Translating English sentences into Logic

Question 1

What must you always remember to do when translating english into logic?

Answer 1

Use a key

Never use pronouns ‘she’ in the key as this is ambiguous. Use names

A = Daphne is a dog

Question 2

Equivalent English words for operators

What are the synonyms for

And, Not, Or, If… then, If and only if, Conclusion.

Answer 2

• And: but, also, as well, too, moreover, in addition, additionally…
• Not: it is not the case that, neither .. nor, un- …
• Or: Either .. or, alternatively, unless …
• If.. then: if, only if, conditional on, when, only when, in case
• If and only if: when and only when, just in case.
• Conclusion: so, hence, thus, therefore, it follows that …

Question 3

What must we do if a sentence has multiple binary connectives?

Answer 3

We must use brackets to make it unambiguous

A proper sentence of formal logic is well formed. (A -> B) & C

An improper sentence of formal logic is ill formed. A -> B & C

Every well formed sentence has exactly one main operator.

Question 4

Disambiguate A -> B & C

Answer 4

Potential 1: (A -> B) & C

This sentence is a conjunction with & as its main operator. The conditional is a sub sentence, enclosed in brackets.

Potential 2: A -> (B & C)

This sentence is a conditional with -> as it’s main operator. The conjunction is a sub sentence.

In logic the main operator is always outside the bracket.

Question 5

Translate this into Logic

“If Hannah and Mary visit the Museum then Jane will either go fishing or she will play the guitar”

Answer 5

Key: H: Hannah will visit the Museum
M: Mary will visit the Museum

F: Jane will go fishing

G: Jane will play the guitar

(H & M) -> (F v G)

Question 6

Is ∼A -> B ambiguous?

Explain why/ why not

Answer 6

It is not

Convention is that ∼ negates the unit exactly to the right of it. If this unit is in brackets then the whole thing is negated.

In this sentence A is negated and -> is the main operator

It is different from ∼(A -> B) where the the main operator is ∼