TU Wien:Einführung in wissensbasierte Systeme VU (Egly)/Übungen WS12/Blatt 2 - Beispiel 4

Consider the following statements:

1. Every politician is bribed by someone.
2. There is someone who bribes all politicians.

Represent 1. and 2. by first-order formulas $\phi$ and $\psi$, respectively, using the unary predicate $p(x)$ expressing that an object is a politician and the binary predicate $bribes(x,y)$ expressing that $x$ bribes $y$.

• a) Show using TC1 that $\psi \models \phi$ holds.
• b) Show that $\phi \models \psi$ does not hold.

Lösungsvorschlag von Thomas

Zum Verständnis: http://en.wikipedia.org/wiki/First-order_logic#Loving_relation

1. $\phi =\forall x\exists y[p(x)\land bribes(y,x)]$
2. $\psi =\exists y\forall x[p(x)\land bribes(y,x)]$

Die Lösung ist Analog zu Blatt 1 Beispiel 5.