Mock Exam 2 — Practice Test (Harder Variant)
Format: 6 questions, 20 marks, 60 min Focus: Tests topics NOT in the sample test (MYCIN CF, entropy, fuzzy logic computation) Rules: Double-sided handwritten A4 page only. No calculator.
Question 1 [5 marks] — Symbolic Logic + Inference
(a) Given the following knowledge base: [3 marks]
- $P \rightarrow Q$
- $Q \rightarrow R$
- $P$
Using Modus Ponens, derive all conclusions that follow. Show each step clearly, naming the inference rule used.
(b) Translate the following into first-order logic: [2 marks]
“There exists a city in New Zealand that has more than one million people.”
Predicates: City(x), InNZ(x), MillionPlus(x)
(i) Write in FOL. [1 mark]
(ii) Is the statement true in reality? Give a counterexample or confirming example. [1 mark]
Question 2 [4 marks] — LNN + Fuzzy Logic
(a) An LNN system uses the following operators. For each, compute the result with inputs $a = 0.6$ and $b = 0.8$: [2 marks]
| Operator | Formula | Result |
|---|---|---|
| Product AND | $a \times b$ | ? |
| Łukasiewicz AND | $\max(0, a+b-1)$ | ? |
| Gödel AND (min) | $\min(a, b)$ | ? |
| Standard NOT | $1 - a$ | ? |
(b) A fuzzy control system for an air conditioner has:
- $\mu_\text{hot}(\text{temperature}) = 0.8$
- $\mu_\text{humid}(\text{humidity}) = 0.6$
Rule: IF hot AND humid THEN fan_speed = high.
Using fuzzy AND = min, what is the firing strength of this rule? If a second rule says “IF hot THEN fan_speed = medium” with $\mu_\text{hot} = 0.8$, which rule fires more strongly? [2 marks]
Question 3 [2 marks] — MYCIN Confidence Factors
A MYCIN knowledge base contains two rules that both conclude the same diagnosis:
- Rule 1: IF symptom_A (CF=0.9) THEN disease_X (rule CF=0.6)
- Rule 2: IF symptom_B (CF=0.7) THEN disease_X (rule CF=0.8)
(a) Calculate the CF of disease_X from each rule separately. [1 mark]
(b) Combine the two CFs into a single confidence factor for disease_X using the combination formula: $CF_{combined} = CF_1 + CF_2 - CF_1 \times CF_2$ (for both positive). [1 mark]
Question 4 [2 marks] — Knowledge Representation
Compare Expert Systems, Ontologies, and Knowledge Graphs by filling in this table (give one key point per cell):
| Aspect | Expert System | Ontology | Knowledge Graph |
|---|---|---|---|
| Representation | ? | ? | ? |
| Main strength | ? | ? | ? |
Question 5 [3 marks] — Entropy & Information Gain
Consider a dataset for predicting whether to play tennis:
| Outlook | Play? |
|---|---|
| Sunny | No |
| Sunny | No |
| Sunny | Yes |
| Overcast | Yes |
| Overcast | Yes |
| Rain | Yes |
| Rain | No |
(a) Calculate the entropy of the target variable (Play?). There are 4 Yes and 3 No out of 7. (Given: $\log_2(4/7) \approx -0.807$, $\log_2(3/7) \approx -1.222$) [1 mark]
(b) Calculate the conditional entropy $H(\text{Play?} | \text{Outlook})$. [1 mark]
(c) Calculate the Information Gain of splitting on Outlook. [1 mark]
Question 6 [4 marks] — Bayesian Reasoning
A university uses a spam filter for student emails. Statistics show:
- 20% of emails are spam: $P(\text{spam}) = 0.2$
- The word “free” appears in 80% of spam: $P(\text{free}|\text{spam}) = 0.8$
- The word “free” appears in 10% of non-spam: $P(\text{free}|\text{not spam}) = 0.1$
(a) Calculate $P(\text{free})$, the overall probability of seeing “free” in an email. [1 mark]
(b) Using Bayes’ theorem, calculate $P(\text{spam}|\text{free})$. [1 mark]
(c) Explain why the result makes intuitive sense. [1 mark]
(d) Is this scenario an example of vagueness or uncertainty? Justify. [1 mark]