I understand the question might be too broad, so let me clarify a little. You're a mathematician/logician and you're facing a novel proof system portraying some notion (say, knowledge) that you haven't encountered, or others haven't studied before. You'd like to examine the consistency of the system. What would be your go-to, first attempts to do the latter? I'm aware of model-construction as a general method for proving consistency. I'm also aware of certain cases where proof-theoretic techniques (such as Gentzen's) are used to show consistency. What I'm interested in is whether there are certain go-to techniques/tricks that, if one encounters a novel proof system, one can give a try at the first attempts.

Any help would be appreciated.

PS: Please let me know if the tags used aren't appropriate -- I wasn't sure where my question belongs to.