## CS 188, Fall 2005, Introduction to Artificial Intelligence Assignment 3, due 10/16, total value 5% of grade plus 1% extra

To be done individually

This assignment is out of 120 pts. Score 100 and you get the full 5% credit towards your course grade. Score 120 and you get an extra bonus 1% towards your course grade!!! Answer the following questions from AIMA (second edition):

• 7.4 (10 pts). Proofs should be based on the definition of entailment, validity, and unsatisfiability in terms of models and on the semantics of the logical connectives.
• 7.5 (5 pts). This question asks for models defined on A, B, C, D.
• 7.8 b, f (5 pts)
• 7.12 (10 pts)
• 7.13 a (5 pts)
• 7.16 (5 pts)
• 8.1 (15 pts)
• 8.2 (5 pts)
• 8.3 (5 pts)
• 8.4 (5 pts)
• 8.6 a, c, e, g, i, j (10 pts)
• 8.9 (20 pts). Your axioms must, as far as possible, state general knowledge that it would be reasonable to provide to an agent, rather than "short-cut" knowledge that happens to answer this specific question. For example, don't write an axiom of the form "If X heard about Y's death then Y cannot hear about X's death"!! Obviously this is not something you knew *explicitly* before reading this question; it is something you inferred from general knowledge about time, events, hearing, life, death, etc. WHY do you believe it to be true? This illustrates a useful guideline. For each sentence S, ask WHY it's true. If you can answer this question, perhaps S doesn't belong in the KB; instead, consider the sentences from which S follows. If your answer is, "Well, S is just true, that's the way it is," or your answer involves recourse to detailed knowledge of cell biology or theoretical physics, then perhaps S is a candidate for the KB.
• (20 pts) Produce a formal proof for the consequence in 8.9, given your knowledge base. You may use any of the inference rules given in the book. You may find the proof doesn't go through; in which case, you may need to modify the KB in your previous answer.