LetD = Dennis, E = Ernie, F = Fred
Happy Not Happy
Thehappiness of Fred is independent of Dennis’ happiness however, itis dependent on Ernie’s happiness. When Fred is happy, it does notmatter whether Dennis is happy or not. However, his happiness isdependent on Ernie’s happiness.
ThereforeD ≠ F, but D = E.
LetP = Paul, Q = Quentin, R = Rick
Quentin’shunger is dependent on Paul’s hunger therefore, P = Q if Paul ishungry then Quentin is hungry
IfPaul is hungry then Rick is hungry P = R
Then,P = Q = R
Thethree have a relationship when it comes to hunger
LetKnights = K and Knaves = N
Truthis associated with the Knights while lies are associated with theKnaves Truth = K AND Lie = N
Fromthe first claim, Dave claims that only a knave would indicate thatBart is a knave. Going by this claim, there are two knaves Dave andBart. This is because Dave is one of the persons that claim Bart tobe a knave. Thus, Dave is a knave. Because he claims that Bart is aknave, then it can be held that Bart is a knave.
Therefore,N = Dave & Bart.
Alternatively,in case one is not a knave, then he or she is a knight. Going by thisclaim, then there are six knights these include Zeke, Sally, Zoey,Bozo, Bob, and Alice. Therefore, this can be symbolized as
K= Zeke, Sally, Zoey, Bozo, Bob, and Alice.
Bochman,Alexander. ALogical Theory of Nonmonotonic Inference and Belief Change.Berlin, Heidelberg: Springer Berlin Heidelberg, 2001.