set of sentences <math>\Im</math>, and a number <math>n\geq1</math> of other assertions or clinical data <math>(\delta_1,\delta_2,.....\delta_n \ )</math>are logically compatible as the union between them <math>\Im\cup\{\delta_1,\delta_2.....\delta_n\}</math> it is coherent.

{{q4|Following the logic of classical language, the dentist is right!|It would seem! but be careful, only in own dental context!}}

{{q4|Following the logic of classical language, the dentist is right!|It would seem! but be careful, only in own dental context!}}

==Final considerations==

==Final considerations==

Saying from the perspective of observation of this type, the Logic of Predicates  can only fortify the dentist’s reasoning and, at the same time, strengthen the <u>principle of the excluded third</u> is strengthened through the compatibility of the additional assertions <math>(a_1,a_2,.....a_n)</math>which give the dentist the complete coherence in the diagnosis and in confirming the sentence <math>\Im</math>: Poor Mary Poppins either has TMD or she has not.

Saying from the perspective of observation of this type, the Logic of Predicates  can only fortify the dentist’s reasoning and, at the same time, strengthen the <u>principle of the excluded third</u> is strengthened through the compatibility of the additional assertions <math>(\delta_1,\delta_2,.....\delta_n \ )</math>which give the dentist the complete coherence in the diagnosis and in confirming the sentence <math>\Im</math>: Poor Mary Poppins either has TMD or she has not.

{{q4|....and if with the advancement of research new phenomena were discovered that would prove the neurologist right instead of the dentist?|}}

{{q4|....and if with the advancement of research new phenomena were discovered that would prove the neurologist right instead of the dentist?|}}

Basically, given the compatibility of the assertions <math>(a_1,a_2,.....a_n)</math> in coherently saying that Orofacial Pain is caused by a Temporomandibular Disorders could become incompatible if another series of assertions <math>(b_1,b_2,.....b_n)</math> were shown to be coherent which would make a different sentence compatible <math>\Im</math> like: could poor Mary Poppins suffer from Orofacial Pain from a neuromotor disorder (_nOP) and not by a Temporomandibular Disorders?

Basically, given the compatibility of the assertions <math>(\delta_1,\delta_2,.....\delta_n \ )</math> in coherently saying that Orofacial Pain is caused by a Temporomandibular Disorders could become incompatible if another series of assertions <math>(\gamma_1,\gamma_2,.....\gamma_n \ )</math> were shown to be coherent which would make a different sentence compatible <math>\Im</math> like: could poor Mary Poppins suffer from Orofacial Pain from a neuromotor disorder (_nOP) and not by a Temporomandibular Disorders?

In the current medical language logic such assertions remain only assertions because the convictions and opinions do not allow a consequent and quick change of the mindset.

In the current medical language logic such assertions remain only assertions because the convictions and opinions do not allow a consequent and quick change of the mindset.