Hmm... where to start :)
First, I'd check out this question here, which explains that inferencing is just the implementation of reasoning.
Second, rule-based reasoning is a core part of the Semantic Web standards: you have the RDFS entailment rules, the OWL 2 RL/RDF entailment rules, as well as various other non-standard rule fragments to support reasoning over the SW schema and ontology languages. You also have the RIF (Core) standard, and other non-standard mechanisms for specifying rules over RDF, including SWRL, SPIN, N3, Jena rules and so forth. There is an important distinction here between schema/ontology languages (RDFS, OWL) that allow you to make well-defined statements directly in RDF, and rule languages (RIF...) that allow you to specify rules over RDF.
Third, it follows that RDF inference can be done using rules: semantic inferencing (as I interpret your meaning) is just a broader notion than rule-based inferencing, not a distinct notion. Again, you have RDFS, RDFS-plus DLP, pD*, OWL LD, OWL 2 RL/RDF, ~OWL 2 EL, SWRL, SPIN, N3, Jena rules—and more besides—enabling semantic inferencing using rules. Again, note that rules can be used for inference over the schema/ontology languages and not just the "pure" rule languages.
Fourth, there are other forms of inferencing applied in the SW domain. One prominent such example is the use of tableau algorithms that can offer more expressive reasoning than rules in the presence of certain constructs. You should check out this question here.
I have read examples of isPartOf, isSiblingOf, etc properties to illustrate the concept, but I think such information can still be obtained by rules/small algorithms in any simple plain programming language or using rule-engines.I.e, without use of any semantic technologies.
Just to add that for lightweight reasoning, rules are often enough. (However, if you want to run complete reasoning over expressive languages like OWL (2) DL, a finite set of rules is not enough.)