Suppose this is one of the rules : If there is a sentence Φ, and another sentence "if Φ then Ψ", then add sentence Ψ to the belief box.

Imagine a belief box with various sentences that express our beliefs, and there is a mechanism that applies rules to those sentences.

Suppose this is one of the rules : If there is a sentence Φ, and another sentence "if Φ then Ψ", then write down Ψ in the belief box.

1. Suppose the belief box contains "if the interest rate is going to rise, the stock market will fall".
2. Suppose a new sentence is added to the belief box, "the interest rate is going to rise".
3. The rule will then add a new sentence to the box "the stock market will fall".

Rule : If there is a sentence Φ, and another sentence (Φ→Ψ), then write down Ψ in the belief box.

Example,

Rule : If there is a sentence Φ, and another sentence (Φ→Ψ)

Rule #1: If a sentence has a small letter, replace that letter with ∃ φ

Suppose the belief box contains various sentences, and there are rules that operate on those sentences.

Rule #1: If a sentence has a small letter, replace that letter with &#exist;