1 Task Details and Instructions Throughout this coursework, you should use
• the syntax, semantics, and grammar of proposition logic; and
• the layout and style of formal proofs presented during the classes. 1.1 A Truth Table and a Transformational Proof Show that p ⇔ q is equivalent to (p ∨ q) ⇒ (p ∧ q) by:
• drawing a truth table;
• writing a transformational proof. Every step of your proof must be fully annotated. Each step should apply just one law of logic. 1.2 Unicorn A document concerning a unicorn contains the following axioms.
• If the unicorn is mythical, then it is immortal, but if it is not mythical, then it is a mortal mammal.
• If the unicorn is either immortal or a mammal, then it is horned.
• The unicorn is magical if it is horned.
The document also contains the following conclusion.
• The unicorn is magical.
1. Identify the atomic propositions.
2. Formalise the argument in propositional logic.
3. Using your intuition and your own words, explain (in English) why the argument appears to be valid.
4. Provide a formal, deductive proof of the validity of the argument. Every step of your proof must be numbered and fully annotated.
1.3 Size of Unicorn’s Search Space
The validity of the conclusion could be shown by drawing a truth table but, due to its size, the table would be rather tedious to prepare manually. What is the minimum size of the truth table for the unicorn argument? Write an explanation which address the following questions.
• How many rows would the table have?
• What is the minimum number of columns in the table?
• What is the minimum number of cells in the table?
Your explanation should include explanations and justifications.
The module specification indicates that you should do 137 hours of independent study. Given that there were classes on propositional logic during four weeks of Semester 2, this suggests that you should have spent hours independently studying propositional logic.
If you attended the classes and studied propositional logic for a further 25 hours then then you should expect to spend up to 15 hours on this assessment.
3 Marking Scheme, Page Limits and Penalties
This is an individual coursework. You must not work in a team. The whole of your submission should be your own work. Please follow the regulations and policies. You are reminded that Artificial Intelligence and Data Mining Assessment Information/Brief penalties will be applied to late submissions, in accordance with the regulations and policies. You must submit a document which includes the following items.
1. Your full name, your student ID, your User name, the assessment title, the module title and the CRN. MAXIMUM SIDE OF A4
2. A truth table and a transformational proof for p ⇔ q ≡ (p ∨ q) ⇒ (p ∧ q).
3. A formalisation of the argument about the unicorn, an intuitive explanation of why it appears to be valid and a formal, deductive proof of its validity.
4. A explanation of the size of the search space.
5. Your reflections on your approach to this assessment and what you have gained from it.
Hence, your complete submission must not exceed four sides of A4.
• Each of the above items must appear in separate clearly labelled sections. The order of the sections must correspond to the order of the items shown above.
• Zero marks will be awarded for parts of your submission which exceed the page limits.
• Citations and references must conform to the APA 6th (Harvard) style.
• Your submission should be typed (rather than hand-written) in, at least, font size 12pt. Do not use colour for emphasis because your submission will be printed in black and white.
• You must submit a single document, in PDF format, via Blackboard. Zero (0) marks will be awarded for supplementary files or files in other formats. Do not submit a zip file.
• The name of your PDF file must include your family name, your student ID and your User name.
4 Recommended Reading, Equipment and Facilities No additional reading is required for this assessment, beyond the recommendations made at the end of lectures. The only equipment and facilities required are those needed to prepare the document described in Section 3.
5 Assessed Intended Learning Outcomes
This coursework assesses the student’s ability to:
• apply AI concepts, terminology and processes;
• use techniques for knowledge representation and searching; and
• formulate problems in logic and use logical inference to reach sound conclusions. 6 Module Aims
The aims of the module are:
• to introduce Artificial Intelligence (AI) and Data Mining (DM) techniques for problem solving;
• to provide experience with AI techniques and terminology for knowledge representation and searching;
• to develop an understanding of DM algorithms;
• to highlight the use of the practical techniques in real world applications.
You can expect to receive marks and feedback within 15 working days of the submission deadline. A completed marking grid will be made available via Grade Centre in Blackboard. An announcement will be made on Blackboard (and emailed to you) when feedback has been released. You will have an opportunity to receive verbal feedback.