Changes

#''<translate>Universal quantifier</translate>'', <translate>which is indicated by the symbol</translate> <math>\forall</math> (for all):

#''<translate>Universal quantifier</translate>'', <translate>which is indicated by the symbol</translate> <math>\forall</math> (for all):

#''<translate>Demonstration</translate>'', <translate>which is indicated by the symbol</translate> <math>\mid</math> (such that): and

#''<translate>Demonstration</translate>'', <translate>which is indicated by the symbol</translate> <math>\mid</math> (such that): and

#''<translate>Membership</translate>'', <translate>which is indicated by the symbol</translate> <math>\in</math> (is an element of) o <math>\not\in</math> (is not an element of):

#''<translate>Membership</translate>'', <translate>which is indicated by the symbol</translate> <math>\in</math> (is an element of) <translate>or by the symbol</translate> <math>\not\in</math> (is not an element of):

===Demonstration by absurdity===

===<translate>Demonstration by absurdity</translate>===

Furthermore, in classical logic there is a principle called the <u>excluded third</u> which declares that a sentence that cannot be false must be taken as true since there is no third possibility.

<translate>Furthermore, in classical logic there is a principle called the <u>excluded third</u> which declares that a sentence that cannot be false must be taken as true since there is no third possibility</translate>.

Suppose we need to prove that the proposition <math>p</math> is true. The procedure consists in showing that the assumption that <math>p</math> is false leads to a logical contradiction. Thus the proposition <math>p</math> cannot be false, and therefore, according to the law of the excluded third, it must be true. This method of demonstration is called ''demonstration by absurdity''<ref>{{Cite book  

<translate>Suppose we need to prove that the proposition <math>p</math> is true</translate>. <translate>The procedure consists in showing that the assumption that <math>p</math> is false leads to a logical contradiction. Thus the proposition <math>p</math> cannot be false, and therefore, according to the law of the excluded third, it must be true. This method of demonstration is called ''demonstration by absurdity''</translate><ref>{{Cite book  

  | autore = Pereira LM

  | autore = Pereira LM

  | autore2 = Pinto AM

  | autore2 = Pinto AM

  }}</ref>

  }}</ref>

===Predicates===

===<translate>Predicates</translate>===

What we have briefly described so far is the logic of propositions. A proposition asserts something about specific mathematical objects such as: '2 is greater than 1, so 1 is less than 2' or 'a square has no 5 sides then a square is not a pentagon'. Many times, however, the mathematical statements concern not the single object but generic objects of a set such as: '''<math>X</math>'' are taller than 2 meters ' where with ''<math>X</math>'' it denotes a generic group (for example all volleyball players). In this case we speak of predicates.

<translate>What we have briefly described so far is the logic of propositions. A proposition asserts something about specific mathematical objects such as: '2 is greater than 1, so 1 is less than 2' or 'a square has no 5 sides then a square is not a pentagon'</translate>. <translate>Many times, however, the mathematical statements concern not the single object, but generic objects of a set such as</translate>: '''<math>X</math>'' <translate>are taller than 2 meters</translate>' <translate>where</translate> ''<math>X</math>'' <translate>denotes a generic group (for example all volleyball players)</translate>. <translate>In this case we speak of predicates</translate>.

Intuitively, a predicate is a sentence concerning a group of elements (which in our medical case will be the patients) and which states something about them.

<translate>Intuitively, a predicate is a sentence concerning a group of elements (which in our medical case will be the patients) and which states something about them</translate>.

{{q4|Then poor Mary Poppins is a TMD patient or she is not !!|let's see what Classical Language Logic tells us}}

{{q4|<translate>Then poor Mary Poppins is a TMD patient or she is not!</translate>|<translate>let's see what Classical Language Logic tells us</translate>}}

In addition to the confirmations derived from the logic of medical language discussed in the previous chapter, the dentist colleague acquires other instrumental data that allow him to confirm his diagnosis. The latter tests concern the analysis of the axiographic traces by using a customized functional paraocclusal clutch which allow the visualization and quantification of the condylar traces in masticatory functions. As can be seen from Figure 4 the flattening of the condylar traces on the right side both in the mediotrusive masticatory kinetics (green colour) and the opening and protrusion cycles (gray colour) confirm the anatomical and functional flattening of the right TMJ in the dynamics chewing. In addition to the axiography, the colleague performs a surface electromyography on the masseters (Fig. 6) asking the patient to exert  the maximum of his muscles force. This type of electromyographic analysis is called "EMG Interferential Pattern" due to the high frequency content of the spikes that undergo phase interference. In fact, Figure 6 shows an asymmetry in the recruitment of the motor units of the right masseter (upper trace) compared to those of the left masseter (lower trace).<ref>{{cite book  

In addition to the confirmations derived from the logic of medical language discussed in the previous chapter, the dentist colleague acquires other instrumental data that allow him to confirm his diagnosis. The latter tests concern the analysis of the axiographic traces by using a customized functional paraocclusal clutch which allow the visualization and quantification of the condylar traces in masticatory functions. As can be seen from Figure 4 the flattening of the condylar traces on the right side both in the mediotrusive masticatory kinetics (green colour) and the opening and protrusion cycles (gray colour) confirm the anatomical and functional flattening of the right TMJ in the dynamics chewing. In addition to the axiography, the colleague performs a surface electromyography on the masseters (Fig. 6) asking the patient to exert  the maximum of his muscles force. This type of electromyographic analysis is called "EMG Interferential Pattern" due to the high frequency content of the spikes that undergo phase interference. In fact, Figure 6 shows an asymmetry in the recruitment of the motor units of the right masseter (upper trace) compared to those of the left masseter (lower trace).<ref>{{cite book