Difference between revisions of "'The logic of the classical language'"

This paradigm shift does not diminish the value of clinical history but enhances it by integrating a computational approach to validate medical diagnostics. "Craniofacial Biology" is explored comprehensively, with pivotal studies by Townsend and Brook challenging existing paradigms and proposing new clinical applications through interdisciplinary approaches.<ref>{{Cite book | autore = Townsend GC | autore2 = Brook AH | titolo = The face, the future, and dental practice | url = https://onlinelibrary.wiley.com/doi/epdf/10.1111/adj.12157 | opera = Aust Dent J | anno = 2014 | DOI = 10.1111/adj.12157 | PMID = 24646132}}</ref><ref>{{Cite book | autore = Sperber GH | autore2 = Sperber SM | titolo = The genesis of craniofacial biology | url = https://onlinelibrary.wiley.com/doi/epdf/10.1111/adj.12131 | opera = Aust Dent J | anno = 2014 | DOI = 10.1111/adj.12131 | PMID = 24495071}}</ref>Additionally, the role of epigenetics and phenomics in this field is underlined, offering new insights into dental and craniofacial anomalies through the genetic, epigenetic, and environmental interplay.<ref>{{Cite book | autore = Williams SD | autore2 = Hughes TE | autore3 = Adler CJ | autore4 = Brook AH | autore5 = Townsend GC | titolo = Epigenetics: a new frontier in dentistry | url = https://onlinelibrary.wiley.com/doi/epdf/10.1111/adj.12155 | opera = Aust Dent J | anno = 2014 | DOI = 10.1111/adj.12155 | PMID = 24611746}}</ref><ref>{{Cite book | autore = Yong R | autore2 = Ranjitkar S | autore3 = Townsend GC | autore4 = Brook AH | autore5 = Smith RN | autore6 = Evans AR | autore7 = Hughes TE | autore8 = Lekkas D | titolo = Dental phenomics | url = https://onlinelibrary.wiley.com/doi/epdf/10.1111/adj.12156 | opera = Aust Dent J | anno = 2014 | DOI = 10.1111/adj.12156 | PMID = 24611797}}</ref>This extensive review also incorporates diverse studies, illustrating the dynamic complexities of craniofacial development and the significant implications for future dental practices<ref>{{Cite book | autore = Peterkova R | autore2 = Hovorakova M | autore3 = Peterka M | autore4 = Lesot H | titolo = Three‐dimensional analysis of the early development of the dentition | url = https://onlinelibrary.wiley.com/doi/epdf/10.1111/adj.12130 | opera = Aust Dent J | anno = 2014 | DOI = 10.1111/adj.12130}}</ref>. In summary, this chapter emphasizes not only the advanced computational methodologies enhancing diagnostic precision but also the critical interdisciplinary perspectives necessary for holistic patient care in craniofacial anomalies.

'''Mathematical Formalism:''' In this chapter, we revisit the clinical case of Mary Poppins, who has been suffering from Orofacial Pain for over ten years due to "Temporomandibular Disorder" (TMD). This section delves into the complexity of using Classic Language Logic to achieve a precise diagnostic definition.

'''Proof by Contradiction:''' This method involves demonstrating that the negation of a proposition leads to a contradiction, thereby proving the original proposition under the principle of the "law of excluded middle". This fundamental aspect of classical logic asserts that a proposition must be true if its negation is false<ref>{{Cite book | author = Pereira LM | author2 = Pinto AM | title = Reductio ad Absurdum Argumentation in Normal Logic Programs | url = http://www-lia.deis.unibo.it/confs/ArgNMR/proceedings/ArgNMR-proceedings.pdf#page=100 | year = 2007 | publisher = Arg NMR | city = Tempe, Arizona - Caparica, Portugal}}</ref>.

Further diagnostic support is provided through the analysis of axiographic traces and surface electromyography, confirming the presence of TMD based on the observed asymmetry and functional abnormalities in masticatory muscles<ref>{{cite book | autore = Castroflorio T | autore2 = Talpone F | autore3 = Deregibus A | autore4 = Piancino MG | autore5 = Bracco P | titolo = Effects of a Functional Appliance on Masticatory Muscles of Young Adults Suffering From Muscle-Related Temporomandibular Disorder | url = https://pubmed.ncbi.nlm.nih.gov/15189308/ | opera = J Oral Rehabil | anno = 2004 | DOI = 10.1111/j.1365-2842.2004.01274.x | PMID = 15189308}}</ref><ref>{{cite book | autore = Maeda N | autore2 = Kodama N | autore3 = Manda Y | autore4 = Kawakami S | autore5 = Oki K | autore6 = Minagi S | titolo = Characteristics of Grouped Discharge Waveforms Observed in Long-term Masseter Muscle Electromyographic Recording: A Preliminary Study | url = http://ousar.lib.okayama-u.ac.jp/files/public/5/56938/20190821181112825794/73_4_357.pdf | opera = Acta Med Okayama | anno = 2019 | DOI = 10.18926/AMO/56938 | PMID = 31439959}}</ref>.

This section presents further clinical evaluations including CT scans and electromyographic analysis which provide deeper insights into the structural and functional status of the temporomandibular joint (TMJ). These findings are critical in confirming the diagnosis of TMD and understanding its impact on orofacial pain.

In an attempt to apply mathematical formalism to interpret the dentist's diagnostic conclusions using classical logic language, we define the following predicates:

We establish that for every normal patient <math>\mathrm{\mathcal{A}}(\text{x})</math>, if they test positive for the TMJ radiographic examination <math>\mathrm{\mathcal{A}}(\text{x})</math> [see Figures 2 and 3], then they are affected by TMD <math>\rightarrow\mathrm{\mathcal{B}}(\text{x})</math>. Consequently <math>\vdash</math> if Mary Poppins tests positive (and is considered a "normal patient") for the TMJ radiographic exam <math>A(a)</math>, it follows that she too is affected by TMD <math>\rightarrow \mathcal{B}(a)</math>. This can be formally expressed as:

| <math>{a \in x \mid \forall \text{x} ; A(\text{x}) \rightarrow {B}(\text{x}) \vdash A( a)\rightarrow B(a) }</math>

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To verify the truthfulness of this proposition, we resort to proof by contradiction. If the negation of the proposition generates a contradiction, we can conclude that the original hypothesis of the dentist is correct:

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Suppose the neurologist contests conclusion (1), arguing that Mary Poppins does not suffer from TMD or that, at least, TMD is not the primary cause of her Orofacial Pain. Instead, he hypothesizes that Mary suffers from neuromotor type Orofacial Pain (_nOP), classifying her not as a 'normal patient' but as a 'specific patient' (atypical for the dental specialist).

The neurologist's position can be formalized as follows:

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To validate this hypothesis through proof by contradiction, consider its negation:

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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:

# 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.