Defeasible RDFS via Rational Closure

In the field of non-monotonic logics, the notion of Rational Closure (RC) is acknowledged as a prominent approach. In recent years, RC has gained even more popularity in the context of Description Logics (DLs), the logic underpinning the semantic web standard ontology language OWL 2, whose main ingredients are classes and roles. In this work, we show how to integrate RC within the triple language RDFS, which together with OWL2 are the two major standard semantic web ontology languages. To do so, we start from ρ df, which is the logic behind RDFS, and then extend it to ρ df_bot, allowing to state that two entities are incompatible. Eventually, we propose defeasible ρ df_bot via a typical RC construction. The main features of our approach are: (i) unlike most other approaches that add an extra non-monotone rule layer on top of monotone RDFS, defeasible ρ df_bot remains syntactically a triple language and is a simple extension of ρ df_bot by introducing some new predicate symbols with specific semantics. In particular, any RDFS reasoner/store may handle them as ordinary terms if it does not want to take account for the extra semantics of the new predicate symbols; (ii) the defeasible ρ df_bot entailment decision procedure is build on top of the ρ df_bot entailment decision procedure, which in turn is an extension of the one for ρ df via some additional inference rules favouring an potential implementation; and (iii) defeasible ρ df_bot entailment can be decided in polynomial time.