Changes

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

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

Let us try to follow the reasoning with practical examples:

<translate>Let us try to follow this reasoning with practical examples</translate>:

The dentist colleague exposes the following sentence:

<translate>The dentist colleague exposes the following sentence</translate>:

<math>\Im</math>: Following the personalized techniques suggested by Xin Liang et al.<ref>{{cite book  

<math>\Im</math>: <translate>Following the personalized techniques suggested by Xin Liang et al</translate>.<ref>{{cite book  

  | autore = Liang X

  | autore = Liang X

  | autore2 = Liu S

  | autore2 = Liu S

  | DOI = 10.1016/j.oooo.2017.05.514

  | DOI = 10.1016/j.oooo.2017.05.514

  | oaf = <!-- qualsiasi valore -->

  | oaf = <!-- qualsiasi valore -->

  }}</ref> which focuses on the quantitative microstructural analysis of the fraction of the bone value, the trabecular number, the trabecular thickness and the trabecular separation on each slice of the CT scan of a TMJ, it appears that Mary Poppins is affected by Temporomandibular Disorders (TMDs) and the consequence causes Orofacial Pain.

  }}</ref> <translate>who focuses on the quantitative microstructural analysis of the fraction of the bone value, the trabecular number, the trabecular thickness and the trabecular separation on each slice of the CT scan of a TMJ, it appears that Mary Poppins is affected by Temporomandibular Disorders (TMDs) and the consequence causes Orofacial Pain</translate>.

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

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

<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  

<math>\delta_1=</math> '''<translate>Bone remodelling</translate>:''' <translate>The flattening of the axiographic traces highlighted in figure 5 indicates the joint remodelling of the right TMJ of Mary Poppins</translate>, <translate>such a report 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</translate>.<ref>{{cite book  

  | autore = Solberg WK

  | autore = Solberg WK

  | autore2 = Bibb CA

  | autore2 = Bibb CA

  | DOI = 10.1016/0002-9416(86)90055-2

  | DOI = 10.1016/0002-9416(86)90055-2

  | oaf = <!-- qualsiasi valore -->

  | oaf = <!-- qualsiasi valore -->

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

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

<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  

<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