Defeasible RDFS via Rational Closure

Abstract

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 OWL 2 are the two major standard semantic web ontology languages. To do so, we start from ρdf, which is the logic behind RDFS, and then extend it to ρdf ⊥ , allowing to state that two entities are incompatible. Eventually, we propose defeasible ρdf ⊥ via a typical RC construction.The main features of our approach are: (i) unlike most other approaches that add an extra nonmonotone rule layer on top of monotone RDFS, defeasible ρdf ⊥ remains syntactically a triple language and is a simple extension of ρdf 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 ρdf ⊥ entailment decision procedure is build on top of the ρdf ⊥ entailment decision procedure, which in turn is an extension of the one for ρdf via some additional inference rules favouring an potential implementation; and (iii) defeasible ρdf ⊥ entailment can be decided in polynomial time. SyntaxWe rely on a fragment of RDFS, called minimal ρdf [63, Def. 15], that covers essential features of RDFS. Specifically, minimal ρdf is defined as the following subset of the RDFS vocabulary: ρdf = {sp, sc, type, dom, range} .Moreover, it does not consider so-called blank nodes and, thus, in what follows, triples and graphs will be ground. In fact, minimal ρdf suffices to illustrate the main concepts and algorithms we will consider in this work and ease the presentation. To avoid unnecessary redundancy, we will just drop the term 'minimal' in what follows.So, consider pairwise disjoint alphabets U and L denoting, respectively, URI references and literals. 2 We assume that U contains the ρdf vocabulary. A literal may be a plain literal (e.g., a string) or a typed literal (e.g., a boolean value) [61]. We call the elements in UL terms. Terms are denoted with lower case letters a, b, . . . with optional super/lower script.A triple is of the form τ = (s, p, o) ∈ UL × U × UL, 3 where s, o / ∈ ρdf. We call s the subject, p the predicate, and o the object.A graph G is a set of triples, the universe of G, denoted uni(G), is the set of terms in UL that occur in the triples of G.We recall that informally (i) (p, sp, q) means that property p is a subproperty of property q; (ii) (c, sc, d) means that class c is a subclass of class d; (iii) (a, type, b) means that a is of type b; (iv) (p, dom, c) means that the domain of property p is c; and (v) (p, range, c) means that the range of property p is c.We extend the vocabulary of ρdf with a new pair of predicates, ⊥ c and ⊥ p , ...