TU Wien:Einführung in wissensbasierte Systeme VU (Egly)/Übungen WS12/Blatt 3 - Beispiel 4

You have the following information:

1. There is a party.
2. When there is a party, Paris is usually attending.
3. When there is a party, Britney is usually attending.
4. When there is a party and Paris is attending, then Britney does definitely not participate.

(a)

Formalise this situation in terms of a default theory. It should have an extension indicating that Paris attends, as well as an extension that states that Britney attends. Use $Party$ for “there is a party,” $Comes\_Paris$ for “Paris is attending the party,” and $Comes\_Britney$ for “Britney is attending the party.”

(b)

Replace information 4. from above by a formalisation of

(4’) If there is a party and Paris attends, then Britney usually does not attend.

How does the default theory change? Which extensions emerge after this replacement? Are all of them plausible?

(c)

Change your defaults in a way that only intuitive extensions emerge.
More precisely: the rule expressing information (4’), determining what Britney does when there is a party that Paris is attending, should have priority over the less specific rule expressing information 3), indicating what Britney is doing when there is a party. You are only allowed to change default justifications.

Lösungsvorschlag 3dm45t3r

a

$T=(W,\Delta )$

$W=\{Party,Party\land Comes\_Paris\rightarrow \lnot Comes\_Britney\}$

$\delta _{1}={\frac {Party:Comes\_Paris}{Comes\_Paris}}$

$\delta _{2}={\frac {Party:Comes\_Britney}{Comes\_Britney}}$

$E_{0}=Cn(W\cup \{Comes\_Paris\})$

$E_{1}=Cn(W\cup \{Comes\_Britney\})$

b

$T=(W,\Delta )$

$W=\{Party\}$

$\delta _{1}={\frac {Party:Comes\_Paris}{Comes\_Paris}}$

$\delta _{2}={\frac {Party:Comes\_Britney}{Comes\_Britney}}$

$\delta _{3}={\frac {Party\land Comes\_Paris:\lnot Comes\_Britney}{\lnot Comes\_Britney}}$

$E_{0}=Cn(W\cup \{Comes\_Paris,\lnot Comes\_Britney\})$

$E_{1}=Cn(W\cup \{Comes\_Paris,Comes\_Britney\})$

$E_{1}$ Scheint nicht plausibel da $\delta _{3}$ sagt, dass Britney gewöhnlich nicht die selbe Party besucht wie Paris.

c

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