COMP4418, 2013 { Assignment 1 Questions 1 & 2 Due: 11:59:59am Wednesday 28 August (Late penalty: 10 marks per day) Questions 3 & 4 Due: 11:59:59am Wednesday 4 September (Late penalty: 10 marks per day) Worth: 13 . 1. [10 Marks] (Propositional Inferences) Prove that the following inferences hold in propositional logic using the truth table method. (a) j= :p _ p (b) p j= q ! p (c) (p ^ q) ^ r j= p ^ (q ^ r) (d) p $ q j= (q $ r) ! (p $ r) (e) p $ q j= (p ^ q) _ (:p ^ :q) Prove that the following inferences hold in propositional logic using resolution. (f) :(p _ q) ` :p (g) p ` p _ q (h) p $ q ` :(p $ :q) (i) ` (:p ^ :q) ! (p $ q) (j) p ! q; :r ! :q ` p ! r 2. [20 Marks] (Logic Puzzle) Donald and Daisy Duck took their nephews aged 4, 5 and 6 on an outing. Each boy wore a tee-shirt with a dierent design on it and of a dierent colour. You are also given the following information: Huey is younger than the boy in the green tee-shirt The ve year-old wore the tee-shirt with the camel design Dewey’s tee-shirt was yellow Louie’s tee-shirt bore the girae design The panda design was not featured on the white tee-shirt (a) Represent these facts as sentences in rst-order logic. (b) Using your formalisation in part (2a), is it possible to conclude the age of each boy together with the colour and design of the tee-shirt they’re wearing? Show semantically how you determined your answer. (c) If your answer to part (2b) was `no’, indicate what further sentences you would need to add to your formalisation so that you could conclude the age of each boy together with the colour and design of the tee-shirt they’re wearing. 1 3. [20 Marks] (Knowledge Representation and Reasoning) Select a method for knowledge representation and reasoning that we have not covered in lectures and write 1{2 pages addressing the following: (a) briey describe how the method represents knowledge and include an example; (b) briey describe the inference procedure(s) adopted by the method for reasoning; and, (c)…