Clarification requests about Description Logic and OWL

Question

I have two main Questions:

1/ If we speak about OWL 2 semantics in academic manuscripts (ex. thesis) : do we include the description provided in this W3C official page, which consists of more than one interpretation functions

OR

the one provided in most Description logic and OWL manuscripts? Which consists just of one interpretation function (papers and thesis)???

2/ If we speak about OWL 2 standard reasoning tasks in academic manuscripts (ex. thesis) :

do we speak about object and data properties reasoning tasks( ex. subsumption, satisfiability...) besides those of classes: because most academic manuscripts speak just about classes reasoning tasks in OWL 2;

thank you for telling me which of these alternatives, in both questions, is more correct and formal.

Answer 1

The trouble is that “OWL 2 Semantics” is ambiguous: OWL is a well-defined interchange format with several incompatible semantic interpretations. If you like you can refer to that particular document, but it’s important to cite it more specifically as the “OWL 2 Direct Semantics”.

In cases where your work doesn’t involve data types or punning, the SROIQ logic is actually a much simpler and cleaner mathematical formalism...with the caveat that the SROIQ literature is typically written for an academic audience, so this simpler model is usually described in a denser style.

Answer 2

Strictly speaking OWL 2 maps to the DL SROIQ(D) extended with DL safe rules (which provides the semantics for hasKey).

Using one interpretation function is the norm in academic texts.

As AKSW pointed out, standard reasoning tasks are reducible to concept satisfiability (resp. class satisfiability in OWL), hence the reason academic texts tend to refer to concept satisfiability.

Role satisfiability (object/data properties satisfiability) reduces to concept satisfiability by checking satisfiability of the concept $\geq 1 r.\top$. However, there are some limitations when considering object/data properties. See Preventing, Detecting, and Revising Flaws in Object Property Expressions.