3 Formalisation in Propositional Logic: 3.2 Logical Form

Question 1

What are the two steps to translate English sentences into L₁ sentences?

Answer 1

1. The sentence is brought into a standardized form;
2. Expressions are replaced with symbols

Question 2

What is the standardized form called?

Answer 2

The ‘propositional logical form’

Question 3

What is the first step in the translation from English to propositional logic?

Answer 3

To check whether the sentence can be broken down into truth-functional connective and one or more subsentences

Question 4

What is the sentence ‘The car doesn’t start because the battery is flat or there is no petrol in the tank’ built up from?

Answer 4

• ‘The car doesn’t start’;
• ‘The battery is flat or there is no petrol in the tank’;
• The connective ‘because’; and,
• The connective ‘or’ within the subsentence

Question 5

What is the connective ‘or’?

Answer 5

It is truth-functional, but it only connects ‘the battery is flat’ and ‘there s no petrol in the tnak’

Question 6

What is the second step in the translation of English into propositional logical form?

Answer 6

If the sentence can be reformulated in a natural way as a sentence built up from one or more sentences with a truth-function connective, do so

Question 7

What is the third step in the translation of English into propositional logical form?

Answer 7

If that truth-functional connective is not one of the standard connectives (and, or, it is not the case that, if… then, if and only if), reformulate the sentence using the standard connectives

Question 8

What is the fourth step in the translation of English into propositional logical form?

Answer 8

Enclose the whole sentence in brackets, unless it is a negated sentence: a sentence starting with ‘it is not the case that’

Question 9

What is the fifth step in the translation of English into propositional logical form?

Answer 9

Repeat the procedure to the next subsentence(s) - sentences without the standard connectives from step 3