Editor, Editors, USER, admin, Bureaucrats, Check users, dev, editor, founder, Interface administrators, member, oversight, Suppressors, Administrators, translator
11,492
edits
Changes
no edit summary
[[File:Spasmo emimasticatorio assiografia.jpg|left|200x200px]]
[[File:Spasmo emimasticatorio assiografia.jpg|left|200x200px]]
'''Classical logic''' will be discussed in this chapter.
'''Classical logic''' will be discussed in this chapter. In the first part, mathematical formalism and the rules that compose it will be illustrated. In the second part, a clinical example will be given to evaluate its effectiveness in determining a diagnosis. In conclusion, it is evident that a classical logic of language, which has an extremely dichotomous approach (either something is white, or it is black), cannot describe the many shades that real clinical situations have. As we shall see, this paper will show that classical logic lacks the necessary precision, forcing us to enhance it with other types of logic languages. {{ArtBy|
In the first part, mathematical formalism and the rules that compose it will be illustrated.
In the second part, a clinical example will be given to evaluate its effectiveness in determining a diagnosis.
In conclusion, it is evident that a classical logic of language, which has an extremely dichotomous approach (either something is white, or it is black), cannot describe the many shades that real clinical situations have. As we shall see, this paper will show that classical logic lacks the necessary precision, forcing us to enhance it with other types of logic languages.
{{ArtBy|
| autore = Gianni Frisardi
| autore = Gianni Frisardi
| autore2 = Riccardo Azzali
| autore2 = Riccardo Azzali
In this review, arguments could not be missing on genetic, epigenetic and environmental influences during morphogenesis that lead to variations in the number, size and shape of the tooth<ref>{{Cite book
In this review, arguments could not be missing on genetic, epigenetic and environmental influences during morphogenesis that lead to variations in the number, size and shape of the tooth<ref>{{Cite book
<nowiki> </nowiki><nowiki>|</nowiki> autore = Brook AH
<nowiki> </nowiki><nowiki>|</nowiki> autore2 = Jernvall J
<nowiki> </nowiki><nowiki>|</nowiki> autore3 = Smith RN
<nowiki> </nowiki><nowiki>|</nowiki> autore4 = Hughes TE
<nowiki> </nowiki><nowiki>|</nowiki> autore5 = Townsend GC
<nowiki> </nowiki><nowiki>|</nowiki> titolo = The Dentition: The Outcomes of Morphogenesis Leading to Variations of Tooth Number, Size and Shape
<nowiki> </nowiki><nowiki>|</nowiki> url = https://onlinelibrary.wiley.com/doi/epdf/10.1111/adj.12160
| volume =
| volume =
| opera = Aust Dent J
| opera = Aust Dent J
This example is Classical Logic Language, as we are going to explain in detail, but now a doubt arises:
This example is Classical Logic Language, as we are going to explain in detail, but now a doubt arises:
'At the time when orthodontic and orthognathics axioms were constructing protocols confirmed by the International Scientific Community, were they aware of the information we discussed in the introduction to this chapter?
Certainly not! because time '''<math>t_n</math>''' '''is the bearer of information''' but despite this cognitive limit we proceeded with a very questionable Classical Language Logic for the safety of the citizen.
Certainly not! because time '''<math>t_n</math>''' '''is the bearer of information''' but despite this cognitive limit we proceeded with a very questionable Classical Language Logic for the safety of the citizen.
If the same case were interpreted with a mindset that followed a 'System's language logic' (it will be discussed in the appropriate chapter) the conclusions would be surprising.
If the same case were interpreted with a mindset that followed a 'System's language logic' (it will be discussed in the appropriate chapter) the conclusions would be surprising.
If we observe the electrophysiological responses performed on the patient with malocclusion in figures 1b, 1c and 1d (with the explanation made directly in the caption to simplify the discussion) and we shallnotice that these data can make us think about anything except a 'Malocclusion' and, therefore, the axioms of type orthodontic and orthognathics 'cause/effect' leave a conceptual void until they guarantee a post-treatment that maintains a State of Coherence of the system in question tested before treatment.
If we observe the electrophysiological responses performed on the patient with malocclusion in figures 1b, 1c and 1d (with the explanation made directly in the caption to simplify the discussion), we shall notice that these data can make us think about anything except a 'Malocclusion' and, therefore, the axioms of type orthodontic and orthognathics 'cause/effect' leave a conceptual void.
<gallery mode="packed-hover" widths="250" heights="182" perrow="3">
<gallery mode="packed-hover" widths="250" heights="182" perrow="3">
File:Occlusal Centric view in open and cross bite patient.jpg|'''Figure 1a:''' Patient with malocclusion, open bite and right posterior crossbite who in rehabilitation terms must be treated with orthodontic therapy and / or orthognathic surgery.
File:Occlusal Centric view in open and cross bite patient.jpg|'''Figure 1a:''' Patient with malocclusion, open bite and right posterior crossbite who in rehabilitation terms must be treated with orthodontic therapy and / or orthognathic surgery.
File:Bilateral Electric Transcranial Stimulation.jpg|'''Figure 1b:''' Motor evoked potential from electrical transcranial stimulation of the trigeminal roots. Note the structural symmetry calculated by the peak-to-peak amplitude on the left and right masseters.
File:Bilateral Electric Transcranial Stimulation.jpg|'''Figure 1b:''' Motor evoked potential from electrical transcranial stimulation of the trigeminal roots.Note the structural symmetry calculated by the peak-to-peak amplitude on the left and right masseters (traces upper and lower respectively)
File:Jaw Jerk .jpg|'''Figure 1c:''' Mandibular reflex evoked or jaw jerk by percussion of the chin through a triggered neurological hammer.
File:Jaw Jerk .jpg|'''Figure 1c:''' Mandibular reflex evoked or jaw jerk by percussion of the chin through a triggered neurological hammer. Note the functional symmetry calculated by the peak-to-peak amplitude on the left and right masseters (traces upper and lower respectively)
File:Mechanic Silent Period.jpg|'''Figure 1d:''' Mechanical silent period evoked by percussion of the chin through a triggered neurological hammer. Note the functional symmetry calculated on the integral area of the right and left masseters.
File:Mechanic Silent Period.jpg|'''Figure 1d:''' Mechanical silent period evoked by percussion of the chin through a triggered neurological hammer. Note the functional symmetry calculated on the integral area of the right and left masseters (traces upper and lower respectively).
</gallery>
</gallery>
==Mathematical formalism==
==Mathematical formalism==
In this chapter we will reconsider the clinical case of the unfortunate Mary Poppins suffering from Orofacial Pain for more than 10 years to which her dentist diagnosed as Temporomandibular Disorders or rather Orofacial Pain from Temporomandibular Disorders (TMDs).
In this chapter, we will reconsider the clinical case of the unfortunate Mary Poppins suffering from Orofacial Pain for more than 10 years to which her dentist diagnosed a 'Temporomandibular Disorders' (TMDs) or rather Orofacial Pain from TMDs. To better understand why the exact diagnostic formulation remains complex with a Logic of Classical Language, we should understand the concept on which the philosophy of classical language is based with a brief introduction to the topic.
To better understand why the exact diagnostic formulation remains complex with a Logic of Classical Language, we should understand the concept on which the philosophy of classical language is based with a brief introduction to the topic.
===Propositions===
===Propositions===
Classical logic is based on propositions. It is often said that a proposition is a sentence that asks whether the proposition is true or false. Indeed a proposition in mathematics is usually either true or false, but this is obviously a little too vague to be a definition. It can at best be taken as a warning: if a sentence, expressed in common language, makes no sense to ask whether it is true or false, it will not be a proposition but something else.
Classical logic is based on propositions. It is often said that a proposition is a sentence that asks whether the proposition is true or false. Indeed a proposition in mathematics is usually either true or false, but this is obviously a little too vague to be a definition. It can at best be taken as a warning: if a sentence, expressed in common language, makes no sense to ask whether it is true or false, it will not be a proposition but something else.
It can be argued whether or not common language sentences are propositions as in many cases it is not often evident if a certain statement is true or false. For example, when one says ‘someone wrote a lot of romances’, some might argue that the romances are not that many while others might object to this argument.
It can be argued whether or not common language sentences are propositions as in many cases it is not often evident if a certain statement is true or false.
‘''Fortunately, mathematical propositions, if well expressed, have no such ambiguities’.''
‘''Fortunately, mathematical propositions, if well expressed, have no such ambiguities’.''
{{q4|Then poor Mary Poppins is a TMD patient or she is not !!|let's see what Classical Language Logic tells us}}
{{q4|Then poor Mary Poppins is a TMD patient or she is not !!|let's see what Classical Language Logic tells us}}
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 performed with a paraocclusal tray 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 tighten to 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 the result of the test and 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
| autore = Castroflorio T
| autore = Castroflorio T
| autore2 = Talpone F
| autore2 = Talpone F
<gallery mode="packed-hover" widths="250" heights="182" perrow="3">
<gallery mode="packed-hover" widths="250" heights="182" perrow="3">
File:Spasmo emimasticatorio.jpg|'''Figure 2:''' Patient reporting "Orofacial Pain in the right hemilateral face
File:Spasmo emimasticatorio.jpg|'''Figure 2:''' Patient reporting 'Orofacial Pain' in the right hemilateral face
File:Spasmo emimasticatorio ATM.jpg|'''Figure 3:''' Patient's TMJ stratigraphy showing signs of condylar flattening and osteophyte
File:Spasmo emimasticatorio ATM.jpg|'''Figure 3:''' Patient's TMJ stratigraphy showing signs of condylar flattening and osteophyte
File:Atm1 sclerodermia.jpg|'''Figure 4:''' Computed Tomography of the TMJ
File:Atm1 sclerodermia.jpg|'''Figure 4:''' Computed Tomography of the TMJ
===Dental propositions===
===Dental propositions===
While seeking to use the mathematical formalism to translate the conclusions reached by the dentist with classical logic language, we consider the following predicates:
*''x'' <math>\equiv</math> Normal patients (normal stands for patients commonly present in the specialist setting)
*''x'' <math>\equiv</math> Normal patients (normal stands for patients commonly present in the specialist setting)
===Neurophysiological proposition===
===Neurophysiological proposition===
Let us imagine that the neurologist disagrees with the conclusion <math>(1)</math> and asserts that Mary Poppins is not affected by TMDs or that at least it is not the main cause of Orofacial Pain but that she is affected by a neuropathic Orofacial Pain (<sub>n</sub>OP), therefore that she does not belong to the group of 'normal patients' but is to be considered a 'non-specific patient' (uncommon in the specialist context).
Let us imagine that the neurologist disagrees with the conclusion <math>(1)</math> and asserts that Mary Poppins is not affected by TMDs or that at least it is not the main cause of Orofacial Pain but that she is affected by a neuromotor Orofacial Pain (<sub>n</sub>OP), therefore that she does not belong to the group of 'normal patients' but is to be considered a 'non-specific patient' (uncommon in the specialist context).
Obviously this dialectic would last indefinitely because both would defend their scientific-clinical context but let us see what happens in the logic of predicates.
Obviously this dialectic would last indefinitely because both would defend their scientific-clinical context but let us see what happens in the logic of predicates.
| DOI = 10.1038/sdata.2017.168
| DOI = 10.1038/sdata.2017.168
| oaf = YES<!-- qualsiasi valore -->
| oaf = YES<!-- qualsiasi valore -->
}}</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 Wass 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>a_2=</math> '''EMG Intereference pattern:''' M.O. Mazzetto and coll.<ref>{{cite book
==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 (for everything A can be either B or not B, no other state of truth is possible).
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.
{{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?|}}
}}</ref> confirm that despite the methodological and population differences, pain in the temporomandibular region appears to be relatively common, occurring in about the 10% of the population we may be led to hypothesize objectively that our Mary Poppins can be included in the 10% of the patients mentioned in the epidemiological study and be contextually classified as a patient suffering from Orofacial Pain from Temporomandibular Disorders (TMDs)
}}</ref> confirm that despite the methodological and population differences, pain in the temporomandibular region appears to be relatively common, occurring in about the 10% of the population we may be led to hypothesize objectively that our Mary Poppins can be included in the 10% of the patients mentioned in the epidemiological study and be contextually classified as a patient suffering from Orofacial Pain from Temporomandibular Disorders (TMDs)
In conclusion, it is evident that a mathematical-classical logic of language, which has an extremely dichotomous approach (either it is white or it is black), cannot depict the many shades that occur in real clinical situations.
In conclusion, it is evident that a classical logic of language, which has an extremely dichotomous approach (either it is white or it is black), cannot depict the many shades that occur in real clinical situations.
We need to find a more convenient and suitable language logic ...
We need to find a more convenient and suitable language logic ...