Assessment Proforma 2024-25
Key Information
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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 1
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Assessment Number
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1 out of 2
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Assessment Weighting
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50%
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Assessment Limits
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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 hand out date and time, (b) the hand in date and time, and (c) the feedback return date for all assessments.
Learning Outcomes
The learning outcomes for this assessment are as follows:
1. Formalize simple problems with a given knowledge representation approach
2. Discuss theoretical properties of different knowledge representation formalisms
3. Explain the basic principles underlying common knowledge representation approaches.
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 “Propositional Logic” and
“Nonmonotonic Reasoning and Belief Revision”, as described in detail in the attachment. The answers should be submitted as a single pdf file.
All files should be submitted via Learning Central. The submission page can be found under ‘Assessment & Feedback’ in the CMT117 module on Learning Central. Your submission should consist of two 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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Answers to all question parts
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Compulsory
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One PDF (.pdf) file
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[student number].pdf
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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.
If you are unable to submit your work due to technical difficulties, please submit your work via e-mail to comsc-submissions@cardiff.ac.ukand notify the module leader.
Staff reserve the right to invite students to a meeting to discuss coursework submissions
Assessment Description
The 2 questions are described in detail in the attachment.
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:
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High
Distinction
80%+
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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.
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Distinction
70-79%
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Students at this level apply theorems and definitions from the module notes effectively and accurately, with only minor inconsistencies. Good understanding 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.
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Merit
60-69%
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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.
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Pass
50-59%
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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.
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Marginal Fail
40-49%
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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.
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Fail
0-39%
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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.
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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 assessment criteria. Feedback and marks will be returned via Learning Central. This will be supplemented with oral feedback via individual meetings. Feedback from this assignment will be useful for Problem Sheet 2 of this module, as well as for CMT215 Automated Reasoning.
ANSWER ALL PARTS OF BOTH QUESTIONS. Each question is worth 25 marks and the number of marks available for each question part is indicated.
Question 1: Propositional Logic
(a) Write down exactly one propositional contradiction such that the only propositional variable appearing in the sentence isp, and the only log- ical connectives are → and ¬ . (Note your answer may use p and each of → and ¬ as many times as you like). [1]
(b) Let L = {p,q} and let v be the valuation such that v(p) = T and v(q) = F. For each of the following sentences in SL, state whether v satisfies that sentence.
(i) ¬p ∧ q [1]
(ii) (p ∨ q) ↔ (p ∨ ¬q) [1]
(c) Consider the following scenario.
Three boxes are presented to you. At least one of the boxes
contains gold. Each box has a clue written on it. These are:
Box 1: “If there is gold in this box, then there is gold in Box 2”
Box 2: “There is no gold in Box 1” Box 3: “There is no gold in Box 2”
Only one clue is false. The other two are true.
(i) Using an appropriate choice of propositional variables, write down a single sentence in propositional logic that represents all you know from the information contained in this scenario. You must explain how you arrive at your answer at each step. [6]
(ii) Is it a logical consequence of the information given in the scenario that there is gold in Box 3? Justify your answer. [5]
(d) Let L = {s,t}. Determine whether there exists a derivation of s → t from s → (t ∨ s) using the rules of Natural Deduction. Justify your answer. [5]
(e) Assume L = {p,q, r}. Consider the sentence A = ¬p → (q ∨ r).
(i) Establish whether there exists a Horn sentence in SL that is log- ically equivalent to A. Justify your answer, stating in full any statement or result from the lecture notes that you rely on in your justification. [4]
(ii) Use your answer to part (i) to briefly illustrate either exactly one advantage or exactly one disadvantage of using Horn logic rather than propositional logic as a logic for knowledge representation. [2]
Question 2: Nonmonotonic Reasoning & Belief Revision
(a) Consider the Monotonicity rule for inference relations |∼ :
A |∼ C A ∧ B |∼ C
Assume L = {p,q}. Show that Monotonicity fails for some rational con- sequence relation, and some specific choice of sentences A,B, C ∈ SL. State clearly any Theorem from the module’s lecture notes that you rely on in your answer. [5]
(b) Consider the following rule for inference relations |∼ , which we call CC:
X ∧ Y |∼ Z X |∼ Y (CC )
X |∼ Z
Show how CC can be derived from the set of KLM rules. You may freely use in your derivation any other rule that was already shown to follow from the KLM rules in the lecture notes (though this must be clearly stated). [4]
(c) Assume L = {p,q} and consider the following ranked model R = (V,⪯) with V = {TT,TF,FT, FF} and ⪯ given in tabular form. as follows:
(each valuation is represented as a pair denoting the truth-values of p,q respectively, and the further to the left a valuation appears in the above table, the more normal it is deemed to be.) State whether the following conditionals hold in R. Justify your answers in each case.
(i) q |∼R p [3]
(ii) p → q |∼R ¬q [3]
(d) Switching now to belief revision, let L = {p,q, r} and let ⪯ be the following plausibility order over the set of valuations:
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TTT FTT FTF
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TFF TFT
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FFT
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TTF FFF
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(each valuation is represented as triple denoting the truth-values of p,q,r respectively, and the further to the left a valuation appears in the above table, the more plausible it is deemed to be.)
(i) What is the belief set K(⪯) associated to this order? (Your answer should be of the form. Cn(A) for some suitable sentence A). [1]
Recall that ∗N denotes natural revision and ∗L denotes lexicographic revision.
(ii) Write down ⪯q(*)Λ(L)(r→p) in tabular form. and give the belief set
K(⪯q(*)Λ(L)(r→p)) associated to this new order (again in the form. Cn(A)
for some suitable sentence A). [4]
(iii) Give some sentence B such that ¬q ∈ K((⪯B(*L))q(*)
first revise ⪯ by B using lexicographic revision, and then revise the result by q ↔ r using natural revision then we end up believing ¬q. Justify your answer. [5]