Reference no: EM132979921

Aims and Procedure

One aim of this assignment is to improve and test your understanding of propositional logic and first-order predicate logic, including their use in mechanised reasoning. A second aim is to develop your skills in analysis and formal reasoning about complex concepts, and to practise writing down formal arguments with clarity.

Challenge 1

As a blade runner, Rick Deckard's task is to identify replicants. These look exactly like humans, but they have in fact been manufactured in the labs of Tyrell Corporation. Some replicants are programmed to always speak the truth, while others are programmed to always lie. Unfortunately the same goes for the humans that Deckard deals with: some are always truthful, and the rest always lie. One day, Deckard interviewed two individuals, X and Y , who made these statements:

X: "Y is a truthful human"
Y : "X is a lying replicant"

Task 1A. Capture, as a single propositional formula, the information that was thereby available to Deckard. You will need to take into account who makes each statement. Use propositional
letters as follows:
P : X is truthful R: X is human
Q: Y is truthful S: Y is human

Task 1B. Deckard, a competent logician, realised that the two statements would not allow him to determine whether either was human or not. Determine which truth assignments to P , Q, R, S make your formula from Task 1A true.

Task 1C. Now, Deckard later found out, from a reliable source, whether Y was truthful or not, and based on that information, he knew exactly whether X was human and also whether Y was human. Given this information, determine, for each of X and Y , whether they are a human or a replicant.