Assessment Proforma 2024-25
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Module Code
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CMT117
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Module Title
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Knowledge Representation
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Assessment Title
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Problem Sheet 2
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Assessment Number
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2 of 2
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Assessment Weighting
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50%
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Assessment Limits
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Hand-out: 09th of January 2025
Hand-in: 16th of January 2025, 09:30AM
Limits are per task as set in the instructions
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The Assessment Calendar can be found under ‘Assessment & Feedback’ in the COMSC-ORG-SCHOOL organisation on Learning Central. This is the single point of truth for (a) the handout date and time, (b) the hand in date and time, and (c) the feedback return date for all assessments.
Learning Outcomes
• Critically evaluate knowledge representation alternatives to solve a given task
• Formalize simple problems with a given knowledge representation approach
• Discuss the theoretical properties of different knowledge representation formalisms
• Explain the basic principles underlying common knowledge representation approaches
• Choose an appropriate knowledge representation approach to address the needs of a given application setting
• Compare how knowledge representation approaches influence the success of a given task
• Explain the nature, strengths and limitations of knowledge representation technique to an audience of non-specialists
Submission Instructions
The coversheet can be found under ‘Assessment & Feedback’ in the COMSC-ORG-SCHOOL organisation on Learning Central.
You are required to answer 2 multi-part questions on “First-order Logic” and “Description Logics”, as described in detail in the attachment. The answers should be submitted as a single pdf file.
All submissions must be via Learning Central. Upload the following files:
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Description
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Type
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Name
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Coversheet
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Compulsory
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One PDF (.pdf) file
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[student
number] Coversheet.pdf
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Answer to all question parts
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Compulsory
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One PDF (.pdf) file
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[studentnumber].pdf
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If you are unable to submit your work due to technical difficulties, please submit your work via e-mailto [email protected] and notify the module leader.
Any deviation from the submission instructions above (including the number and types of files submitted) may result in a reduction in marks for the assessment.
All submissions will be compared to each other and checked against other work available on the Internet and elsewhere to identify cases of potential unfair practice.
Staff reserve the right to invite students to a meeting to discuss coursework submissions.
Assessment Description
Answer all parts of Questions 1 and 2 below. The first question is worth 25 marks and the second question is worth 15 marks. The number of marks available for each question part is indicated.
Question 1: First-Order Logic
1. Translate the sentences below from English into first-order logic. For each translated sentence provide an explanation of why your first-order sentence captures its En- glish counterpart.
Use the signature S consisting of the unary predicate symbol Region and the binary predicate symbols Disjoint, Included and Overlap and the constant symbols dorset, fife, scotland,england.
(a) Any two regions are either disjoint, overlapping, or one of them is included in another. [0.5 marks]
(b) Every region is included in itself. [0.5 mark]
(c) If two regions are disjoint, they are not overlapping. [0.5 marks]
(d) If two regions are overlapping, none of them is included in another. [0.5 marks]
(e) If one region is included in another, then they are not disjoint. [0.5 marks]
(f) If two regions are disjoint, then any region included in the first one is disjoint from the second one. [0.5 marks]
(g) Dorset and England are regions, Dorset is included in England. [0.5 marks]
(h) Fife and Scotland are regions, Fife is included in Scotland. [0.5 marks]
(i) Scotland and England are disjoint. [0.5 marks]
2. Do the sentences from Part 1 above logically entail that Dorset does not overlap with Scotland? Justify your answer by providing a proof using precise semantic argu- ments or by providing a counter-example. [4.5 marks]
3. Does ∃x.(A(x) ∨ B(x)) |= ∃x.A(x) ∨ ∃x.B(x) hold? Justify your answer by providing a proof using semantic arguments or by providing a counter-example. [4 marks]
4. Does ∀x.A(x) → ∀x.B(x) |= ∀x.(A(x) → B(x)) hold? Justify your answer by provid- ing a proof using semantic arguments or by providing a counter-example. [4 marks]
5. We want to prove that the following argument is true:
If all quakers are reformists and if there is a protestant that is also a quaker, then there must be a protestant who is also a reformist.
Define a set of FOL sentences X and a sentence G capturing this argument and show that X |= G using semantic arguments. Justify why X and G properly capture the argument.
Hint: You can define the FOL sentences in X and the sentence G using the unary predicate symbols: Quaker, Reformist and Protestant. [8 marks]
Question 2: Description Logics
1. Describe an application scenario in which there exist three advantages and one dis- advantage of using the description logic ALC , rather than propositional logic as a language for Knowledge Representation. You need to justify why they are advantages and disadvantages in the context of the proposed application scenario. This does not mean copy-paste from the lecture’s material. [4 marks]
2. Write down the following
(a) A satisfiable ALC-TBox T such that all the atomic concepts occurring in T are unsatisfiable w.r.t. T. Write down a model of T. [1 mark]
(b) A satisfiable ALC-knowledge base such that all its models contain at least two domain individuals. Justify your answer. [1 mark ]
(c) An unsatisfiable ALC-knowledge base whoseTBox is empty. Justify your answer. [1 mark]
(d) An unsatisfiable ALC-TBox. Justify your answer. [1 mark]
3. For a chosen application scenario define an EL KB (T, A) capturing relevant termino- logical and assertional knowledge. The EL TBox T must contain at least five GCIs and the ABox A at least five assertions. Explain what each GCI and assertion is modeling. Define the used vocabulary: concept, role and individual names. [7 marks]