Mock Exam 1 — Practice Test
Format: 6 questions, 20 marks, 60 min (5 reading + 55 answering) Rules: Double-sided handwritten A4 page only. No calculator. Tip: Do this under timed conditions. Check answers AFTER.
Question 1 [5 marks] — Symbolic Logic
(a) Consider the following scenario: [3 marks]
A fire alarm activates if it detects smoke (S) or high temperature (T):
$(S \vee T) \rightarrow A$
Today, the alarm did NOT activate ($\neg A$).
Use propositional logic to deduce what must be true about S and T. Show your steps with a truth table.
(b) Consider the statement: [2 marks]
“Every student who studies hard passes the exam.”
Domain: all students. StudyHard(x) = x studies hard. Pass(x) = x passes.
(i) Write this in formal first-order logic. [1 mark]
(ii) Write the negation of this statement in FOL and explain what it means in English. [1 mark]
Question 2 [4 marks] — Logic Neural Networks
A medical triage system uses LNN. The rule is:
ShouldTest $\leftarrow$ HighFever $\otimes$ ContactWithPatient
(a) What does this rule mean in natural language? How does LNN’s treatment differ from classical Boolean logic? [2 marks]
(b) Given HighFever = 0.7, ContactWithPatient = 0.5:
Compute ShouldTest using the Łukasiewicz t-norm. Would the system recommend testing at threshold 0.3? At threshold 0.5? [2 marks]
Question 3 [2 marks] — Knowledge Graphs
A TransE model is trained on these facts with embeddings:
- Auckland → (0.2, 0.5, 0.3), NewZealand → (0.6, 0.8, 0.7)
- Australia → (0.7, 0.9, 0.8), Oceania → (0.9, 1.0, 1.1)
- located_in → (0.4, 0.3, 0.4)
The model correctly represents (Auckland, located_in, NewZealand).
Query: (Sydney, located_in, ?). Given that Sydney’s embedding can be inferred from (Sydney, located_in, Australia), which entity would TransE predict? Show your L1 distance calculations.
Question 4 [2 marks] — MYCIN / Expert Systems
(a) Explain the difference between forward chaining and backward chaining. Which does MYCIN use and why? [1 mark]
(b) A MYCIN rule states: “IF fever (CF = 0.8) AND rash (CF = 0.5), THEN measles (rule CF = 0.7).” Calculate the confidence factor for measles. [1 mark]
Question 5 [3 marks] — Decision Trees & Ensembles
A node in a decision tree has 6 positive and 4 negative examples.
(a) Calculate the entropy. (Given: $\log_2(0.6) \approx -0.737$, $\log_2(0.4) \approx -1.322$) [1 mark]
(b) Explain the difference between bagging and boosting — specifically, how each builds and combines models. [1 mark]
(c) In AdaBoost, a weak classifier has weighted error $\epsilon = 0.3$. Calculate $\alpha$. (Given: $\ln(7/3) \approx 0.847$) [1 mark]
Question 6 [4 marks] — Soft Computing
For each scenario, state whether it involves vagueness or uncertainty. Justify in one sentence.
- A weather app says “60% chance of rain tomorrow.”
- A review describes food as “reasonably good.”
- A doctor says the patient is “mildly obese.”
- An ML model predicts an image is a cat with 85% confidence.