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Sentences with more than one connective

This step takes a first look at sentences containing more than one sentence-connective.
A close-up of the sentence 'P ampersand tilde Q'
© Barry Lee
We now have two sentence-operators in our formal language: ampersand (‘&’) and tilde (‘~’). This highlights the possibility of having sentences which contain two sentence operators.

(That possibility was present already: for instance, we could have had something equivalent to ‘It’s raining and it’s cold and it’s windy’.)

Sentences with two or more operators are common in natural languages. For example

  • It’s warm and it’s not raining

We could represent this in our formal language. First we create our dictionary:

  • W: It’s warm
  • R: It’s raining

Then we can construct our sentence:

  • (W & ~R)

© University of York
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Logic: The Language of Truth

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