Defeasible RDFS via rational closure

In the field of non-monotonic logics, the notion of Rational Closure (RC) is acknowledged as a notable approach. In recent years, RC has gained popularity in the context of Description Logics (DLs), the logic underpinning the standard semantic Web Ontology Language OWL 2, whose main ingredients are classes, the relationship among classes and roles, which are used to describe the properties of classes. In this work, we show instead how to integrate RC within the triple language RDFS (Resource Description Framework Schema), which together with OWL 2 is a major standard semantic web ontology language. To do so, we start from rdf, a minimal, but significant RDFS fragment that covers the essential features of RDFS, and then extend it to rdf_\bot, allowing to state that two entities are incompatible/disjoint with each other. Eventually, we propose defeasible rdf_\bot via a typical RC construction allowing to state default class/property inclusions. Furthermore, to overcome the main weaknesses of RC in our context, i.e., the "drowning problem" (viz. the "inheritance blocking problem"), we further extend our construction by leveraging Defeasible Inheritance Networks (DIN) defining a new non-monotonic inference relation that combines the advantages of both (RC and DIN). To the best of our knowledge this is the first time of such an attempt. In summary, the main features of our approach are: (i) the defeasible rdf_\bot we propose here remains syntactically a triple language by extending it with new predicate symbols with specific semantics; (ii) the logic is defined in such a way that any RDFS reasoner/store may handle the new predicates as ordinary terms if it does not want to take account of the extra non-monotonic capabilities; (iii) the defeasible entailment decision procedure is built on top of the rdf_\bot entailment decision procedure, which in turn is an extension of the one for rdf via some additional inference rules favouring a potential implementation; (iv) the computational complexity of deciding entailment in rdf and rdf_\bot are the same; and (v) defeasible entailment can be decided via a polynomial number of calls to an oracle deciding ground triple entailment in rdf_\bot and, in particular, deciding defeasible entailment can be done in polynomial time.