Semantic Reasoners

A semantic reasoner, reasoning engine, rules engine, or simply a reasoner, is a piece of software able to infer logical consequences from a set of asserted facts or axioms. The notion of a semantic reasoner generalizes that of aninference engine, by providing a richer set of mechanisms to work with. The inference rules are commonly specified by means of an ontology language, and often a description language. Many reasoners use first-order predicate logic to perform reasoning; inference commonly proceeds by forward chaining and backward chaining. There are also examples of probabilistic reasoners, including Pei Wang's non-axiomatic reasoning system, Novamente's probabilistic logic network, which tip their hat to reasoning Bayesian networks, and Pronto - probabilistic description logic reasoner.

Some open - source reasoners  than can be used with Protege and OWL API are:

Pellet

Fact ++

and HermiT