The logical capabilities of the prover are more than ample for the needs of the logic implemented in Loglan, although the underlying logical paradigm is somewhat different. Propositional calculus is the logic of the propositional connectives no , a , e , o , u and their kin in Loglan.
Quantifiers are a more complex problem.
I will be attempting to design an interface which will allow one to talk to this prover in Loglan. If the answers to these questions about LIP turn out to be the best possible, it might be possible to avert creation of a special Loglan subset and have the prover accept full Loglan from the outset. Before I can answer that question, we need to know where are we in the logical language project. We've built a LIP-loadable grammar, one which, with remarkably few additions, has proved equal to everything we've asked it to do, or to be easily augmented to handle those few things it wasn't equal to. Still, all of our usages have, from the beginning of Loglandian time, been built with precise interpretability in mind.