# Why translating language to propositional logic is tough?

1. Feb 1, 2014

### Avichal

Why is it so hard to convert natural language to propositional logic. We are so comfortable in understanding and interpreting english or any other language we know.
But when we need to convert it into something formal, we have to think. It does not come that naturally. Why?

(I am not sure if this thread belongs here. Please move it appropriately if it belongs elsewhere)

2. Feb 1, 2014

### kurros

Well, interpreting natural language sentences involves a truly ridiculous amount of inference based on context. We also say a lot of really vague things which get an immediate point across, but don't have a very well defined meaning if you dig even a little bit into it. On the other hand formal logic in some sense assumes that whatever proposition you are using, everybody should agree on what it means, down to the last nuance. This is really quite a tough burden to meet.

We leave a lot unsaid in most sentences, but to be formal you have to put all that information back in.

3. Feb 1, 2014

### Stephen Tashi

Usually translating natural language to propositional logic lacks the context that surrounds natural language. So you must include enough in the logic to make explicit what a hearer of natural language infers from context. For example "There's a psych major in every dormitory" isn't interpreted to mean that there is a single psych major who has a room in each dormitory.

Also, natural language doesn't exclusively communicate logical statements. (For example, to the man-in-the-street, the word "logical" may mean "true" or"plausible" or "probable" or "appropriate".)

I The truth value of $P(x)$ → $Q(x)$