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

[[File:Spasmo emimasticatorio.jpg|left|300x300px]]In the previous chapter, dedicated to the "[[Logic of medical language|Logic of Medical Language]]", we shifted focus from traditional clinical signs to an encrypted machine language, highlighting the innovative contributions of Donald E. Stanley, Daniel G. Campos, and Pat Croskerry. They emphasized the use of time as an information vector in diagnostics<ref>{{Cite book | autore = Stanley DE | autore2 = Campos DG | titolo = The logic of medical diagnosis | url = https://pubmed.ncbi.nlm.nih.gov/23974509/ | opera = Perspect Biol Med | anno = 2013 | DOI = 10.1353/pbm.2013.0019 | PMID = 23974509}}</ref><ref>{{Cite book | autore = Croskerry P | titolo = Adaptive expertise in medical decision making | url = https://www.tandfonline.com/doi/abs/10.1080/0142159X.2018.1484898 | opera = Med Teach | anno = 2018 | DOI = 10.1080/0142159X.2018.1484898 | PMID = 30033794}}</ref>.

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.

'''Propositions''' The simplest propositions in logic can be combined using logical operators and quantifiers to construct complex logical statements, enhancing the precision and rigor required in mathematical and scientific reasoning. Key logical operators include:

*'''Universal quantifier''' (<math>\forall</math>),

*'''Existential quantifier''' (<math>\exists</math>).

These tools help form the backbone of logical reasoning used to navigate complex diagnostic processes in medical practice.

'''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>.

 

<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>

 

 

 

 

 

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

*<math>x \equiv</math> Normal patients (where "normal" refers to patients commonly encountered in a specialist setting)

*<math>A(x) \equiv</math> Presence of bone remodeling with detected osteophyte from stratigraphic exams and condylar CT

 

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>

 

 

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:

 

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

 

 

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:

{|

|<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>(3)</math>

 

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:  

 

 

 

 

 

 

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