Mock Exam 3 — Practice Test (Comprehensive)

Format: 6 questions, 20 marks, 60 min Focus: Balanced mix of all topics; includes computation-heavy questions Rules: Double-sided handwritten A4 page only. No calculator.

Question 1 [5 marks] — Symbolic Logic

(a) Consider the following rules in a security system: [3 marks]

Rule 1: $(A \wedge B) \rightarrow C$ Rule 2: $C \rightarrow D$ Rule 3: $A$ Rule 4: $B$

Using Modus Ponens, derive all possible conclusions. Show each inference step and name the rule used.

(b) A database administrator says: “No unauthorised user can access the server.” [2 marks]

Predicates: Authorised(x), CanAccess(x), domain = all users.

(i) Write in FOL. [1 mark]

(ii) The negation of this statement would mean what? Write in FOL and in English. [1 mark]

Question 2 [4 marks] — LNN

An LNN-based recommendation system uses this rule:

Recommend $\leftarrow$ HighRating $\otimes$ RecentlyViewed

(a) Given:

• HighRating = 0.8, RecentlyViewed = 0.3

Compute Recommend using ALL THREE t-norms (product, Łukasiewicz, Gödel). Which t-norm gives the highest value? Which gives the lowest? [2 marks]

(b) The system also has a NOT operator. If HighRating = 0.8, what is $\neg$HighRating?

Now compute: $\neg\text{HighRating} \vee \text{RecentlyViewed}$ using Łukasiewicz OR.

Show that this equals the Łukasiewicz implication $\text{HighRating} \rightarrow \text{RecentlyViewed}$. [2 marks]

Question 3 [2 marks] — TransE Computation

Given the following TransE embeddings:

Query: (Einstein, born_in, ?)

Compute $h + r$ and find the closest entity using L1 distance. Show all calculations.

Question 4 [2 marks] — Fuzzy Logic

A fuzzy control system for a washing machine has:

• $\mu_\text{dirty}(\text{clothes}) = 0.7$
• $\mu_\text{large}(\text{load}) = 0.4$

Rules:

• Rule A: IF dirty AND large THEN wash_time = long
• Rule B: IF dirty THEN wash_time = medium

(a) Using fuzzy AND = min, calculate the firing strength of each rule. [1 mark]

(b) Compute the fuzzy implication dirty $\rightarrow$ large using BOTH the standard formula ($\max(1-A, B)$) and the Gödel formula. Which is more intuitive and why? [1 mark]

Question 5 [3 marks] — Ensembles & Bayesian

(a) In a Random Forest with 400 features, how many features would typically be considered at each split? Explain the formula and why this specific number is chosen. [1 mark]

(b) A Naïve Bayes classifier for medical diagnosis has:

• $P(\text{disease}) = 0.01$
• $P(\text{symptom}_1|\text{disease}) = 0.9$, $P(\text{symptom}_1|\text{no disease}) = 0.05$
• $P(\text{symptom}_2|\text{disease}) = 0.7$, $P(\text{symptom}_2|\text{no disease}) = 0.1$

A patient shows BOTH symptoms. Calculate $P(\text{disease}|\text{symptom}_1, \text{symptom}_2)$ up to proportionality. Which class (disease or no disease) has higher posterior? [2 marks]

Question 6 [4 marks] — Mixed Short Answer

(a) Name ONE limitation of TransE and explain how TransH addresses it. [1 mark]

(b) In the context of RAG (Retrieval-Augmented Generation), explain the three main steps of the pipeline. [1 mark]

(c) What is the “knowledge acquisition bottleneck” in expert systems? [1 mark]

(d) Explain why AdaBoost’s classifier weight $\alpha_t$ is larger when the error $\epsilon_t$ is smaller. What does this mean for the ensemble? [1 mark]