Extended RDF: Computability and complexity issues

Abstract

Abstract. ERDF stable model semantics is a recently proposed semantics for ERDF ontologies and a faithful extension of RDFS semantics on RDF graphs. In this paper, we elaborate on the computability and complexity issues of the ERDF stable model semantics. Based on the undecidability result of ERDF stable model semantics, decidability under this semantics cannot be achieved, unless ERDF ontologies of restricted syntax are considered. Therefore, we propose a slightly modified semantics for ERDF ontologies, called ERDF #n-stable model semantics. We show that entailment under this semantics is, in general, decidable and also extends RDFS entailment. Equivalence statements between the two semantics are provided. Additionally, we provide algorithms that compute the ERDF #n-stable models of syntax-restricted and general ERDF ontologies. Further, we provide complexity results for the ERDF #n-stable model semantics on syntax-restricted and general ERDF ontologies. Finally, we provide complexity results for the ERDF stable model semantics on syntax-restricted ERDF ontologies.

A Minimal Deductive System for RDFS with Negative Statements

“…In [6] and related works [8,1,2,3,4,5,7,16] the authors deal with Extended RDF (ERDF), a non-monotonic logic, where an ERDF ontology consists of two parts: an ERDF graph and an ERDF logic program. An ERDF graph allows negated RDF triples of the form ¬(s, p, o), informally in FOL terms ¬p(s, o), while in the body of rules all the classical connectives ¬, ⊃, ∧, ∨, ∀, ∃, plus the weak negation (negation-as-failure) ∼ are allowed.…”

“…Various "stable model" semantics have been proposed. From a computational complexity point view, decision problems in ERDF are non-polynomial [8]. E.g., deciding model existence and, thus, model existence is not guaranteed, ranges from NP to PSPACE, while query answering goes from co-NP to PSPACE, depending on the setting.…”

“…E.g., deciding model existence and, thus, model existence is not guaranteed, ranges from NP to PSPACE, while query answering goes from co-NP to PSPACE, depending on the setting. 8 In comparison, ρdf ¬ ⊥ does not use a rule layer, the triple language is more expressive, model existence is guaranteed and the computational complexity ranges between P and NP. Of course, all inference rules for ρdf ¬ ⊥ can be implemented in the rule layer of ERDF (and in Datalog in general).…”

“…9 A vocabulary is a subset of UL and we assume that U contains the ρdf vocabulary (see Equation 4). A triple is of the form 8 There are also many more works that use rule languages on top of RDFS, which however we are not going to discuss here (see, e.g., [15]. 9 All symbols may have upper or lower script.…”

“…Later the works [28,29,30,31] have been inspired by the same idea, though also to model some sort of relevance entailment, besides being paraconsistent. More recently, a similar idea has been considered also in the context of RDFS [7,5,4,8], which is also the semantics we start from and are going to adapt and extend to meet the before mentioned objectives.…”