Definite descriptions

Using the following symbolization key:

• domain:

  people

• $K(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ knows the combination to the safe

• $S(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is a spy

• $V(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is a vegetarian

• $T(x,y)$:

  $\underline{\hskip 15.00002pt}_{x}$ trusts $\underline{\hskip 15.00002pt}_{y}$

• $h$:

  Hofthor

• $i$:

  Ingmar

symbolize the following sentences in FOL:

1. Hofthor trusts a vegetarian.

2. Everyone who trusts Ingmar trusts a vegetarian.

3. Everyone who trusts Ingmar trusts someone who trusts a vegetarian.

4. Only Ingmar knows the combination to the s…

Using the following symbolization key:

• domain:

  cards in a standard deck

• $B(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is black

• $C(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is a club

• $D(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is a deuce

• $J(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is a jack

• $M(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is a man with an axe

• $O(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is one-eyed

• $W(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is wild

symbolize each sentence in FOL:

1. All clubs are black cards.

2. There are no wild cards.

3. There are at least two clubs.

4. There is more than one one-eyed jack.

5. There are at most two one-eyed jacks.

6. There are…

Using the following symbolization key:

• domain:

  animals in the world

• $B(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is in Farmer Brown’s field

• $H(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is a horse

• $P(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ is a Pegasus

• $W(x)$:

  $\underline{\hskip 15.00002pt}_{x}$ has wings

symbolize the following sentences in FOL:

1. There are at least three horses in the world.

2. There are at least three animals in the world.

3. There is more than one horse in Farmer Brown’s field.

4. There are three horses in Farmer Brown’s field.

5. The…

In this chapter, we symbolized ‘Nick is the traitor’ by ‘$\exists x(T(x)\wedge\forall y(T(y)\rightarrow x=y)\wedge x=n)$’. Explain why these would be equally good symbolisations:

• $T(n)\wedge\forall y(T(y)\rightarrow n=y)$

• $\forall y(T(y)\leftrightarrow y=n)$