Difference between revisions of "The logic of the classical language"
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==Introduction== | ==Introduction== | ||
In the previous chapter, dedicated to the "[[Logic of | 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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The fundamental logical operators include: | 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. | * '''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. | * '''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. | * '''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. | * '''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. | * '''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. | * '''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. | * '''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. | * '''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). | 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 | <ref>{{cite book | ||
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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". | ||
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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 | # 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 | # 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. | ||
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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. | '''<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 | <ref>{{cite book | ||
| autore = Solberg WK | | autore = Solberg WK | ||
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| oaf = <!-- qualsiasi valore --> | | oaf = <!-- qualsiasi valore --> | ||
}}</ref> The provided scientific references support the compatibility of the assertion. | }}</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. | 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. | ||
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}}</ref> | }}</ref> | ||
<math>\delta_3=</math> Alteration in Condylar Paths: | '''<math>\delta_3=</math> Alteration in Condylar Paths:''' | ||
Urbano Santana-Mora and colleagues | Urbano Santana-Mora and colleagues | ||
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| oaf = YES<!-- qualsiasi valore --> | | 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). | }}</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. | 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> | <ref>[https://www.myotronics.com/ Myotronics Inc., Kent, WA, US]</ref> | ||
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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 | M.O. Mazzetto and collaborators | ||
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<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 | 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!}} | ||
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==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 | 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>, | 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 | Considering also the risk associated with such a change, the analysis of recent studies on the epidemiology of Temporomandibular Disorders | ||