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From what I've understood as reading the book Foundations of Semantic Web Technologies concerning owl formal semantics, Hitzler et al have put forward two kinds of model-theoretic semantics for SROIQ: one is the model checking like approach (where we check different interpretations to find the models of our KB) and the other is via predicate logic. In the latter approach, the book just translates SROIQ into predicate logic.

However, the book is a bit confusing for me and I do not know if I have gotten some points right, so here are my questions:

  1. Is model-checking a kind of model-theoretic semantics?

  2. Is translating your SROIQ into predicate logic also a model-theoretic semantics?

  3. How is translating SROIQ into predicate logic a kind of "semantics"? Is that because after the conversion, we can pick up FOL semantics and algorithms?

Thanks!

P.S. This is a link to the book! Just in case!

Sara
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  • I'm wondering why you call processes like "model-checking" and "translating" semantics? – UninformedUser Jun 07 '19 at 11:44
  • Well, you're right. I don't see them as "semantics" now either. I take them as different methods to inspect inference in a logic. – Sara Jun 07 '19 at 13:10
  • But since they come under the "model theoretic semantics" section in the book, I got a bit confused. – Sara Jun 07 '19 at 13:10
  • Truth is, I don't get what the word "model-theoretic" actually means and how it is related to translation and model checking. So I keep confusing it with other concepts. As I said, I take translation and model checking as different ways to derive inferences. But I don't know how they all come under the "model theoretic" semantics category. – Sara Jun 07 '19 at 13:12
  • Note that OWL comes with a set of standards, some related to syntaxes, some related to semantics. There are 2 official formal semantics in OWL: the direct semantics, which is the one based on SROIQ(D), that is used to interpret the structural specification of OWL 2 ontologies; and the RDF-based semantics, which is a way to interpret RDF graphs such that entailment over OWL 2 ontologies in RDF-graph form is mostly compatible with the direct semantics. Related question: [Why does OWL have two different semantics?](https://www.emse.fr/~zimmermann/QA/q.html) – Antoine Zimmermann Jun 07 '19 at 16:47
  • Thanks for the link! It helped! – Sara Jun 07 '19 at 20:49

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Model theoretic semantics is how you determine the meaning of axioms - i.e., what rules are available to build a model or to check it is a valid one. Two examples: OWL semantics and RDF semantics. They have a lot of overlap but are not identical.

Model checking does not define semantics, it applies semantic rules defined in a model to actual knowledge bases. Translation to another formalism, e.g., predicates, might maintain the same semantics (i.e., all models stay the same in both formalisms), but this depends on the formalism involved.

Ignazio
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