Dec1999 CO230 : Cognitive Science (Question 3)

(a)

With the aid of an example,define the term “predicate ”.

[3]

(b)

Make use of the following predicates and rules for this part of the question:

Employees ={jo,tom}
Department={sales,purchases}

manager(X,Y)X is the manager of department Y
works in(X,Y)X works in department Y

(i)Restate the predicate expression ~Y: Employees works_in(Y,sales) as an English sentence. [1 mark ]

(ii)Restate the predicate expression ~Y:Employees ~ works_in(Y,sales)as an English sentence which contains the phrase “At least one ”.[1 mark ]

(iii)Restate the predicate expression ~Y:Department ~ works_in(tom,Y) as an English sentence which contains the word “all ”.[1 mark ]

(iv)Restate the predicate expression X:Employees Y:Department
works in(X,Y)as an English sentence which contains the word “all ”and the phrase “at least one ”.[2 marks]

[5]

(c)

Make use of the following predicates and rules for this part of the question:

BallGame ={basketball,hockey,soccer,football}
Team ={myteam,localteam,regionalteam}

plays(X,Y)team X plays game Y
good(X,Y)team X is good at game Y
lose(X,Y)team X loses game Y

Express the following natural language sentences as quantified predicate expressions:

(i)There is a BallGame that my team plays that it is good at.[1 mark ]

(ii)My team will not lose a ball game that it is good at.[1 mark ]

(iii)My team plays all BallGames but it is good at only some of them.
[2 marks ]

(iv)If we introduce another predicate win(X,Y)(team X wins game Y),state if the sentences “My team will not lose the BallGames it is good at ”and “My team will win the BallGames it is good at ”are logical equivalents.Explain your answer, stating any reasonable assumptions that are made.(Note:no marks will be awarded if justification for the answer is not given)[3 marks ]

[7]