So not an expert in this area, would love if someone corrects me. My understanding is generally FOL is infeasible. Propositional logic even can be computationaly difficult [1]. My understanding is that most of the semantic web stuff is done using a description logic of some flavor. These will be named based on the properties of the logic. The important thing is that they are generally decidable, and you can use something like MALET or some other solver to infer things from your database or ontology.(You give up some expressivity for decidability) Not sure how much stuff is going on with that these days. Played with a petrology ontology in protegé some back in college, but haven't followed the space. I remember OWL being important, but can't remember why at the moment.

[1] For example if you try to figure out if a formula is satisfiable. You can for sure do this using truth tables. The catch is that you're looking at 2^n complexity where n is the number of propositions in your formula.