R1Acade
Minimum attendance
A(s)A(s) ↔ attendance(s) ≥ 75
91% satisfies the attendance threshold.
91%
Expected ≥ 75%
Updated
∀x
Academic Logic Lab
Regula
AR-4.2 · 2026
Predicate calculus verifier · Deterministic & explainable
Academic decisions,proved step by step.
Turn university policy into formal predicates, test student facts against every regulation, and show exactly why a decision follows.
Inference pipeline
1Facts
→2Rules
→3Engine
→4Proof
Live verification workspace
Test the inference engine
Choose a reliable demo case or enter a custom student record.
Student facts · Domain S
Input record
Rule base · AR-4.2
Configurable policy constants
Adjust a threshold, then rerun verification to derive a new verdict.
✓
Verification complete
Registration verified
Every academic and administrative predicate evaluates to true.
CSE-2022-041B.Tech CSESemester 8Graduation: Ready
Derived proof trace
Universal rule instantiated for Meera Sharma.
∀x [RegistrationVerified(x) ↔ A(x) ∧ C(x) ∧ B(x) ∧ K(x) ∧ F(x) ∧ D(x)]
Substitute x := Meera
= T ∧ T ∧ T ∧ T ∧ T ∧ T
∴ RegistrationVerified(Meera) = TRUE
Predicate truth table
Rule-by-rule evidence
True
R2Acade
Academic standing
C(s)C(s) ↔ cgpa(s) ≥ 5.0
CGPA 8.4 satisfies the academic minimum.
8.4
Expected ≥ 5.0
R3Acade
Permitted backlogs
B(s)B(s) ↔ backlogs(s) ≤ 3
0 active backlogs is within the limit.
0
Expected ≤ 3
R4Acade
Credit progression
K(s)K(s) ↔ credits(s) ≥ requiredCredits(semester(s))
160 earned credits meet the Semester 8 requirement.
160 credits
Expected ≥ 112 for Sem 8
R5Admin
Financial clearance
F(s)F(s) ↔ feesCleared(s)
The financial-clearance fact is true.
Cleared
Expected Cleared
R6Admin
Conduct clearance
D(s)D(s) ↔ ¬ disciplinaryHold(s)
No disciplinary hold exists.
No hold
Expected No hold
R7Gradu
Graduation completion
G(s)G(s) ↔ Sem8(s) ∧ credits(s) ≥ 160 ∧ backlogs(s)=0 ∧ internship(s) ∧ capstone(s)
All graduation predicates are satisfied.
Complete
Expected All conditions true
Formal method
From policy prose to a proof.
The engine models each regulation as a Boolean predicate over the student domain. Conjunction derives the final verdict; any false predicate becomes a traceable counterexample.
Domain: S = all student records
∀s ∈ S [Eligible(s) ↔
A(s) ∧ C(s) ∧ B(s) ∧ K(s)
∧ F(s) ∧ D(s)]
Symbol legend
- ∀
- For every student in the domain
- ↔
- Logically equivalent to
- ∧
- AND — every condition must hold
- ¬
- NOT — negates the fact that follows
Inference discipline
- 1. Validate facts. Missing inputs stop inference.
- 2. Evaluate predicates. Each rule returns true or false.
- 3. Apply precedence. Academic failure outranks an administrative hold.
- 4. Emit proof. The verdict and evidence remain aligned.
Boundary tests
Expected deterministic outcomes
| Test case | Boundary | Expected | Reason |
|---|---|---|---|
| Exact attendance | 75% ≥ 75% | TRUE | Inclusive minimum |
| Backlog limit | 3 ≤ 3 | TRUE | Maximum is permitted |
| Disciplinary hold | ¬ TRUE | FALSE | Negated conduct predicate |