I have a question about ontologies on Protege. When we create an ontology with inference rules on Protege, will this ontology be in OWL FULL or in OWL DL?
Protégé is an ontology editor that can edit any ontology that follows the OWL 2 Structural Specification. If you are using Protégé without any additional plugins, then the resulting ontology follows this specification. However, there are ontologies that are structurally conformant but are not OWL 2 DL ontologies. For example, using Protégé, you could define a property chain axiom that has an irreflexive property as part of the chain, which is dissallowed by the OWL 2 DL profile.
Additionally, Protégé has plugins that allows you to define rules, like SWRL. If you add SWRL rules to your ontology, it's probably going to be outside OWL 2 DL. However, there are OWL 2 DL reasoners that are also able to handle SWRL rules (with some restrictions) like HermiT or Pellet. If your rules are not in SWRL, such as SPIN rules or RIF rules, then the ontology will probably not be in OWL 2 DL and I don't know how this is supported by OWL 2 DL reasoners.
In any case, being in OWL 2 DL is not necessarily a must, depending on what you want to achieve. There are many use cases for ontologies outside of OWL 2 DL.