How to translate sentence into a well-formed formula of propositional logic?

Question

The sentence is: "Excluding Saturdays, I eat apples every day."

I am unsure of what statements to represent with propositional variables.

Answer 1

There are two types of entity in the sentence you proposed: days and apples. When talking about days, you are only interested in checking if the day is a Saturday. So, the variable of interest, here, might be $is\_saturday$, or $s$ for brevity. Its value is true if it is Saturday and false otherwise. Similarly, you can model the behaviour of eating apples in a day by a variable $eat\_apples\_today$, or $e$ for brevity.

Now, you have some equivalent ways to express the sentence in propositional logic. Personally, I would use $s \implies \neg e$.

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The main idea is that you should first find out which entities are involved in the sentence and represent them by means of propositional variables; then, you should find their relationships (causal, coordinate, equivalent etc.) and represent these by means of logical operators.

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The emphasis on "personally" is because there is no universal recipe to translate English (or many other spoken/written languages) sentences into propositional logic.