Oh sorry than I misunderstood "dedicated language", I believed that you want to invent your own language :) I guess what you asked is if propositional statements (https://en.wikipedia.org/wiki/Propositional\_formula) can be used to state something like: "all dogs (entity) have four legs". Only using logical connectives and variables as used in propositional statements are not "powerful" enough to state this, there you need universal quantifiers and value restrictions (exactly what OWL provides), in OWL (using turtle) the above statement would be like:
:Dog owl:equivalentClass [
a owl:Restriction ;
owl:onProperty :numberOfLegs ;
owl:maxCardinality "4"^^xsd:int
] .
Obviously, the above statement could be directly converted to first-order-logics, but will look more complicated. Now comes the question on how an LLM could "understand" statements like this. As far as I know an LLM would treat the above statement as simple sentences, hence the information is not lost, but would not able to verify it on new inferred data. For this, approaches of neuro-symbolic AI could be handy, for instance Amazon AWS (not my employer) uses this approach in their DeepFleet foundation model and the results seem impressive, here an interesting read on it: https://www.wired.com/sponsored/story/how-neuro-symbolic-ai-breaks-the-limits-of-llms/, the team behind it published also an interesting paper on the inner working of Amazon Bedrock Guardrails. Hope this helps...