In what follows we provide an oversimplified introduction to some basic choices related to the implementation of semantic repositories with inference functionality.

Two main reasoning strategies can be outlined:

• Forward-chaining: to start from the known facts and to perform the inference in an inductive fashion. This kind of reasoning can have diverse objectives, for instance: to compute the inferred closure; to answer a particular query; to infer a particular sort of knowledge (e.g. the class taxonomy); etc.
• Backward-chaining: to start from a particular fact or from a query and by means of using deductive reasoning to try to verify that fact or to obtain all possible results of the query. Typically, the reasoner decomposes the fact into simpler facts that can be found in the knowledge base or transforms it into alternative facts that can be proven applying further recursive transformations.

Here, the term inferred closure is defined as follows: the extension of a KB (or, in the case of RDF/OWL semantic repository, the extension of a graph of RDF triples) with all the implicit facts (triples), that could be inferred from it, using the enforced semantics.

Consider a repository capable to reason by means of total forward-chaining; after each update to the KB made, the repository assures that the inferred closure is computed or updated and made available for query evaluation or retrieval. Generally, this strategy is known as materialization. In order to avoid confusion with various partial materialization approaches, let us call total materialization such an inference strategy, when applied under monotonic semantics. The main advantages and disadvantages of such a schema can be summarized as follows:

• The upload/store/addition of new facts is relatively slow, because after each transaction that leads to a modification, the repository tries to extend the inferred closure;
• Deletion of facts is slow, because the repository should remove from the inferred closure all the previously inferred facts which are not true (because they many not be inferred) any longer.
• The maintenance of the inferred closure usually requires considerable additional space (in the RAM, on an external storage, or both, depending on the implementation);
• Query and retrieval operations are fast, because no deduction, satisfiability check, or other sorts of reasoning is required. In effect, the evaluation of a query is computationally comparable with the same task for relational database management systems (RDBMS).

Probably, the most important advantage of inductive systems, based on total materialization, is that they can easily benefit from RDBMS-like query optimization techniques, as long as all the data is available at query time. The availability of all the data enables that the query evaluation engine use statistics and other means to make "educated" guesses about the cost of evaluation of a particular constraint and the cardinality of the result. Such optimizations are much more complex in case of deductive query evaluation.

As a reasoning strategy, total materialization is adapted in a number of the popular Semantic Web repositories, including some of the standard configurations of Sesame and Jena. Experiments, like the performance tests of OWLIM, suggest that an efficient implementation of total materialization often can outperform systems based on more complicated reasoning strategies.

Under a monotonic logic, the addition of new explicit facts (or statements) to the knowledge base (or repository) has the effect that new implicit facts may extend the inferred closure, while at the same time the removal of facts, which were part of the inferred closure, is disallowed. In other words, the addition of new facts can only extend the inferred closure monotonically.

An interesting discussion on the relevance and the utility of monotonic logics for the Semantic Web between Ian Horrocks, Pat Hayes, and Seth Russell can be found in the W3C archives. A broader overview on the subject is provided by Seth Russell here. The semantics of RDFS is monotonic.