Seminar VII

The exercises for this seminar are concerned with the predicate calculus.

I. Provide appropriate translations into the predicate calculus for the following sentences:

1. Fido is barking
2. Fido's owner is shouting
3. A dog is barking
4. A dog is chasing a cat
5. A dog is chasing its tail
6. Every cat is sleeping
7. Every dog is chasing a cat

II. Provide approprate English paraphrases for the sentences of predicate logic given below, assuming the following (informal) interpretations for individual constants and predicate symbols.

$$\begin{eqnarray*} t & = & \mbox{\lq\lq Tweety''} \\ f & = & \mbox{\lq\lq Felix''} \\ B &... ...''} \\ F & = & \mbox{\lq\lq can fly''} \\ S & = & \mbox{\lq\lq stalks''} \end{eqnarray*}$$

1. $B(t) \rightarrow F(t)$
2. $C(t) \vee C(f)$
3. $\exists x. (C(x) \wedge S(x,t))$
4. $\forall x . (B(x) \rightarrow F(x))$
5. $\exists x. (B(x) \wedge \neg F(x))$