CMT117 Knowledge Representation

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Assessment Proforma 2024-25

Module Code
CMT117
Module Title
Knowledge Representation
Module Leader
V´ıctor Gutierrez-Basulto ´
Module Moderator
Steven Schockaert
Assessment Title
Problem Sheet 2
Assessment Number
2 of 2
Assessment Weighting
50%
Assessment Limits
Hand-out: 09th of January 2025
Hand-in: 16th of January 2025, 09:30AM
Limits are per task as set in the instructions

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 hand out 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:

Description
Type
Name
Coversheet
Compulsory
One PDF (.pdf) file
[student number] Coversheet.pdf
Answer to all question parts
Compulsory
One PDF (.pdf) file
[studentnumber].pdf

If you are unable to submit your work due to technical difficulties, please submit your work via e-mail to [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 inanother. [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 providing 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 whose TBox 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]

Assessment Criteria
Credit will be awarded against the following criteria.
• [Correctness] Do the answers correctly address the requirements of each task?
• [Clarity] Are explanations and summaries easily understandable?
• [Understanding of concepts] Do the answers show an understanding of basic concepts?

Indication of level of attainment:

Fail
0 − 39%
At this level, there is a fundamental misunderstanding or absence of knowledge of module material. Failure in correctly and consistently applying theorems and definitions, and inappropriate or no use of examples is observed. The student makes many errors and demonstrates minimal or flawed usage of KR formalisms. Minimum requirements of most or all questions are not met.
Marginal Fail
40 − 49%
Marginal fails signify a poor understanding of key concepts and incorrect or inconsistent application of theorems and definitions. Justifications are often missing or lack appropriate use of examples. Errors are common, and KR formalisms are used incorrectly or inappropriately. Minimum question requirements can be unmet frequently.
Pass
50 − 58%
Students at this level demonstrate a basic understanding of module concepts and can apply theorems and definitions in a mostly correct manner. Justifications may lack depth or use of examples where appropriate. Errors could surface regularly but are minor, and there might be misguided usage of KR formalisms. The minimum requirements of each question are mostly met..
Merit
60 − 69%
Merit level students aptly apply theorems and definitions, though there may be some inaccuracies. A decent understanding of key concepts is shown. Examples might not always be utilized effectively in justifications. There could also be some inaccuracies, but they do not significantly impair the overall quality. Usage of KR formalisms is overall good but can show some incorrect choices. Such students meet the minimum requirements of most questions.
Distinction
70 − 79%
Students at this level apply theorems and definitions from the module notes effectively and accurately, with only minor inconsistencies. Good under standing of main concepts is demonstrated. Most answers are well justified, and appropriate use of examples is displayed where necessary. There may be a minor error or two, but the overall quality is high. Usage of KR formalisms is competent and thoughtful most of the time. A distinction level student provides convincing justifications for most answers and meets all minimum question requirements.
High Distinction
80+
At this level, students consistently and accurately apply theorems and definitions from the module notes. There is full understanding of concepts, and answers are justified with detailed examples where appropriate. The assessment is essentially without errors. Usage of KR formalisms to model situations is exemplary. All justifications are clear, well-argued, and convincing. The student not only meets but exceeds the minimum requirements of each question.

Help and Support

Questions about the assessment can be asked on the Discussion Board on the module’s Learning Central pages, or via email to the module team.

Feedback

Feedback on your coursework will address the above criteria. Feedback and marks will be returned via Learning Central. This will be supplemented with individual feedback on
request via e-mail.

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