= Normalization = == De-normalized database form == === Global set of attributes === {{{ R = { doctor_id, d_first_name, d_last_name, d_email, level_id, level_name, specialization_id, specialization_name, department_id, department_name, patient_id, p_first_name, p_last_name, p_email, date_of_birth, blood_type, gender, phone_number, embg, admin_id, admin_username, admin_name, admin_lastname, admin_email, technician_id, tech_username, tech_name, tech_lastname, tech_email, user_id, users_username, users_password, users_role, users_first_name, users_last_name, is_active, appointment_id, appointment_date, appointment_time, appointment_status, appt_patient_id, appt_doctor_id, diagnosis_id, diagnosis_name, diagnosis_description, diag_patient_id, diag_doctor_id, procedure_id, procedure_type, procedure_sched_date, procedure_description, procedure_cost, proc_doctor_id, proc_result_id, proc_result_description, proc_result_date, performed_id, perf_proc_id, perf_doctor_id, perf_patient_id, perf_diagnosis_id, perf_date, perf_notes, test_id, test_name, test_description, test_cost, lab_result_id, lab_result_value, lab_result_date, performed_test_id, pt_test_id, pt_patient_id, pt_doctor_id, pt_technician_id, pt_test_date, pt_notes, pt_created_at, prescription_id, medication_name, restriction_id, restriction_description, dosage, frequency, duration, prescription_notes, allergy_id, allergy_name, allergy_severity, record_allergy_reaction, record_allergy_severity, symptom_id, symptom_name, symptom_description, record_symptom_severity, record_id, referral_id, referral_reason, referral_date, ref_from_doctor_id, ref_to_doctor_id, report_id, report_description, report_date, report_doctor_id, bill_id, total_cost, payment_status, payment_date, billing_admin_id, billing_created_at } }}} === Functional dependencies === `Doctor` {{{ F1 level_id -> level_name F2 specialization_id -> specialization_name F3 department_id -> department_name F4 doctor_id -> d_first_name, d_last_name, d_email, level_id, specialization_id, department_id, user_id }}} `Patient` {{{ F5 patient_id -> p_first_name, p_last_name, p_email, date_of_birth, blood_type, gender, phone_number, embg, user_id }}} `Admin` {{{ F6 admin_id -> admin_username, admin_name, admin_lastname, admin_email, user_id }}} `Lab Technician` {{{ F7 technician_id -> tech_username, tech_name, tech_lastname, tech_email, user_id }}} `User` {{{ F8 user_id -> users_username, users_password, users_role, users_first_name, users_last_name, is_active }}} Unlike a typical subtype design where the supertype (`Users`) would hold nullable foreign keys to each subtype, this schema does it the other way around: `Doctors`, `Patients`, `Admin`, and `LabTechnician` each carry their own mandatory `user_id` foreign key back to `Users`, so it is the subtype row that points up to its login row, not the reverse. Because of that, `doctor_id -> user_id`, `patient_id -> user_id`, `admin_id -> user_id`, and `technician_id -> user_id` all hold (folded into F4, F5, F6, F7 above), while `user_id` itself does not determine any of `doctor_id`, `patient_id`, `admin_id`, or `technician_id`, since a `Users` row need not have any subtype row pointing to it at all (e.g. a system administrator account with no linked profile). This is the same subtype idea used for `Admin`, `Clients`, and `Owners` elsewhere, except here the four subtypes each own the foreign key to their shared supertype `users` table instead of the supertype holding a pointer to each of them. `Appointment` {{{ F9 appointment_id -> appointment_date, appointment_time, appointment_status, appt_patient_id, appt_doctor_id }}} `Diagnosis` {{{ F10 diagnosis_id -> diagnosis_name, diagnosis_description, diag_patient_id, diag_doctor_id }}} `Procedure` {{{ F11 procedure_id -> procedure_type, procedure_sched_date, procedure_description, procedure_cost, proc_doctor_id F12 proc_result_id -> proc_result_description, proc_result_date, procedure_id F13 performed_id -> perf_proc_id, perf_doctor_id, perf_patient_id, perf_diagnosis_id, perf_date, perf_notes }}} `Prescription` {{{ F14 prescription_id -> medication_name F15 restriction_id -> restriction_description, prescription_id }}} `Lab test` {{{ F16 test_id -> test_name, test_description, test_cost F17 lab_result_id -> lab_result_value, lab_result_date, test_id F18 performed_test_id -> pt_test_id, pt_patient_id, pt_doctor_id, pt_technician_id, pt_test_date, pt_notes, pt_created_at }}} `Medical record` {{{ F19 record_id -> patient_id }}} `Allergy` {{{ F20 allergy_id -> allergy_name, allergy_severity }}} `Symptom` {{{ F21 symptom_id -> symptom_name, symptom_description }}} `Referral` {{{ F22 referral_id -> referral_reason, referral_date, record_id, ref_from_doctor_id, ref_to_doctor_id }}} `Medical report` {{{ F23 report_id -> report_description, report_date, record_id, report_doctor_id }}} `Billing` {{{ F24 bill_id -> total_cost, payment_status, payment_date, record_id, billing_admin_id, billing_created_at }}} `Medical record associations (composite key attributes)` {{{ F25 {record_id, symptom_id} -> record_symptom_severity F26 {record_id, allergy_id} -> record_allergy_reaction, record_allergy_severity F27 {prescription_id, record_id} -> dosage, frequency, duration, prescription_notes }}} `Many-to-many association tables (no dependent attribute, trivial so FDs only on the full pair)` {{{ {record_id, procedure_id} {record_id, lab_result_id} {patient_id, allergy_id} {patient_id, symptom_id} {diagnosis_id, symptom_id} {specialization_id, procedure_id} {department_id, procedure_id} {bill_id, procedure_id} {bill_id, test_id} {report_id, lab_result_id} {allergy_id, restriction_id} {diagnosis_id, record_id} }}} ---- === Candidate keys and primary key === A candidate key of the de-normalized relation is found by picking a minimal set of identifiers whose closure reaches every attribute of R. Several identifiers already determine others through chains inside the FD set — for instance: proc_result_id -> procedure_id lab_result_id -> test_id restriction_id -> prescription_id referral_id -> record_id, and in turn record_id -> patient_id doctor_id -> level_id, specialization_id, department_id, user_id These chains matter because whatever gets reached this way (procedure_id, test_id, prescription_id, record_id, patient_id, level_id, specialization_id, department_id, and — because of the corrected foreign-key direction discussed under `User` above — user_id) does not need to be included in the key separately as it is already recoverable once its determinant is present. In particular, `user_id` is reachable via `doctor_id -> user_id` (F4) the moment `doctor_id` is in the key, so unlike an earlier draft of this analysis that assumed `Users` held the foreign keys, `user_id` is *not* one of the irreducible identifiers below. '''Left-hand side only''' (identifiers that never appear as a dependent on the right side of any FD, and therefore cannot be reached this way): `doctor_id, admin_id, technician_id, appointment_id, diagnosis_id, proc_result_id, performed_id, restriction_id, lab_result_id, performed_test_id, allergy_id, symptom_id, referral_id, report_id, bill_id` Since none of these 15 identifiers can be derived from anything else in R, every candidate key of R is required to contain all of them: {{{ K = { doctor_id, admin_id, technician_id, appointment_id, diagnosis_id, proc_result_id, performed_id, restriction_id, lab_result_id, performed_test_id, allergy_id, symptom_id, referral_id, report_id, bill_id } }}} === Closure proof for K === {{{ Start: K+ = {doctor_id, admin_id, technician_id, appointment_id, diagnosis_id, proc_result_id, performed_id, restriction_id, lab_result_id, performed_test_id, allergy_id, symptom_id, referral_id, report_id, bill_id} From F4: doctor_id -> d_first_name, d_last_name, d_email, level_id, specialization_id, department_id, user_id From F1 using level_id: level_id -> level_name From F2 using specialization_id: specialization_id -> specialization_name From F3 using department_id: department_id -> department_name From F8 using user_id (just derived from F4): user_id -> users_username, users_password, users_role, users_first_name, users_last_name, is_active From F6: admin_id -> admin_username, admin_name, admin_lastname, admin_email, user_id From F7: technician_id -> tech_username, tech_name, tech_lastname, tech_email, user_id From F9: appointment_id -> appointment_date, appointment_time, appointment_status, appt_patient_id, appt_doctor_id From F10: diagnosis_id -> diagnosis_name, diagnosis_description, diag_patient_id, diag_doctor_id From F12: proc_result_id -> proc_result_description, proc_result_date, procedure_id From F11 using procedure_id: procedure_id -> procedure_type, procedure_sched_date, procedure_description, procedure_cost, proc_doctor_id From F13: performed_id -> perf_proc_id, perf_doctor_id, perf_patient_id, perf_diagnosis_id, perf_date, perf_notes From F15: restriction_id -> restriction_description, prescription_id From F14 using prescription_id: prescription_id -> medication_name From F17: lab_result_id -> lab_result_value, lab_result_date, test_id From F16 using test_id: test_id -> test_name, test_description, test_cost From F18: performed_test_id -> pt_test_id, pt_patient_id, pt_doctor_id, pt_technician_id, pt_test_date, pt_notes, pt_created_at From F20: allergy_id -> allergy_name, allergy_severity From F21: symptom_id -> symptom_name, symptom_description From F22: referral_id -> referral_reason, referral_date, record_id, ref_from_doctor_id, ref_to_doctor_id From F19 using record_id: record_id -> patient_id From F5 using patient_id: patient_id -> p_first_name, p_last_name, p_email, date_of_birth, blood_type, gender, phone_number, embg, user_id From F23: report_id -> report_description, report_date, record_id, report_doctor_id From F24: bill_id -> total_cost, payment_status, payment_date, record_id, billing_admin_id, billing_created_at From F25 using record_id and symptom_id: {record_id, symptom_id} -> record_symptom_severity From F26 using record_id and allergy_id: {record_id, allergy_id} -> record_allergy_reaction, record_allergy_severity From F27 using prescription_id and record_id: {prescription_id, record_id} -> dosage, frequency, duration, prescription_notes }}} Therefore, K+ determines all attributes of R, so K is a `superkey`. === Minimality / uniqueness === To promote K from only "a candidate key" to the chosen primary key, we also need to show that no other candidate key exists. None of the 15 identifiers in K is functionally determined by another determinant in the given FD set: **doctor_id** does not appear on the right-hand side of any FD, so it cannot be derived. **admin_id** does not appear on the right-hand side of any FD, so it cannot be derived. **technician_id** does not appear on the right-hand side of any FD, so it cannot be derived. **appointment_id** does not appear on the right-hand side of any FD, so it cannot be derived. **diagnosis_id** does not appear on the right-hand side of any FD, so it cannot be derived. **proc_result_id** does not appear on the right-hand side of any FD, so it cannot be derived. **performed_id** does not appear on the right-hand side of any FD, so it cannot be derived. **restriction_id** does not appear on the right-hand side of any FD, so it cannot be derived. **lab_result_id** does not appear on the right-hand side of any FD, so it cannot be derived. **performed_test_id** does not appear on the right-hand side of any FD, so it cannot be derived. **allergy_id** does not appear on the right-hand side of any FD, so it cannot be derived. **symptom_id** does not appear on the right-hand side of any FD, so it cannot be derived. **referral_id** does not appear on the right-hand side of any FD, so it cannot be derived. **report_id** does not appear on the right-hand side of any FD, so it cannot be derived. **bill_id** does not appear on the right-hand side of any FD, so it cannot be derived. `user_id` is deliberately excluded from this list: it *does* appear on the right-hand side of F4 (`doctor_id -> ..., user_id`), so it is derivable once `doctor_id` — already irreducible and already in K — is known, and including it separately in K would be redundant. Every superkey of R must contain all attributes in: {{{ E = { doctor_id, admin_id, technician_id, appointment_id, diagnosis_id, proc_result_id, performed_id, restriction_id, lab_result_id, performed_test_id, allergy_id, symptom_id, referral_id, report_id, bill_id } }}} Because K and E are the same set, and we already showed K+ = R, K qualifies as a superkey. And because every superkey is required to contain E, so nothing smaller than K could ever work as a key. There's also no way to swap out one of these 15 attributes for a different one and still get a valid candidate key, since none of the attributes in E can be reached from any other determinant in the functional dependency set so there's simply no substitute available for any of them. This means K stands as the sole candidate key of the de-normalized relation, given the functional dependencies defined above. '''Primary key of the de-normalized relation:''' {{{ PK = { doctor_id, admin_id, technician_id, appointment_id, diagnosis_id, proc_result_id, performed_id, restriction_id, lab_result_id, performed_test_id, allergy_id, symptom_id, referral_id, report_id, bill_id } }}} ---- == 1NF decomposition == Every attribute in `R` is single valued and atomic, and the composite `PK` above uniquely identifies each row, so '''`R` satisfies 1NF'''. ---- == 2NF decomposition == R has a composite primary key of 15 attributes, and none of its non-key attributes depends on the whole 15 attribute keys as each one is reachable from just one or two members of K, either directly (F4, F5, F6, ... etc) or through a short chain (e.g. proc_result_id -> procedure_id -> procedure_type, referral_id -> record_id -> patient_id). Either way, that is a partial dependency with respect to K, so R violates 2NF. Examples: {{{ doctor_id -> d_first_name, d_last_name, d_email, level_id, specialization_id, department_id, user_id diagnosis_id -> diagnosis_name, diagnosis_description, diag_patient_id, diag_doctor_id proc_result_id -> proc_result_description, proc_result_date, procedure_id referral_id -> referral_reason, referral_date, record_id, ref_from_doctor_id, ref_to_doctor_id }}} === Grouping by determinants === {{{ doctor_id -> d_first_name, d_last_name, d_email, level_id, specialization_id, department_id, user_id level_id -> level_name specialization_id-> specialization_name department_id -> department_name patient_id -> p_first_name, p_last_name, p_email, date_of_birth, blood_type, gender, phone_number, embg, user_id admin_id -> admin_username, admin_name, admin_lastname, admin_email, user_id technician_id -> tech_username, tech_name, tech_lastname, tech_email, user_id user_id -> users_username, users_password, users_role, users_first_name, users_last_name, is_active appointment_id -> appt_patient_id, appt_doctor_id, appointment_date, appointment_time, appointment_status diagnosis_id -> diagnosis_name, diagnosis_description, diag_patient_id, diag_doctor_id procedure_id -> procedure_type, procedure_sched_date, procedure_description, procedure_cost, proc_doctor_id proc_result_id -> proc_result_description, proc_result_date, procedure_id performed_id -> perf_proc_id, perf_doctor_id, perf_patient_id, perf_diagnosis_id, perf_date, perf_notes prescription_id -> medication_name restriction_id -> restriction_description, prescription_id test_id -> test_name, test_description, test_cost lab_result_id -> lab_result_value, lab_result_date, test_id performed_test_id-> pt_test_id, pt_patient_id, pt_doctor_id, pt_technician_id, pt_test_date, pt_notes, pt_created_at record_id -> patient_id allergy_id -> allergy_name, allergy_severity symptom_id -> symptom_name, symptom_description referral_id -> referral_reason, referral_date, record_id, ref_from_doctor_id, ref_to_doctor_id report_id -> report_description, report_date, record_id, report_doctor_id bill_id -> total_cost, payment_status, payment_date, record_id, billing_admin_id, billing_created_at {record_id, symptom_id} -> record_symptom_severity {record_id, allergy_id} -> record_allergy_reaction, record_allergy_severity {prescription_id, record_id} -> dosage, frequency, duration, prescription_notes }}} MedicalRecordSymptoms, MedicalRecordAllergies and PrescriptionRecords already depend on their whole composite key so these three are already 2NF compliant and are not split further. === 2NF relations === {{{ Doctors(doctor_id, d_first_name, d_last_name, d_email, level_id, specialization_id, department_id, user_id) DoctorLevels(level_id, level_name) Specializations(specialization_id, specialization_name) Departments(department_id, department_name) Patients(patient_id, p_first_name, p_last_name, p_email, date_of_birth, blood_type, gender, phone_number, embg, user_id) Admin(admin_id, admin_username, admin_name, admin_lastname, admin_email, user_id) LabTechnician(technician_id, tech_username, tech_name, tech_lastname, tech_email, user_id) Users(user_id, users_username, users_password, users_role, users_first_name, users_last_name, is_active) Appointments(appointment_id, appt_patient_id, appt_doctor_id, appointment_date, appointment_time, appointment_status) Diagnoses(diagnosis_id, diagnosis_name, diagnosis_description, diag_patient_id, diag_doctor_id) Procedures(procedure_id, procedure_type, procedure_sched_date, procedure_description, procedure_cost, proc_doctor_id) ProcedureResults(proc_result_id, proc_result_description, proc_result_date, procedure_id) PerformedProcedures(performed_id, perf_proc_id, perf_doctor_id, perf_patient_id, perf_diagnosis_id, perf_date, perf_notes) Prescriptions(prescription_id, medication_name) PrescriptionRestrictions(restriction_id, restriction_description, prescription_id) LabTests(test_id, test_name, test_description, test_cost) LabResults(lab_result_id, lab_result_value, lab_result_date, test_id) PerformedLabTests(performed_test_id, pt_test_id, pt_patient_id, pt_doctor_id, pt_technician_id, pt_test_date, pt_notes, pt_created_at) MedicalRecords(record_id, patient_id) Allergies(allergy_id, allergy_name, allergy_severity) Symptoms(symptom_id, symptom_name, symptom_description) Referrals(referral_id, referral_reason, referral_date, record_id, ref_from_doctor_id, ref_to_doctor_id) MedicalReports(report_id, report_description, report_date, record_id, report_doctor_id) Billing(bill_id, total_cost, payment_status, payment_date, record_id, billing_admin_id, billing_created_at) MedicalRecordSymptoms(record_id, symptom_id, record_symptom_severity) MedicalRecordAllergies(record_id, allergy_id, record_allergy_reaction, record_allergy_severity) PrescriptionRecords(prescription_id, record_id, dosage, frequency, duration, prescription_notes) }}} === Lossless join === A split of relation R into R1 and R2 keeps every row reconstructable as long as the columns R1 and R2 have in common are by themselves sufficient to pin down one of the two sides completely: {{{ (R1 ∩ R2) -> R1 or (R1 ∩ R2) -> R2 }}} Each relation below comes from one FD: its determinant becomes the new table's key, and that same determinant stays behind as a foreign key connecting it to the rest. Because the FD already guarantees the determinant decides everything in the new table, every split passes the lossless-join test automatically. === Decomposition into relations === '''`Doctors`(doctor_id, d_first_name, d_last_name, d_email, level_id, specialization_id, department_id, user_id)''' R1 = R - {d_first_name, d_last_name, d_email} (level_id, specialization_id, department_id, user_id remain in R since they are needed as determinants for steps 2-4 and for `Users`) Lossless join: The shared column with R is `doctor_id`. Since `doctor_id -> Doctors` holds (F4), the relation can be reconstructed via join on `doctor_id`. Dependency preservation: F4 is preserved entirely within the new relation `Doctors`. '''`DoctorLevels`(level_id, level_name)''' R2 = R1 - {level_name, level_id} Lossless join: Shared column is `level_id`. `level_id -> DoctorLevels` holds (F1), so the relation is reconstructed via join on `level_id`. Dependency preservation: F1 preserved entirely in `DoctorLevels`. '''`Specializations`(specialization_id, specialization_name)''' R3 = R2 - {specialization_name, specialization_id} Lossless join: Shared column `specialization_id`. `specialization_id -> Specializations` holds (F2). Dependency preservation: F2 preserved entirely in `Specializations`. '''`Departments`(department_id, department_name)''' R4 = R3 - {department_name, department_id} Lossless join: Shared column `department_id`. `department_id -> Departments` holds (F3). Dependency preservation: F3 preserved entirely in `Departments`. '''`Patients`(patient_id, p_first_name, p_last_name, p_email, date_of_birth, blood_type, gender, phone_number, embg, user_id)''' R5 = R4 - {p_first_name, p_last_name, p_email, date_of_birth, blood_type, gender, phone_number, embg} (patient_id remains in R - needed later for MedicalRecords; user_id remains - needed for `Users`) Lossless join: Shared column `patient_id`. `patient_id -> Patients` holds (F5). Dependency preservation: F5 preserved entirely in `Patients`. '''`Admin`(admin_id, admin_username, admin_name, admin_lastname, admin_email, user_id)''' R6 = R5 - {admin_username, admin_name, admin_lastname, admin_email} (user_id remains - needed for `Users`) Lossless join: Shared column `admin_id`. `admin_id -> Admin` holds (F6). Dependency preservation: F6 preserved entirely in `Admin`. '''`LabTechnician`(technician_id, tech_username, tech_name, tech_lastname, tech_email, user_id)''' R7 = R6 - {tech_username, tech_name, tech_lastname, tech_email} (user_id remains - needed for `Users`) Lossless join: Shared column `technician_id`. `technician_id -> LabTechnician` holds (F7). Dependency preservation: F7 preserved entirely in `LabTechnician`. '''`Users`(user_id, users_username, users_password, users_role, users_first_name, users_last_name, is_active)''' R8 = R7 - {users_username, users_password, users_role, users_first_name, users_last_name, is_active, user_id} (user_id itself is dropped here too, since once `Users` is split off, every remaining relation that needs it — `Doctors`, `Patients`, `Admin`, `LabTechnician` — already carries it as its own foreign key) Lossless join: Shared column `user_id`. `user_id -> Users` holds (F8), and `user_id` is already present in `Doctors`, `Patients`, `Admin`, and `LabTechnician` from steps 1, 5, 6, 7, so the join back is via any of those four tables' `user_id` column. Dependency preservation: F8 preserved entirely in `Users`. '''`Appointments`(appointment_id, appt_patient_id, appt_doctor_id, appointment_date, appointment_time, appointment_status)''' R9 = R8 - {appt_patient_id, appt_doctor_id, appointment_date, appointment_time, appointment_status} Lossless join: Shared column `appointment_id`. `appointment_id -> Appointments` holds (F9). Dependency preservation: F9 preserved entirely in `Appointments`. '''`Diagnoses`(diagnosis_id, diagnosis_name, diagnosis_description, diag_patient_id, diag_doctor_id)''' R10 = R9 - {diagnosis_name, diagnosis_description, diag_patient_id, diag_doctor_id} Lossless join: Shared column `diagnosis_id`. `diagnosis_id -> Diagnoses` holds (F10). Dependency preservation: F10 preserved entirely in `Diagnoses`. '''`Procedures`(procedure_id, procedure_type, procedure_sched_date, procedure_description, procedure_cost, proc_doctor_id)''' R11 = R10 - {procedure_type, procedure_sched_date, procedure_description, procedure_cost, proc_doctor_id} (procedure_id remains - needed for ProcedureResults) Lossless join: Shared column `procedure_id`. `procedure_id -> Procedures` holds (F11). Dependency preservation: F11 preserved entirely in `Procedures`. '''`ProcedureResults`(proc_result_id, proc_result_description, proc_result_date, procedure_id)''' R12 = R11 - {proc_result_description, proc_result_date, procedure_id} Lossless join: Shared column `proc_result_id`. `proc_result_id -> ProcedureResults` holds (F12). Dependency preservation: F12 preserved entirely in `ProcedureResults`. '''`PerformedProcedures`(performed_id, perf_proc_id, perf_doctor_id, perf_patient_id, perf_diagnosis_id, perf_date, perf_notes)''' R13 = R12 - {perf_proc_id, perf_doctor_id, perf_patient_id, perf_diagnosis_id, perf_date, perf_notes} Lossless join: Shared column `performed_id`. `performed_id -> PerformedProcedures` holds (F13). Dependency preservation: F13 preserved entirely in `PerformedProcedures`. '''`Prescriptions`(prescription_id, medication_name)''' R14 = R13 - {medication_name} (prescription_id remains - needed for PrescriptionRestrictions and PrescriptionRecords) Lossless join: Shared column `prescription_id`. `prescription_id -> Prescriptions` holds (F14). Dependency preservation: F14 preserved entirely in `Prescriptions`. '''`PrescriptionRestrictions`(restriction_id, restriction_description, prescription_id)''' R15 = R14 - {restriction_description} Lossless join: Shared column `restriction_id`. `restriction_id -> PrescriptionRestrictions` holds (F15). Dependency preservation: F15 preserved entirely in `PrescriptionRestrictions`. '''`LabTests`(test_id, test_name, test_description, test_cost)''' R16 = R15 - {test_name, test_description, test_cost} (test_id remains - needed for LabResults) Lossless join: Shared column `test_id`. `test_id -> LabTests` holds (F16). Dependency preservation: F16 preserved entirely in `LabTests`. '''`LabResults`(lab_result_id, lab_result_value, lab_result_date, test_id)''' R17 = R16 - {lab_result_value, lab_result_date, test_id} Lossless join: Shared column `lab_result_id`. `lab_result_id -> LabResults` holds (F17). Dependency preservation: F17 preserved entirely in `LabResults`. '''`PerformedLabTests`(performed_test_id, pt_test_id, pt_patient_id, pt_doctor_id, pt_technician_id, pt_test_date, pt_notes, pt_created_at)''' R18 = R17 - {pt_test_id, pt_patient_id, pt_doctor_id, pt_technician_id, pt_test_date, pt_notes, pt_created_at} Lossless join: Shared column `performed_test_id`. `performed_test_id -> PerformedLabTests` holds (F18). Dependency preservation: F18 preserved entirely in `PerformedLabTests`. '''`MedicalRecords`(record_id, patient_id)''' R19 = R18 - {patient_id} (record_id remains - needed for Referrals, MedicalReports, Billing, and the three composite-key relations) Lossless join: Shared column `record_id`. `record_id -> MedicalRecords` holds (F19). Dependency preservation: F19 preserved entirely in `MedicalRecords`. '''`Allergies`(allergy_id, allergy_name, allergy_severity)''' R20 = R19 - {allergy_name, allergy_severity} Lossless join: Shared column `allergy_id`. `allergy_id -> Allergies` holds (F20). Dependency preservation: F20 preserved entirely in `Allergies`. '''`Symptoms`(symptom_id, symptom_name, symptom_description)''' R21 = R20 - {symptom_name, symptom_description} Lossless join: Shared column `symptom_id`. `symptom_id -> Symptoms` holds (F21). Dependency preservation: F21 preserved entirely in `Symptoms`. '''`Referrals`(referral_id, referral_reason, referral_date, record_id, ref_from_doctor_id, ref_to_doctor_id)''' R22 = R21 - {referral_reason, referral_date, ref_from_doctor_id, ref_to_doctor_id} Lossless join: Shared column `referral_id`. `referral_id -> Referrals` holds (F22). Dependency preservation: F22 preserved entirely in `Referrals`. '''`MedicalReports`(report_id, report_description, report_date, record_id, report_doctor_id)''' R23 = R22 - {report_description, report_date, report_doctor_id} Lossless join: Shared column `report_id`. `report_id -> MedicalReports` holds (F23). Dependency preservation: F23 preserved entirely in `MedicalReports`. '''`Billing`(bill_id, total_cost, payment_status, payment_date, record_id, billing_admin_id, billing_created_at)''' R24 = R23 - {total_cost, payment_status, payment_date, billing_admin_id, billing_created_at} Lossless join: Shared column `bill_id`. `bill_id -> Billing` holds (F24). Dependency preservation: F24 preserved entirely in `Billing`. '''`MedicalRecordSymptoms`(record_id, symptom_id, record_symptom_severity)''' R25 = R24 - {record_symptom_severity} Lossless join: Shared column {`record_id`, `symptom_id`}. `{record_id,symptom_id} -> MedicalRecordSymptoms` holds (F25) - the same principle, just with a composite determinant. Dependency preservation: F25 preserved entirely; the relation already depends on the whole composite key, so it is not split further. '''`MedicalRecordAllergies`(record_id, allergy_id, record_allergy_reaction, record_allergy_severity)''' R26 = R25 - {record_allergy_reaction, record_allergy_severity} Lossless join: Shared column {`record_id`, `allergy_id`}. `{record_id,allergy_id} -> MedicalRecordAllergies` holds (F26). Dependency preservation: F26 preserved entirely; already depends on the whole composite key. '''`PrescriptionRecords`(prescription_id, record_id, dosage, frequency, duration, prescription_notes)''' R27 = R26 - {dosage, frequency, duration, prescription_notes, prescription_id, record_id} Lossless join: Shared column {`prescription_id`, `record_id`}. `{prescription_id,record_id} -> PrescriptionRecords` holds (F27). Dependency preservation: F27 preserved entirely; already depends on the whole composite key. ---- '''Final result:''' after step 27, R27 = { doctor_id, admin_id, technician_id, appointment_id, diagnosis_id, proc_result_id, performed_id, restriction_id, lab_result_id, performed_test_id, allergy_id, symptom_id, referral_id, report_id, bill_id } - exactly the 15 PK attributes, nothing more. This confirms the decomposition is complete: everything partially dependent has been removed, leaving only the composite key that "links" the rest through foreign keys in all 27 new relations. Since each of the 27 splits is lossless on its own, the whole chain of decompositions is lossless too (joining all the pieces back together, one at a time, reconstructs R exactly). Likewise, every FD from F1 through F27 is fully contained within a single relation, none split across tables, which means the decomposition is also dependency preserving. ---- == 3NF check == 2NF removed partial dependencies. We now check whether any transitive dependency remains — i.e. a non-key attribute reachable only through another non-key attribute. Because the 2NF grouping step split on every determinant found in F1–F27, no relation ended up keeping a borrowed descriptive attribute alongside the foreign key that points to where it actually lives — so no transitive dependency survived into the 2NF output. A few examples confirm this: * `Doctors` keeps level_id, specialization_id, department_id, and user_id as foreign keys, but level_name, specialization_name, department_name, and the rest of the login account's own fields stay in `DoctorLevels`, `Specializations`, `Departments`, and `Users` respectively — they are never duplicated back into `Doctors`. * `ProcedureResults` keeps only the foreign key procedure_id, the procedure's own procedure_type, procedure_cost, etc. stay in `Procedures`. * `LabResults` keeps only the foreign key test_id. test_name, test_description and test_cost stay in `LabTests`. * `Referrals`, `MedicalReports`, `Billing`, `Appointments`, `PerformedProcedures`, `PerformedLabTests`, `PrescriptionRestrictions` each carry only foreign keys back to record_id / doctor_id / patient_id / admin_id / technician_id / procedure_id / test_id / prescription_id and never the descriptive attributes belonging to the entity on the other end of that key. `MedicalRecordSymptoms`, `MedicalRecordAllergies`, `PrescriptionRecords` have composite keys with no non-key attribute that could point through another non-key attribute, so they aren't affected either way. In conclusion, every non-key attribute in every relation depends only and fully on that relation's own key. The schema is in 3NF. This is a by-product of how the 2NF split was done, rather than something that required a separate fix — so no further decomposition is needed at this stage. == BCNF check == BCNF requires every non-trivial determinant to be a superkey. This is stronger than 3NF, which still allows a non-superkey determinant as long as the dependent attribute is itself part of some candidate key. Below is a check of each 3NF relation. The primary key is bolded. ||= Relation =||= Key =||= BCNF? =|| || `DoctorLevels` || '''level_id''', alt. key `level_name` || Yes || || `Specializations` || '''specialization_id''', alt. key `specialization_name` || Yes || || `Departments` || '''department_id''', alt. key `department_name` || Yes || || `Doctors` || '''doctor_id''', alt. keys `d_email`, `user_id` || Yes || || `Patients` || '''patient_id''', alt. keys `embg`, `user_id` || Yes || || `Admin` || '''admin_id''', alt. keys `admin_username`, `admin_email`, `user_id` || Yes || || `LabTechnician` || '''technician_id''', alt. keys `tech_username`, `tech_email`, `user_id` || Yes || || `Users` || '''user_id''', alt. key `users_username` || Yes || || `Appointments` || '''appointment_id''' || Yes || || `Diagnoses` || '''diagnosis_id''' || Yes || || `Procedures` || '''procedure_id''' || Yes || || `ProcedureResults` || '''proc_result_id''' || Yes || || `PerformedProcedures` || '''performed_id''' || Yes || || `Prescriptions` || '''prescription_id''' || Yes || || `PrescriptionRestrictions` || '''restriction_id''' || Yes || || `LabTests` || '''test_id''' || Yes || || `LabResults` || '''lab_result_id''' || Yes || || `PerformedLabTests` || '''performed_test_id''' || Yes || || `MedicalRecords` || '''record_id''' || Yes || || `Allergies` || '''allergy_id''', alt. key `allergy_name` || Yes || || `Symptoms` || '''symptom_id''', alt. key `symptom_name` || Yes || || `Referrals` || '''referral_id''' || Yes || || `MedicalReports` || '''report_id''' || Yes || || `Billing` || '''bill_id''' || Yes || || `MedicalRecordSymptoms` || '''{record_id, symptom_id}''' || Yes || || `MedicalRecordAllergies` || '''{record_id, allergy_id}''' || Yes || || `PrescriptionRecords` || '''{prescription_id, record_id}''' || Yes || `p_email` is left off as an alternate key because it carries a `UNIQUE` constraint but is nullable, so it doesn't function as a true candidate key under the relational model. `user_id` in `Doctors`, `Patients`, `Admin`, and `LabTechnician` is a genuine alternate key: each carries its own `UNIQUE` constraint and is required (`NOT NULL`). No relation has a non-key attribute determining part of a candidate key without itself being a superkey, so the schema **satisfies BCNF**. ---- == 4NF check == BCNF only removes anomalies caused by functional dependencies. This domain still has the twelve pure many-to-many pairs listed at the end of the FD section, and none of them was involved in any FD above, so BCNF does not evaluate them at all. Three entities in this schema each sit at the center of more than one independent many-to-many relationship at once. That's exactly the situation that produces a genuine multivalued dependency. If you tried to store two of those relationships in the same table, you'd be forced to repeat every combination of the two, even though the two facts have nothing to do with each other. * A '''medical record''' can be linked to several diagnoses, several procedures, and several lab results, and each of those three lists grows and shrinks on its own. Adding another diagnosis to a record says nothing about how many procedures or lab results are attached to that same record. (A record's link to its doctors is not modeled as a separate many-to-many relationship in this schema — a doctor is reached only indirectly, through the diagnoses, procedures and reports already tied to that record — so there is no fourth competing group here.) * A '''procedure''' can be linked to several specializations qualified to perform it, several departments that perform it, and several bills it appears on. * A '''patient''' can be linked to several allergies and several symptoms, tracked completely separately from one another. This gives eight multivalued dependencies: {{{ record_id ->> diagnosis_id record_id ->> procedure_id record_id ->> lab_result_id procedure_id ->> specialization_id procedure_id ->> department_id procedure_id ->> bill_id patient_id ->> allergy_id patient_id ->> symptom_id }}} The remaining four pairs, `{diagnosis_id, symptom_id}`, `{test_id, bill_id}`, `{report_id, lab_result_id}`, and `{allergy_id, restriction_id}`, are different. Each one is the only many-to-many link at its anchor, so there's no competing relationship to collide with. They still need their own table, since a plain many-to-many link can never be expressed as a functional dependency, but they aren't 4NF violations the way the three groups above are. None of the MVDs above is trivial. In each case, the right side isn't already part of the left side, and the left side isn't a key of any table that currently holds both sides together. So '''4NF is violated''' until all twelve pairs — the eight grouped above plus these four standalone ones — each gets their own table. ---- == MVD check == Nothing is actually being split here. These twelve pairs were already separate, attribute-only tables back in the FD section, since none of them ever had an extra column that would tie them to something else during 2NF. This section just confirms that keeping them separate was correct. If any two had been merged, that would create redundant, repeated rows. Keeping each pair on its own avoids that. === Lossless join & dependency preservation per relation === '''`DiagnosisMedicalRecords`(diagnosis_id, record_id)''' MVD: `record_id ->> diagnosis_id` Lossless join: The general MVD theorem states that for a relation containing `X`, `Y`, and other attributes `Z` where `X ->> Y` holds, splitting into `(X, Y)` and `(X, Z)` reconstructs the original without loss. Here `X = record_id`, `Y = diagnosis_id`, so `(record_id, diagnosis_id)` and the rest of `MedicalRecords`'s attributes split losslessly. Dependency preservation: This relation carries no non-trivial FD of its own. Both attributes are needed together simply to identify a membership row. '''`MedicalRecordProcedures`(record_id, procedure_id)''' MVD: `record_id ->> procedure_id` Lossless join: `X = record_id`, `Y = procedure_id`. `record_id ->> procedure_id` holds, so `(record_id, procedure_id)` splits losslessly from the rest. Dependency preservation: This relation carries no non-trivial FD of its own. Both attributes are needed together simply to identify a membership row. '''`MedicalRecordLabResults`(record_id, lab_result_id)''' MVD: `record_id ->> lab_result_id` Lossless join: `X = record_id`, `Y = lab_result_id`. `record_id ->> lab_result_id` holds, so `(record_id, lab_result_id)` splits losslessly from the rest. Dependency preservation: This relation carries no non-trivial FD of its own. Both attributes are needed together simply to identify a membership row. '''`SpecializationProcedures`(specialization_id, procedure_id)''' MVD: `procedure_id ->> specialization_id` Lossless join: `X = procedure_id`, `Y = specialization_id`. `procedure_id ->> specialization_id` holds, so `(procedure_id, specialization_id)` splits losslessly from the rest. Dependency preservation: This relation carries no non-trivial FD of its own. Both attributes are needed together simply to identify a membership row. '''`DepartmentProcedures`(department_id, procedure_id)''' MVD: `procedure_id ->> department_id` Lossless join: `X = procedure_id`, `Y = department_id`. `procedure_id ->> department_id` holds, so `(procedure_id, department_id)` splits losslessly from the rest. Dependency preservation: This relation carries no non-trivial FD of its own. Both attributes are needed together simply to identify a membership row. '''`BillingProcedures`(bill_id, procedure_id)''' MVD: `procedure_id ->> bill_id` Lossless join: `X = procedure_id`, `Y = bill_id`. `procedure_id ->> bill_id` holds, so `(procedure_id, bill_id)` splits losslessly from the rest. Dependency preservation: This relation carries no non-trivial FD of its own. Both attributes are needed together simply to identify a membership row. '''`PatientAllergies`(patient_id, allergy_id)''' MVD: `patient_id ->> allergy_id` Lossless join: `X = patient_id`, `Y = allergy_id`. `patient_id ->> allergy_id` holds, so `(patient_id, allergy_id)` splits losslessly from the rest. Dependency preservation: This relation carries no non-trivial FD of its own. Both attributes are needed together simply to identify a membership row. '''`PatientSymptoms`(patient_id, symptom_id)''' MVD: `patient_id ->> symptom_id` Lossless join: `X = patient_id`, `Y = symptom_id`. `patient_id ->> symptom_id` holds, so `(patient_id, symptom_id)` splits losslessly from the rest. Dependency preservation: This relation carries no non-trivial FD of its own. Both attributes are needed together simply to identify a membership row. ---- The remaining four pairs are standalone many-to-many links rather than part of a competing MVD group, so they were never at risk of collision, but they still need their own table since a plain many-to-many relationship can't be expressed as a functional dependency: '''`DiagnosisSymptoms`(diagnosis_id, symptom_id)''' Lossless join: `{diagnosis_id, symptom_id}` is the only many-to-many link at either anchor (diagnosis no longer links to procedures directly), so it was never combined with a competing multivalued group in any table produced. The pairing is kept in its own relation, which trivially reconstructs via join on `{diagnosis_id, symptom_id}`. Dependency preservation: This relation carries no non-trivial FD of its own. Both attributes are needed together simply to identify a membership row. '''`BillingLabTests`(bill_id, test_id)''' Lossless join: `{bill_id, test_id}` is the only many-to-many link at either anchor, so this pair was never combined with a competing multivalued group in any table produced. The pairing is kept in its own relation, which trivially reconstructs via join on `{bill_id, test_id}`. Dependency preservation: This relation carries no non-trivial FD of its own. Both attributes are needed together simply to identify a membership row. '''`MedicalReportLabResults`(report_id, lab_result_id)''' Lossless join: `{report_id, lab_result_id}` is the only many-to-many link at either anchor, kept in its own relation, trivially reconstructed via join on `{report_id, lab_result_id}`. Dependency preservation: This relation carries no non-trivial FD of its own. Both attributes are needed together simply to identify a membership row. '''`AllergyPrescriptionRestrictions`(allergy_id, restriction_id)''' Lossless join: `{allergy_id, restriction_id}` is the only many-to-many link at either anchor, kept in its own relation, trivially reconstructed via join on `{allergy_id, restriction_id}`. Dependency preservation: This relation carries no non-trivial FD of its own. Both attributes are needed together simply to identify a membership row. ---- The schema satisfies '''4NF'''. * {{{DoctorLevels(level_id, level_name)}}} * {{{Specializations(specialization_id, specialization_name)}}} * {{{Departments(department_id, department_name)}}} * {{{Doctors(doctor_id, d_first_name, d_last_name, d_email, level_id, specialization_id, department_id, user_id)}}} * {{{Patients(patient_id, p_first_name, p_last_name, p_email, date_of_birth, blood_type, gender, phone_number, embg, user_id)}}} * {{{Admin(admin_id, admin_username, admin_name, admin_lastname, admin_email, user_id)}}} * {{{LabTechnician(technician_id, tech_username, tech_name, tech_lastname, tech_email, user_id)}}} * {{{Users(user_id, users_username, users_password, users_role, users_first_name, users_last_name, is_active)}}} * {{{Appointments(appointment_id, appt_patient_id, appt_doctor_id, appointment_date, appointment_time, appointment_status)}}} * {{{Diagnoses(diagnosis_id, diagnosis_name, diagnosis_description, diag_patient_id, diag_doctor_id)}}} * {{{Procedures(procedure_id, procedure_type, procedure_sched_date, procedure_description, procedure_cost, proc_doctor_id)}}} * {{{ProcedureResults(proc_result_id, proc_result_description, proc_result_date, procedure_id)}}} * {{{PerformedProcedures(performed_id, perf_proc_id, perf_doctor_id, perf_patient_id, perf_diagnosis_id, perf_date, perf_notes)}}} * {{{LabTests(test_id, test_name, test_description, test_cost)}}} * {{{LabResults(lab_result_id, lab_result_value, lab_result_date, test_id)}}} * {{{PerformedLabTests(performed_test_id, pt_test_id, pt_patient_id, pt_doctor_id, pt_technician_id, pt_test_date, pt_notes, pt_created_at)}}} * {{{MedicalRecords(record_id, patient_id)}}} * {{{Referrals(referral_id, referral_reason, referral_date, record_id, ref_from_doctor_id, ref_to_doctor_id)}}} * {{{MedicalReports(report_id, report_description, report_date, record_id, report_doctor_id)}}} * {{{Billing(bill_id, total_cost, payment_status, payment_date, record_id, billing_admin_id, billing_created_at)}}} * {{{Prescriptions(prescription_id, medication_name)}}} * {{{PrescriptionRestrictions(restriction_id, restriction_description, prescription_id)}}} * {{{Allergies(allergy_id, allergy_name, allergy_severity)}}} * {{{Symptoms(symptom_id, symptom_name, symptom_description)}}} * {{{MedicalRecordSymptoms(record_id, symptom_id, record_symptom_severity)}}} * {{{MedicalRecordAllergies(record_id, allergy_id, record_allergy_reaction, record_allergy_severity)}}} * {{{PrescriptionRecords(prescription_id, record_id, dosage, frequency, duration, prescription_notes)}}} * {{{DiagnosisMedicalRecords(diagnosis_id, record_id)}}} * {{{MedicalRecordProcedures(record_id, procedure_id)}}} * {{{MedicalRecordLabResults(record_id, lab_result_id)}}} * {{{PatientAllergies(patient_id, allergy_id)}}} * {{{PatientSymptoms(patient_id, symptom_id)}}} * {{{DiagnosisSymptoms(diagnosis_id, symptom_id)}}} * {{{SpecializationProcedures(specialization_id, procedure_id)}}} * {{{DepartmentProcedures(department_id, procedure_id)}}} * {{{BillingProcedures(bill_id, procedure_id)}}} * {{{BillingLabTests(bill_id, test_id)}}} * {{{MedicalReportLabResults(report_id, lab_result_id)}}} * {{{AllergyPrescriptionRestrictions(allergy_id, restriction_id)}}} ---- == Conclusion == Decomposing the de-normalized relation from scratch, following only the formal rules through 1NF, 2NF, 3NF, BCNF, and 4NF, produced the same 39 relations already present in the Phase 2 design the same keys, same columns, same many-to-many tables. The normalization process confirms the same structural design obtained from the ER model in Phase 2.