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==Introduction==
{{main menu}}
In the previous chapter, dedicated to the "[[Logic of Medical Language: Introduction to Quantum Probability in the Masticatory System|Logic of Medical Language]]", we aimed to shift the focus from symptoms or clinical signs to an encrypted machine language. In this context, the arguments of Donald E. Stanley, Daniel G. Campos, and Pat Croskerry are particularly pertinent, especially when connected to the concept of time '''<math>t_n</math>''' as an information vector (anticipating the symptom) and to the consideration of the message as a machine language rather than a verbal language).
 
{{ArtBy|
| autore = Gianni Frisardi
| autore2 = Riccardo Azzali
| autore3 = Flavio Frisardi
}}
'''Abstract:''' This chapter explores the complexities of medical language, particularly within the context of diagnosis and treatment of Temporomandibular Disorders (TMD) and Orofacial Pain (OP). Medical language often leads to misunderstandings due to its hybrid nature, blending everyday language with specialized terms, which can be interpreted differently across medical disciplines. This is exemplified in the clinical case of Mary Poppins, who has suffered from OP for over a decade, with conflicting diagnoses from a dentist and a neurologist. The dentist diagnosed her with TMD based on clinical tests like axiography, electromyography (EMG), and radiographic imaging, while the neurologist attributed her pain to a neuromotor disorder (nOP).
 
The chapter examines how classical logic language, used in traditional medical diagnostics, supports the dentist's diagnosis, focusing on the compatibility of evidence like condylar remodeling and masticatory muscle activity. However, the chapter also highlights the limitations of this approach, showing that new electrophysiological data could challenge the dentist’s assumptions and open the door to different interpretations of OP’s origins.
 
In light of this, the chapter introduces the concept of "system logic language," which moves beyond cause-and-effect models to consider the masticatory system as a complex, dynamic entity. This perspective encourages a more nuanced understanding of patient conditions, recognizing that symptoms may not always align neatly with classical diagnostic frameworks. By analyzing Mary Poppins' case through both classical and system logic, the chapter calls for a reevaluation of medical language and diagnostic approaches, proposing a shift toward probabilistic and interdisciplinary methods for more accurate diagnoses.
 
Ultimately, this chapter suggests that a deeper understanding of medical language and logic can improve clinical decision-making, reduce diagnostic errors, and foster a more comprehensive approach to patient care.
 
==Introduction to the Logic of Medical Language==
In the previous chapter, dedicated to the "[[Logic of medical language|Logic of Medical Language]]", we aimed to shift the focus from symptoms or clinical signs to an encrypted machine language. In this context, the arguments of Donald E. Stanley, Daniel G. Campos, and Pat Croskerry are particularly pertinent, especially when connected to the concept of time '''<math>t_n</math>''' as an information vector (anticipating the symptom) and to the consideration of the message as a machine language rather than a verbal language).
<ref>{{Cite book  
<ref>{{Cite book  
  | autore = Stanley DE
  | autore = Stanley DE
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We cannot limit ourselves to providing a conventional answer, as science progresses not through baseless assertions but through questions and reflections that have passed the scrutiny of scientific validation. This compels us to explore and give voice to thoughts, perplexities, and doubts raised by certain key concepts discussed in various scientific articles.
We cannot limit ourselves to providing a conventional answer, as science progresses not through baseless assertions but through questions and reflections that have passed the scrutiny of scientific validation. This compels us to explore and give voice to thoughts, perplexities, and doubts raised by certain key concepts discussed in various scientific articles.


Among these critical topics is "Craniofacial Biology".
Among these critical topics is "'''Craniofacial Biology'''".


==='''Craniofacial Biology'''===
We begin with an influential study by Townsend and Brook,
We begin with an influential study by Townsend and Brook,
<ref name=":0">{{Cite book  
<ref name=":0">{{Cite book  
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----
----
{{q2|So, how does the classic language logic connect to this context? |The contrast with the "system language logic" highlights the interpretive limits of traditional approaches to malocclusion. This suggests that orthodontic models of cause/effect might need a critical review in light of new electrophysiological evidence.}}
{{q2|So, how does the classic language logic connect to this context? |The contrast with the "system language logic" highlights the interpretive limits of traditional approaches to malocclusion. This suggests that orthodontic models of cause/effect might need a critical review in light of new electrophysiological evidence.}}
==Mathematical Formalism==
== Mathematical Formalism==
In this chapter, we will revisit the clinical case of Mary Poppins, who has been suffering from Orofacial Pain for over ten years, with a diagnosis of "Temporomandibular Disorder" (TMD) confirmed by her dentist, or, more specifically, Orofacial Pain associated with TMD. To understand the complexity in arriving at a precise diagnostic definition using Classic Language Logic, it is fundamental to introduce and analyze the concept at the basis of the philosophy of classical language.
In this chapter, we will revisit the clinical case of Mary Poppins, who has been suffering from Orofacial Pain for over ten years, with a diagnosis of "Temporomandibular Disorder" (TMD) confirmed by her dentist, or, more specifically, Orofacial Pain associated with TMD. To understand the complexity in arriving at a precise diagnostic definition using Classic Language Logic, it is fundamental to introduce and analyze the concept at the basis of the philosophy of classical language.


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"The simplest propositions can be combined with each other to form new and more complex propositions through the use of logical operators and quantifier connectors. These tools of logic allow us to construct broader statements starting from basic concepts, thus facilitating the formulation of theorems and proofs in mathematics and other disciplines that require precision and rigor.
"The simplest propositions can be combined with each other to form new and more complex propositions through the use of logical operators and quantifier connectors. These tools of logic allow us to construct broader statements starting from basic concepts, thus facilitating the formulation of theorems and proofs in mathematics and other disciplines that require precision and rigor.


The fundamental logical operators include:<ref><!--68-->For the sake of simplicity of exposition and reading, we will deal in this chapter with the ''symbol of belonging'', the ''symbol of consequence'' and the "''such that''" as if they were quantifiers and connectives of propositions in classical logic.<br><!--69-->Strictly speaking, within classical logic they should not be treated as such, but even if we do, this does not absolutely change the meaning of the speech and no inconsistencies of any kind are created.</ref>
The fundamental logical operators include:
 
*'''Conjunction''', denoted by the symbol <math>\land</math> (and): represents the logical operation "AND". A compound proposition formed by two propositions joined with "and" is true only if both propositions are true.
*'''Disjunction''', denoted by the symbol <math>\lor</math> (or): represents the logical operation "OR". A compound proposition is true if at least one of the component propositions is true.
*'''Negation''', denoted by the symbol <math>\urcorner</math> (not): reverses the truth value of a proposition. If a proposition is true, its negation is false, and vice versa.
*'''Implication''', denoted by the symbol ⇒ (if... then): expresses a conditional relationship between two propositions. If the antecedent (first proposition) is true, then the consequent (second proposition) must be true for the implication to be true.
*'''Logical consequence''', denoted by the symbol <math>\vdash</math> (it follows that): indicates that a proposition is a logical consequence of the previous ones within a given logical system.
*'''Universal quantifier''', denoted by the symbol <math>\forall</math> (for all): expresses that the following proposition is true for all elements of a certain set.
* '''Proof''', often indicated by reasonings that lead to the conclusion symbolized with <math>\mid</math> (thus): indicates the culmination of an argument or logical reasoning that leads to a conclusion.
*'''Membership''', denoted by the symbol <math>\in</math> (belongs to) or <math>\not\in</math> (does not belong to): used to indicate whether an element belongs or does not belong to a set.


'''Conjunction''', denoted by the symbol <math>\land</math> (and): represents the logical operation "AND". A compound proposition formed by two propositions joined with "and" is true only if both propositions are true.
'''Disjunction''', denoted by the symbol <math>\lor</math> (or): represents the logical operation "OR". A compound proposition is true if at least one of the component propositions is true.
'''Negation''', denoted by the symbol <math>\urcorner</math> (not): reverses the truth value of a proposition. If a proposition is true, its negation is false, and vice versa.
'''Implication''', denoted by the symbol ⇒ (if... then): expresses a conditional relationship between two propositions. If the antecedent (first proposition) is true, then the consequent (second proposition) must be true for the implication to be true.
'''Logical consequence''', denoted by the symbol <math>\vdash</math> (it follows that): indicates that a proposition is a logical consequence of the previous ones within a given logical system.
'''Universal quantifier''', denoted by the symbol <math>\forall</math> (for all): expresses that the following proposition is true for all elements of a certain set.
'''Proof''', often indicated by reasonings that lead to the conclusion symbolized with <math>\mid</math> (thus): indicates the culmination of an argument or logical reasoning that leads to a conclusion.
'''Membership''', denoted by the symbol <math>\in</math> (belongs to) or <math>\not\in</math> (does not belong to): used to indicate whether an element belongs or does not belong to a set.
Quantifier connectors, such as the universal quantifier (<math>\forall</math>) and the existential quantifier (<math>\exists</math>), allow for extending statements to sets of elements, offering a way to express propositions concerning 'all elements' of a certain set or 'at least one element' of such a set.
Quantifier connectors, such as the universal quantifier (<math>\forall</math>) and the existential quantifier (<math>\exists</math>), allow for extending statements to sets of elements, offering a way to express propositions concerning 'all elements' of a certain set or 'at least one element' of such a set.


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| OCLC =
| OCLC =
}}</ref>
}}</ref>
----
===Predicates===
===Predicates===


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In addition to the confirmations derived from the medical language logic discussed in the previous chapter, the dentist acquires further instrumental data that strengthen his diagnosis. These tests include the analysis of axiographic traces, obtained through the use of a custom-made functional paraocclusal fork. This tool allows for the visualization and quantification of the condylar paths during masticatory functions. As shown in Figure 4, the flattening of the condylar traces on the right side, both in the mediotrusive masticatory kinetics (indicated in green) and in the opening and protrusion cycles (in grey), confirms the anatomical and functional flattening of the right TMJ during the dynamics of mastication.
In addition to the confirmations derived from the medical language logic discussed in the previous chapter, the dentist acquires further instrumental data that strengthen his diagnosis. These tests include the analysis of axiographic traces, obtained through the use of a custom-made functional paraocclusal fork. This tool allows for the visualization and quantification of the condylar paths during masticatory functions. As shown in Figure 4, the flattening of the condylar traces on the right side, both in the mediotrusive masticatory kinetics (indicated in green) and in the opening and protrusion cycles (in grey), confirms the anatomical and functional flattening of the right TMJ during the dynamics of mastication.
----
 
In addition to axiography, surface electromyography on the masseter muscles is performed (see Figure 6), during which the patient is asked to exert maximum muscle force. This type of electromyographic analysis, called 'EMG Interferential Pattern', is characterized by the high-frequency content of the peaks showing phase interference. Indeed, Figure 6 highlights an asymmetry in the recruitment of motor units between the right masseter (upper trace) and the left masseter (lower trace).<ref>{{cite book
In addition to axiography, surface electromyography on the masseter muscles is performed (see Figure 6), during which the patient is asked to exert maximum muscle force. This type of electromyographic analysis, called 'EMG Interferential Pattern', is characterized by the high-frequency content of the peaks showing phase interference. Indeed, Figure 6 highlights an asymmetry in the recruitment of motor units between the right masseter (upper trace) and the left masseter (lower trace).
| author = Castroflorio T
<ref>{{cite book  
| author2 = Talpone F
| autore = Castroflorio T
| author3 = Deregibus A
| autore2 = Talpone F
| author4 = Piancino MG
| autore3 = Deregibus A
| author5 = Bracco P
| autore4 = Piancino MG
| title = Effects of a Functional Appliance on Masticatory Muscles of Young Adults Suffering From Muscle-Related Temporomandibular Disorder
| autore5 = Bracco P
| url = https://pubmed.ncbi.nlm.nih.gov/15189308/
| titolo = Effects of a Functional Appliance on Masticatory Muscles of Young Adults Suffering From Muscle-Related Temporomandibular Disorder
| volume =
| url = https://pubmed.ncbi.nlm.nih.gov/15189308/
| work = J Oral Rehabil
| volume =  
| year = 2004
| opera = J Oral Rehabil
| publisher =
| anno = 2004
| city =
| editore =  
| ISBN =
| città =  
| PMID = 15189308
| ISBN =  
| PMCID =
| PMID = 15189308
| DOI = 10.1111/j.1365-2842.2004.01274.x
| PMCID =  
| oaf = <!-- any value -->
| DOI = 10.1111/j.1365-2842.2004.01274.x
}}</ref><ref>{{cite book
| oaf = <!-- qualsiasi valore -->
| author = Maeda N
}}</ref><ref>{{cite book  
| author2 = Kodama N
| autore = Maeda N  
| author3 = Manda Y
| autore2 = Kodama N
| author4 = Kawakami S
| autore3 = Manda Y
| author5 = Oki K
| autore4 = Kawakami S
| author6 = Minagi S
| autore5 = Oki K
| title = Characteristics of Grouped Discharge Waveforms Observed in Long-term Masseter Muscle Electromyographic Recording: A Preliminary Study
| autore6 = Minagi S
| url = http://ousar.lib.okayama-u.ac.jp/files/public/5/56938/20190821181112825794/73_4_357.pdf
| titolo = Characteristics of Grouped Discharge Waveforms Observed in Long-term Masseter Muscle Electromyographic Recording: A Preliminary Study
| volume =
| url = http://ousar.lib.okayama-u.ac.jp/files/public/5/56938/20190821181112825794/73_4_357.pdf
| work = Acta Med Okayama
| volume =  
| year = 2019
| opera = Acta Med Okayama
| publisher = Okayama University Medical School
| anno = 2019
| city = Okayama, Japan
| editore = Okayama University Medical School
| ISBN =
| città = Okayama, Japan
| PMID = 31439959
| ISBN =  
| PMCID =
| PMID = 31439959
| DOI = 10.18926/AMO/56938
| PMCID =  
| oaf = <!-- any value -->
| DOI = 10.18926/AMO/56938
}}</ref><ref>{{cite book
| oaf = <!-- qualsiasi valore -->
| author = Rudy TE
}}</ref><ref>{{cite book  
| title = Psychophysiological Assessment in Chronic Orofacial Pain
| autore = Rudy TE
| url = https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2190318/pdf/anesthprog00262-0036.pdf
| titolo = Psychophysiological Assessment in Chronic Orofacial Pain
| volume =
| url = https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2190318/pdf/anesthprog00262-0036.pdf
| work = Anesth Prog
| volume =  
| year = 1990
| opera = Anesth Prog
| publisher = American Dental Society of Anesthesiology
| anno = 1990
| city =
| editore = American Dental Society of Anesthesiology
| ISSN = 0003-3006/90
| città =  
| ISBN =
| ISSN = 0003-3006/90
| PMID = 2085203
| ISBN =  
| PMCID = PMC2190318
| PMID = 2085203
| DOI =
| PMCID = PMC2190318
| oaf = <!-- any value -->
| DOI =  
}}</ref><ref>{{cite book
| oaf = <!-- qualsiasi valore -->
| author = Woźniak K
}}</ref><ref>{{cite book  
| author2 = Piątkowska D
| autore = Woźniak K
| author3 = Lipski M
| autore2 = Piątkowska D
| author4 = Mehr K
| autore3 = Lipski M
| title = Surface electromyography in orthodontics - a literature review
| autore4 = Mehr K
| url = https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3673808/pdf/medscimonit-19-416.pdf
| titolo = Surface electromyography in orthodontics - a literature review
| volume =
| url = https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3673808/pdf/medscimonit-19-416.pdf
| work = Med Sci Monit
| volume =  
| year = 2013
| opera = Med Sci Monit
| publisher =
| anno = 2013
| city =
| editore =  
| ISBN =
| città =  
| E-ISSN = 1643-3750
| ISBN =  
| PMID = 23722255
| E-ISSN = 1643-3750
| PMCID = PMC3673808
| PMID = 23722255
| DOI = 10.12659/MSM.883927
| PMCID = PMC3673808
| oaf = <!-- any value -->
| DOI = 10.12659/MSM.883927
}}</ref><center>
| oaf = <!-- qualsiasi valore -->
}}</ref><center>
==2nd Clinical Approach==
==2nd Clinical Approach==
(Hover over the images)
(Hover over the images)
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{|
{|
|
|
|<math>{a \not\in x \mid \forall \text{x} ; A(\text{x}) \rightarrow {B}(\text{x}) \and A( a)\rightarrow \urcorner B(a) }</math>
|<math>{a \not\in x \mid \forall \text{x} ; A(\text{x}) \rightarrow {B}(\text{x}) \and A( a)\rightarrow \urcorner B(a) }</math>  
|
|
|
|
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{{q2|so the dentist triumphs!|don't take it for granted}}
{{q2|so the dentist triumphs!|don't take it for granted}}
----
===Compatibility and Incompatibility of Statements ===
===Compatibility and Incompatibility of Statements===
The complexity arises when the dentist presents a series of statements based on clinical reports, such as stratigraphy and computed tomography (CT) of the temporomandibular joint (TMJ), indicating an anatomical flattening of the joint, axiography of the condylar paths with a reduction of cinematic convexity, and an electromyographic (EMG) interference pattern showing asymmetry on the masseters. These evidences can be considered co-causes of damage to the temporomandibular joint and, consequently, responsible for "Orofacial Pain".
The complexity arises when the dentist presents a series of statements based on clinical reports, such as stratigraphy and computed tomography (CT) of the temporomandibular joint (TMJ), indicating an anatomical flattening of the joint, axiography of the condylar paths with a reduction of cinematic convexity, and an electromyographic (EMG) interference pattern showing asymmetry on the masseters. These evidences can be considered co-causes of damage to the temporomandibular joint and, consequently, responsible for "Orofacial Pain".


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


A set of sentences <math>\Im</math> and a number <math>n\geq1</math> of other sentences or statements <math>(\delta_1,\delta_2,.....\delta_n \ )</math> are logically compatible if, and only if, their union <math>\Im\cup{\delta_1,\delta_2.....\delta_n}</math> is consistent.
#A set of sentences <math>\Im</math> and a number <math>n\geq1</math> of other sentences or statements <math>(\delta_1,\delta_2,.....\delta_n \ )</math> are logically compatible if, and only if, their union <math>\Im\cup{\delta_1,\delta_2.....\delta_n}</math> is coherent.
A set of sentences <math>\Im</math> and a number <math>n\geq1</math> of other sentences or statements <math>(\delta_1,\delta_2,.....\delta_n \ )</math> are logically incompatible if, and only if, their union <math>\Im\cup{\delta_1,\delta_2.....\delta_n}</math> is inconsistent.
#A set of sentences <math>\Im</math> and a number <math>n\geq1</math> of other sentences or statements <math>(\delta_1,\delta_2,.....\delta_n \ )</math> are logically incompatible if, and only if, their union <math>\Im\cup{\delta_1,\delta_2.....\delta_n}</math> is incoherent.
 
Let's examine this concept with practical examples.
Let's examine this concept with practical examples.


The dentist presents the following statement:
The dentist presents the following statement:


<math>\Im</math>: Following the personalized techniques suggested by Xin Liang et al.<ref>{{cite book
<math>\Im</math>: Following the personalized techniques suggested by Xin Liang et al.
| author = Liang X
<ref>{{cite book  
| author2 = Liu S
| autore = Liang X
| author3 = Qu X
| autore2 = Liu S
| author4 = Wang Z
| autore3 = Qu X
| author5 = Zheng J
| autore4 = Wang Z
| author6 = Xie X
| autore5 = Zheng J
| author7 = Ma G
| autore6 = Xie X
| author8 = Zhang Z
| autore7 = Ma G
| author9 = Ma X
| autore8 = Zhang Z
| title = Evaluation of Trabecular Structure Changes in Osteoarthritis of the Temporomandibular Joint With Cone Beam Computed Tomography Imaging
| autore9 = Ma X
| url = https://pubmed.ncbi.nlm.nih.gov/28732700/
| titolo = Evaluation of Trabecular Structure Changes in Osteoarthritis of the Temporomandibular Joint With Cone Beam Computed Tomography Imaging
| volume =
| url = https://pubmed.ncbi.nlm.nih.gov/28732700/
| work = Oral Surg Oral Med Oral Pathol Oral Radiol
| volume =  
| year = 2017
| opera = Oral Surg Oral Med Oral Pathol Oral Radiol
| publisher =
| anno = 2017
| city =
| editore =  
| ISBN =
| città =  
| PMID = 28732700
| ISBN =  
| PMCID =
| PMID = 28732700
| DOI = 10.1016/j.oooo.2017.05.514
| PMCID =  
| oaf = <!-- any value -->
| DOI = 10.1016/j.oooo.2017.05.514
}}</ref> that focuses on the quantitative microstructural analysis of the bone value fraction, trabecular number, trabecular thickness, and trabecular separation on each slice of a TMJ CT, it appears that Mary Poppins is affected by Temporomandibular Disorders (TMDs) and the consequence causes orofacial pain.
| oaf = <!-- qualsiasi valore -->
}}</ref> that focuses on the quantitative microstructural analysis of the bone value fraction, trabecular number, trabecular thickness, and trabecular separation on each slice of a TMJ CT, it appears that Mary Poppins is affected by Temporomandibular Disorders (TMDs) and the consequence causes orofacial pain.


However, to further confirm the diagnosis, the dentist presents a series of additional assertions that should pass the compatibility filter described above, thus establishing a coherent basis for the diagnosis of TMD in Mary Poppins.
However, to further confirm the diagnosis, the dentist presents a series of additional assertions that should pass the compatibility filter described above, thus establishing a coherent basis for the diagnosis of TMD in Mary Poppins.


<math>\delta_1=</math> Bone remodeling: The flattening of the axiographic traces shown in Figure 5 indicates the joint remodeling of Mary Poppins' right TMJ. This report can be related to a series of research and articles confirming how malocclusion can be associated with morphological changes of the temporomandibular joints, particularly if related to age. Indeed, the presence of chronic malocclusion can aggravate the scenario of bone remodeling.<ref>{{cite book
'''<math>\delta_1=</math> Bone remodeling:''' The flattening of the axiographic traces shown in Figure 5 indicates the joint remodeling of Mary Poppins' right TMJ. This report can be related to a series of research and articles confirming how malocclusion can be associated with morphological changes of the temporomandibular joints, particularly if related to age. Indeed, the presence of chronic malocclusion can aggravate the scenario of bone remodeling.
| author = Solberg WK
<ref>{{cite book  
| author2 = Bibb CA
| autore = Solberg WK
| author3 = Nordström BB
| autore2 = Bibb CA
| author4 = Hansson TL
| autore3 = Nordström BB
| title = Malocclusion Associated With Temporomandibular Joint Changes in Young Adults at Autopsy
| autore4 = Hansson TL
| url = https://pubmed.ncbi.nlm.nih.gov/3457531/
| titolo = Malocclusion Associated With Temporomandibular Joint Changes in Young Adults at Autopsy
| volume =
| url = https://pubmed.ncbi.nlm.nih.gov/3457531/
| work = Am J Orthod
| volume =  
| year = 1986
| opera = Am J Orthod
| publisher =
| anno = 1986
| city =
| editore =  
| ISBN =
| città =  
| PMID = 3457531
| ISBN =  
| PMCID =
| PMID = 3457531
| DOI = 10.1016/0002-9416(86)90055-2
| PMCID =  
| oaf = <!-- any value -->
| DOI = 10.1016/0002-9416(86)90055-2
}}</ref> The provided scientific references support the compatibility of the assertion.
| oaf = <!-- qualsiasi valore -->
----
}}</ref> The provided scientific references support the compatibility of the assertion.
<math>\delta_2=</math> Sensitivity and Specificity of the Axiographic Measurement:
 
'''<math>\delta_2=</math> Sensitivity and Specificity of the Axiographic Measurement:'''
 
A study was conducted to evaluate the sensitivity and specificity of the data obtained from a sample of patients with temporomandibular joint disorders, using the ARCUSdigma axiographic system.
<ref>[https://www.kavo.com/de-de/ KaVo Dental GmbH, Biberach / Ris]</ref>
The results showed a sensitivity of 84.21% for the right TMJ and 92.86% for the left TMJ, with a specificity of 93.75% and 95.65%, respectively.
<ref>{{cite book
| autore = Kobs G
| autore2 = Didziulyte A
| autore3 = Kirlys R
| autore4 = Stacevicius M
| titolo = Reliability of ARCUSdigma (KaVo) in Diagnosing Temporomandibular Joint Pathology
| url = https://sbdmj.lsmuni.lt/072/072-03.pdf
| volume =
| opera = Stomatologija
| anno = 2007
| editore =
| città =
| ISBN =
| PMID = 17637527
| PMCID =
| DOI =
| oaf = <!-- qualsiasi valore -->
}}</ref> These scientifically validated data support the compatibility of the statement in the dental field, given the consistency of related studies.
<ref>{{cite book
| autore = Piancino MG
| autore2 = Roberi L
| autore3 = Frongia G
| autore4 = Reverdito M
| autore5 = Slavicek R
| autore6 = Bracco P
| titolo = Computerized axiography in TMD patients before and after therapy with 'function generating bites'
| volume =
| opera = J Oral Rehabil
| anno = 2008
| editore =
| città =
| ISBN =
| PMID = 18197841
| PMCID =
| DOI = 10.1111/j.1365-2842.2007.01815.x
| oaf = <!-- qualsiasi valore -->
}}</ref>


A study was conducted to evaluate the sensitivity and specificity of the data obtained from a sample of patients with temporomandibular joint disorders, using the ARCUSdigma axiographic system.<ref>[https://www.kavo.com/de-de/ KaVo Dental GmbH, Biberach / Ris]</ref> The results showed a sensitivity of 84.21% for the right TMJ and 92.86% for the left TMJ, with a specificity of 93.75% and 95.65%, respectively.<ref>{{cite book
'''<math>\delta_3=</math> Alteration in Condylar Paths:'''
| author = Kobs G
| author2 = Didziulyte A
| author3 = Kirlys R
| author4 = Stacevicius M
| title = Reliability of ARCUSdigma (KaVo) in Diagnosing Temporomandibular Joint Pathology
| url = https://sbdmj.lsmuni.lt/072/072-03.pdf
| volume =
| work = Stomatologija
| year = 2007
| publisher =
| city =
| ISBN =
| PMID = 17637527
| PMCID =
| DOI =
| oaf = <!-- any value -->
}}</ref> These scientifically validated data support the compatibility of the statement in the dental field, given the consistency of related studies.<ref>{{cite book
| author = Piancino MG
| author2 = Roberi L
| author3 = Frongia G
| author4 = Reverdito M
| author5 = Slavicek R
| author6 = Bracco P
| title = Computerized axiography in TMD patients before and after therapy with 'function generating bites'
| volume =
| work = J Oral Rehabil
| year = 2008
| publisher =
| city =
| ISBN =
| PMID = 18197841
| PMCID =
| DOI = 10.1111/j.1365-2842.2007.01815.x
| oaf = <!-- any value -->
}}</ref>


<math>\delta_3=</math> Alteration in Condylar Paths:
Urbano Santana-Mora and colleagues
<ref>{{cite book
| autore = López-Cedrún J
| autore2 = Santana-Mora U
| autore3 = Pombo M
| autore4 = Pérez Del Palomar A
| autore5 = Alonso De la Peña V
| autore6 = Mora MJ
| autore7 = Santana U
| titolo = Jaw Biodynamic Data for 24 Patients With Chronic Unilateral Temporomandibular Disorder
| url = https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5674825/pdf/sdata2017168.pdf
| volume =
| opera = Sci Data
| anno = 2017
| editore =
| città =
| ISBN =
| PMID =  29112190
| PMCID = PMC5674825
| DOI = 10.1038/sdata.2017.168
| oaf = YES<!-- qualsiasi valore -->
}}</ref> conducted a study on 24 adult patients suffering from severe chronic unilateral pain, diagnosed with Temporomandibular Disorders (TMD). The research focused on the analysis of various functional and dynamic factors, including masticatory function, the remodeling of the temporomandibular joint (TMJ) or condylar paths (CP), and lateral jaw movement or lateral guidance (LG).


Urbano Santana-Mora and colleagues<ref>{{cite book
The CPs were evaluated using conventional axiography, while the LG was examined through kinesiographic tracing analysis.
| author = López-Cedrún J
<ref>[https://www.myotronics.com/ Myotronics Inc., Kent, WA, US]</ref>  
| author2 = Santana-Mora U
It was found that seventeen patients, corresponding to 71% of the total sample, habitually preferred to chew on one side. The mean and standard deviation of the CP angles were 47.90 (± 9.24) degrees, while the mean of the LG angles was 42.95 (± 11.78) degrees.
| author3 = Pombo M
| author4 = Pérez Del Palomar A
| author5 = Alonso De la Peña V
| author6 = Mora MJ
| author7 = Santana U
| title = Jaw Biodynamic Data for 24 Patients With Chronic Unilateral Temporomandibular Disorder
| url = https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5674825/pdf/sdata2017168.pdf
| volume =
| work = Sci Data
| year = 2017
| publisher =
| city =
| ISBN =
| PMID = 29112190
| PMCID = PMC5674825
| DOI = 10.1038/sdata.2017.168
| oaf = YES<!-- any value -->
}}</ref> conducted a study on 24 adult patients suffering from severe chronic unilateral pain, diagnosed with Temporomandibular Disorders (TMD). The research focused on the analysis of various functional and dynamic factors, including masticatory function, the remodeling of the temporomandibular joint (TMJ) or condylar paths (CP), and lateral jaw movement or lateral guidance (LG).
----
The CPs were evaluated using conventional axiography, while the LG was examined through kinesiographic tracing analysis.<ref>[https://www.myotronics.com/ Myotronics Inc., Kent, WA, US]</ref> It was found that seventeen patients, corresponding to 71% of the total sample, habitually preferred to chew on one side. The mean and standard deviation of the CP angles were 47.90 (± 9.24) degrees, while the mean of the LG angles was 42.95 (± 11.78) degrees.


The study results contributed to the definition of a new paradigm for TMDs, suggesting that the side affected by the disorder might coincide with the habitual chewing side, especially when the lateral mandibular cinematic angle is flatter. This parameter further supports the dental assertion regarding the correlation between chewing habits and the development of TMDs.
The study results contributed to the definition of a new paradigm for TMDs, suggesting that the side affected by the disorder might coincide with the habitual chewing side, especially when the lateral mandibular cinematic angle is flatter. This parameter further supports the dental assertion regarding the correlation between chewing habits and the development of TMDs.


<math>\delta_4=</math> EMG Interference Pattern:
'''<math>\delta_4=</math> EMG Interference Pattern:'''


M.O. Mazzetto and collaborators<ref>{{cite book
M.O. Mazzetto and collaborators
| author = Oliveira Mazzetto M
<ref>{{cite book  
| author2 = Almeida Rodrigues C
| autore = Oliveira Mazzetto M
| author3 = Valencise Magri L
| autore2 = Almeida Rodrigues C
| author4 = Oliveira Melchior M
| autore3 = Valencise Magri L
| author5 = Paiva G
| autore4 = Oliveira Melchior M
| title = Severity of TMD Related to Age, Sex and Electromyographic Analysis
| autore5 = Paiva G
| url = https://www.scielo.br/scielo.php?script=sci_arttext&pid=S0103-64402014000100054&lng=en&nrm=iso&tlng=en
| titolo = Severity of TMD Related to Age, Sex and Electromyographic Analysis
| volume =
| url = https://www.scielo.br/scielo.php?script=sci_arttext&pid=S0103-64402014000100054&lng=en&nrm=iso&tlng=en
| work = Braz Dent J
| volume =  
| year = 2014
| opera = Braz Dent J
| publisher =
| anno = 2014
| city =
| editore =  
| ISBN =
| città =  
| PMID =
| ISBN =  
| PMCID =
| PMID =  
| DOI = 10.1590/0103-6440201302310
| PMCID =  
| oaf = <!-- any value -->
| DOI = 10.1590/0103-6440201302310
}}</ref> demonstrated that there is a positive correlation between the electromyographic activity of the anterior temporal muscles and the masseter and the 'Cranio-Mandibular Index' (CMI), with a value of <math>P=0,01</math>. This suggests that the use of CMI to quantify the severity of Temporomandibular Disorders (TMD) and electromyography (EMG) to assess the function of the masticatory muscles can represent a significant diagnostic and therapeutic element. Such scientific references support the compatibility of the assertion.
| oaf = <!-- qualsiasi valore -->
}}</ref> demonstrated that there is a positive correlation between the electromyographic activity of the anterior temporal muscles and the masseter and the 'Cranio-Mandibular Index' (CMI), with a value of <math>P=0,01</math>. This suggests that the use of CMI to quantify the severity of Temporomandibular Disorders (TMD) and electromyography (EMG) to assess the function of the masticatory muscles can represent a significant diagnostic and therapeutic element. Such scientific references support the compatibility of the assertion.


<math>\delta_n=?</math>
<math>\delta_n=?</math>


Given the evidence presented and the statements made, the dentist can legitimately claim that the set of sentences <math>\Im</math>, and a number <math>n\geq1</math> of other positive clinical assertions or data <math>(\delta_1,\delta_2,.....\delta_n \ )</math>​ are logically compatible. This is because their union, <math>\Im\cup{\delta_1,\delta_2.....\delta_n}</math>, turns out to be consistent.
Given the evidence presented and the statements made, the dentist can legitimately claim that the set of sentences <math>\Im</math>, and a number <math>n\geq1</math> of other positive clinical assertions or data <math>(\delta_1,\delta_2,.....\delta_n \ )</math>​ are logically compatible. This is because their union, <math>\Im\cup{\delta_1,\delta_2.....\delta_n}</math>, turns out to be coherent.


{{q2|Following classical language logic, the dentist is right!|It would seem so! But beware, only in their own dental context!}}
{{q2|Following classical language logic, the dentist is right!|It would seem so! But beware, only in their own dental context!}}
Line 849: Line 873:


==Final Considerations==
==Final Considerations==
Within the scope of this observation, the application of Predicate Logic significantly contributes to strengthening the dentist's deductive process, concurrently solidifying the principle of excluded middle. This principle is emphasized by the coherence of the supplementary statements <math>(\delta_1,\delta_2,...,\delta_n)</math>, providing the dentist with a solid foundation for a consistent diagnosis and to affirm with certainty that 'Poor Mary Poppins is, without a shadow of a doubt, affected by TMD or not.'
Within the scope of this observation, the application of Predicate Logic significantly contributes to strengthening the dentist's deductive process, concurrently solidifying the principle of excluded middle. This principle is emphasized by the coherence of the supplementary statements <math>(\delta_1,\delta_2,...,\delta_n)</math>, providing the dentist with a solid foundation for a coherent diagnosis and to affirm with certainty that 'Poor Mary Poppins is, without a shadow of a doubt, affected by TMD or not.'


{{q2|And what if, as research advances, new phenomena emerge supporting the neurologist's theories rather than the dentist's?|}}
{{q2|And what if, as research advances, new phenomena emerge supporting the neurologist's theories rather than the dentist's?|}}
----
----
In essence, considering the compatibility of the assertions <math>(\delta_1,\delta_2,.....\delta_n)</math>, consistently supporting that Orofacial Pain is caused by a Temporomandibular Disorder might become incompatible if another set of equally coherent assertions <math>(\gamma_1,\gamma_2,.....\gamma_n)</math> emerged. This scenario would pave the way for a new interpretation <math>\Im</math>: Mary Poppins could be suffering from Orofacial Pain due to a Neuromotor Disorder (<sub>n</sub>OP), not directly from Temporomandibular Disorders. Within the current medical language, such assertions remain purely theoretical, given that prevailing beliefs and opinions do not facilitate a rapid paradigm shift.
In essence, considering the compatibility of the assertions <math>(\delta_1,\delta_2,.....\delta_n)</math>, coherently supporting that Orofacial Pain is caused by a Temporomandibular Disorder might become incompatible if another set of equally coherent assertions <math>(\gamma_1,\gamma_2,.....\gamma_n)</math> emerged. This scenario would pave the way for a new interpretation <math>\Im</math>: Mary Poppins could be suffering from Orofacial Pain due to a Neuromotor Disorder (<sub>n</sub>OP), not directly from Temporomandibular Disorders. Within the current medical language, such assertions remain purely theoretical, given that prevailing beliefs and opinions do not facilitate a rapid paradigm shift.


Considering also the risk associated with such a change, the analysis of recent studies on the epidemiology of Temporomandibular Disorders<ref>{{cite book | author = LeResche L | title = Epidemiology of temporomandibular disorders: implications for the investigation of etiologic factors | url = https://pubmed.ncbi.nlm.nih.gov/9260045/ | volume = | work = Crit Rev Oral Biol Med | year = 1997 | publisher = | city = | ISBN = | PMID = 9260045 | PMCID = | DOI = 10.1177/10454411970080030401 | oaf = <!-- any value --> }}</ref> could prove useful. These studies indicate that, despite methodological and sampling differences, pain in the temporomandibular region is relatively common, affecting about 10% of the population. Therefore, it is reasonable to hypothesize that Mary Poppins could fall within this percentage, classifying her as a patient suffering from Orofacial Pain due to Temporomandibular Disorders (TMD).
Considering also the risk associated with such a change, the analysis of recent studies on the epidemiology of Temporomandibular Disorders
<ref>{{cite book | autore = LeResche L | titolo = Epidemiology of temporomandibular disorders: implications for the investigation of etiologic factors | url = https://pubmed.ncbi.nlm.nih.gov/9260045/ | volume = | opera = Crit Rev Oral Biol Med | anno = 1997 | editore = | città = | ISBN = | PMID = 9260045 | PMCID = | DOI = 10.1177/10454411970080030401 | oaf = <!-- qualsiasi valore --> }}</ref> could prove useful. These studies indicate that, despite methodological and sampling differences, pain in the temporomandibular region is relatively common, affecting about 10% of the population. Therefore, it is reasonable to hypothesize that Mary Poppins could fall within this percentage, classifying her as a patient suffering from Orofacial Pain due to Temporomandibular Disorders (TMD).


In conclusion, adopting a classical dichotomous approach in medical language, which tends to categorize conditions in black or white, fails to capture the numerous nuances present in clinical realities. Therefore, exploring a more flexible and suitable linguistic approach is necessary...
In conclusion, adopting a classical dichotomous approach in medical language, which tends to categorize conditions in black or white, fails to capture the numerous nuances present in clinical realities. Therefore, exploring a more flexible and suitable linguistic approach is necessary...
Gianni
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