268 research outputs found
Reasoning about Typicality and Probabilities in Preferential Description Logics
In this work we describe preferential Description Logics of typicality, a
nonmonotonic extension of standard Description Logics by means of a typicality
operator T allowing to extend a knowledge base with inclusions of the form T(C)
v D, whose intuitive meaning is that normally/typically Cs are also Ds. This
extension is based on a minimal model semantics corresponding to a notion of
rational closure, built upon preferential models. We recall the basic concepts
underlying preferential Description Logics. We also present two extensions of
the preferential semantics: on the one hand, we consider probabilistic
extensions, based on a distributed semantics that is suitable for tackling the
problem of commonsense concept combination, on the other hand, we consider
other strengthening of the rational closure semantics and construction to avoid
the so-called blocking of property inheritance problem.Comment: 17 pages. arXiv admin note: text overlap with arXiv:1811.0236
Reasoning about exceptions in ontologies: from the lexicographic closure to the skeptical closure
Reasoning about exceptions in ontologies is nowadays one of the challenges
the description logics community is facing. The paper describes a preferential
approach for dealing with exceptions in Description Logics, based on the
rational closure. The rational closure has the merit of providing a simple and
efficient approach for reasoning with exceptions, but it does not allow
independent handling of the inheritance of different defeasible properties of
concepts. In this work we outline a possible solution to this problem by
introducing a variant of the lexicographical closure, that we call skeptical
closure, which requires to construct a single base. We develop a bi-preference
semantics semantics for defining a characterization of the skeptical closure
Defeasible Reasoning in SROEL: from Rational Entailment to Rational Closure
In this work we study a rational extension of the low complexity
description logic SROEL, which underlies the OWL EL ontology language. The
extension involves a typicality operator T, whose semantics is based on Lehmann
and Magidor's ranked models and allows for the definition of defeasible
inclusions. We consider both rational entailment and minimal entailment. We
show that deciding instance checking under minimal entailment is in general
-hard, while, under rational entailment, instance checking can be
computed in polynomial time. We develop a Datalog calculus for instance
checking under rational entailment and exploit it, with stratified negation,
for computing the rational closure of simple KBs in polynomial time.Comment: Accepted for publication on Fundamenta Informatica
A strengthening of rational closure in DLs: reasoning about multiple aspects
We propose a logical analysis of the concept of typicality, central in human
cognition (Rosch,1978). We start from a previously proposed extension of the
basic Description Logic ALC (a computationally tractable fragment of First
Order Logic, used to represent concept inclusions and ontologies) with a
typicality operator T that allows to consistently represent the attribution to
classes of individuals of properties with exceptions (as in the classic example
(i) typical birds fly, (ii) penguins are birds but (iii) typical penguins don't
fly). We then strengthen this extension in order to separately reason about the
typicality with respect to different aspects (e.g., flying, having nice
feather: in the previous example, penguins may not inherit the property of
flying, for which they are exceptional, but can nonetheless inherit other
properties, such as having nice feather)
A reconstruction of the multipreference closure
The paper describes a preferential approach for dealing with exceptions in
KLM preferential logics, based on the rational closure. It is well known that
the rational closure does not allow an independent handling of the inheritance
of different defeasible properties of concepts. Several solutions have been
proposed to face this problem and the lexicographic closure is the most notable
one. In this work, we consider an alternative closure construction, called the
Multi Preference closure (MP-closure), that has been first considered for
reasoning with exceptions in DLs. Here, we reconstruct the notion of MP-closure
in the propositional case and we show that it is a natural variant of Lehmann's
lexicographic closure. Abandoning Maximal Entropy (an alternative route already
considered but not explored by Lehmann) leads to a construction which exploits
a different lexicographic ordering w.r.t. the lexicographic closure, and
determines a preferential consequence relation rather than a rational
consequence relation. We show that, building on the MP-closure semantics,
rationality can be recovered, at least from the semantic point of view,
resulting in a rational consequence relation which is stronger than the
rational closure, but incomparable with the lexicographic closure. We also show
that the MP-closure is stronger than the Relevant Closure.Comment: 57 page
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