3 research outputs found
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 , which is the logic
behind RDFS, and then extend it to , allowing to state that two
entities are incompatible. Eventually, we propose defeasible 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 remains syntactically a triple
language and is a simple extension of 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 entailment decision procedure is build on top of the
entailment decision procedure, which in turn is an extension of
the one for via some additional inference rules favouring an
potential implementation; and (iii) defeasible entailment can be
decided in polynomial time.Comment: 47 pages. Preprint versio
From iterated revision to iterated contraction: extending the Harper Identity
The study of iterated belief change has principally focused on revision, with the other main operator of AGM belief change theory, namely contraction, receiving comparatively little attention. In this paper we show how principles of iterated revision can be carried over to iterated contraction by generalising a principle known as the ‘Harper Identity’. The Harper Identity provides a recipe for defining the belief set resulting from contraction by a sentence A in terms of (i) the initial belief set and (ii) the belief set resulting from revision by ¬A. Here, we look at ways to similarly define the conditional belief set resulting from contraction by A. After noting that the most straightforward proposal of this kind leads to triviality, we characterise a promising family of alternative suggestions that avoid such a result. One member of that family, which involves the operation of rational closure, is noted to be particularly theoretically fruitful and normatively appealing