Natural language can be extremely ambiguous though, and while the ambiguity may be resolved easily from context, someone in OP's situation doesn't have that context. The precision mathematical notation can afford (more readily than, say, English) actually helps. But of course, only of one knows the meaning...

I'm in a somewhat similar position to OP, it's extremely rare that I'd find a whole paper accessible, the best way I know is just to get gradually more specific, from a broad undergraduate textbook on 'logic' or whatever other similarly broad area, and hone in on the more specific area of interest. Notation will be introduced, and by the time the last 5% is, 80% will be second nature, and the remaining 15% will be familiar and 'let's see.. I think it was used in this book..'