20 research outputs found
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
On the KLM properties of a fuzzy DL with Typicality
The paper investigates the properties of a fuzzy logic of typicality. The
extension of fuzzy logic with a typicality operator was proposed in recent work
to define a fuzzy multipreference semantics for Multilayer Perceptrons, by
regarding the deep neural network as a conditional knowledge base. In this
paper, we study its properties. First, a monotonic extension of a fuzzy ALC
with typicality is considered (called ALC^FT) and a reformulation the KLM
properties of a preferential consequence relation for this logic is devised.
Most of the properties are satisfied, depending on the reformulation and on the
fuzzy combination functions considered. We then strengthen ALC^FT with a
closure construction by introducing a notion of faithful model of a weighted
knowledge base, which generalizes the notion of coherent model of a conditional
knowledge base previously introduced, and we study its properties.Comment: 15 page
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
Combining open and closed world reasoning for the semantic web
Dissertação para obtenção do Grau de Doutor
em InformáticaOne important problem in the ongoing standardization of knowledge representation
languages for the Semantic Web is combining open world ontology languages, such as the OWL-based ones, and closed world rule-based languages.
The main difficulty of such a combination is that both formalisms are quite orthogonal w.r.t. expressiveness and how decidability is achieved. Combining non-monotonic rules and ontologies is thus a challenging task
that requires careful balancing between expressiveness of the knowledge representation language and the computational complexity of reasoning.
In this thesis, we will argue in favor of a combination of ontologies and nonmonotonic
rules that tightly integrates the two formalisms involved, that has a computational complexity that is as low as possible, and that allows us to query for information instead of calculating the whole model. As our starting point we choose the mature approach of hybrid MKNF knowledge
bases, which is based on an adaptation of the Stable Model Semantics to knowledge bases consisting of ontology axioms and rules. We extend the two-valued framework of MKNF logics to a three-valued logics, and we propose a well-founded semantics for non-disjunctive hybrid MKNF knowledge bases. This new semantics promises to provide better efficiency of reasoning,and it is faithful w.r.t. the original two-valued MKNF semantics and compatible with both the OWL-based semantics and the traditional Well-
Founded Semantics for logic programs. We provide an algorithm based on operators to compute the unique model, and we extend SLG resolution with tabling to a general framework that allows us to query a combination of non-monotonic rules and any given ontology language. Finally, we
investigate concrete instances of that procedure w.r.t. three tractable ontology
languages, namely the three description logics underlying the OWL 2 pro les.Fundação para a Ciência e Tecnologia - grant contract SFRH/BD/28745/200
Typicality-based revision for handling exceptions in Description Logics
Abstract. We continue our investigation on how to revise a Description Logic knowledge base when detecting exceptions. Our approach relies on the methodology for debugging a Description Logic terminology, addressing the problem of diagnosing inconsistent ontologies by identifying a minimal subset of axioms responsible for an inconsistency. In the approach we propose, once the source of the inconsistency has been localized, the identified TBox inclusions are revised in order to obtain a consistent knowledge base including the detected exception. We define a revision operator whose aim is to replace inclusions of the form "Cs are Ds" with "typical Cs are Ds", admitting the existence of exceptions, obtaining a knowledge base in the nonmonotonic logic ALC R min T which corresponds to a notion of rational closure for Description Logics of typicality. We also describe an algorithm implementing such a revision operator
Reasoning with Forest Logic Programs and f-hybrid Knowledge Bases
Open Answer Set Programming (OASP) is an undecidable framework for
integrating ontologies and rules. Although several decidable fragments of OASP
have been identified, few reasoning procedures exist. In this article, we
provide a sound, complete, and terminating algorithm for satisfiability
checking w.r.t. Forest Logic Programs (FoLPs), a fragment of OASP where rules
have a tree shape and allow for inequality atoms and constants. The algorithm
establishes a decidability result for FoLPs. Although believed to be decidable,
so far only the decidability for two small subsets of FoLPs, local FoLPs and
acyclic FoLPs, has been shown. We further introduce f-hybrid knowledge bases, a
hybrid framework where \SHOQ{} knowledge bases and forest logic programs
co-exist, and we show that reasoning with such knowledge bases can be reduced
to reasoning with forest logic programs only. We note that f-hybrid knowledge
bases do not require the usual (weakly) DL-safety of the rule component,
providing thus a genuine alternative approach to current integration approaches
of ontologies and rules
OPTIMIZATION OF NONSTANDARD REASONING SERVICES
The increasing adoption of semantic technologies and the corresponding increasing complexity of application requirements are motivating extensions to the standard reasoning paradigms and services supported by such technologies. This thesis focuses on two of such extensions: nonmonotonic reasoning and inference-proof access control.
Expressing knowledge via general rules that admit exceptions is an approach that has been commonly adopted for centuries in areas such as law and science, and more recently in object-oriented programming and computer security. The experiences in developing complex biomedical knowledge bases reported in the literature show that a direct support to defeasible properties and exceptions would be of great help.
On the other hand, there is ample evidence of the need for knowledge confidentiality measures. Ontology languages and Linked Open Data are increasingly being used to encode the private knowledge of companies and public organizations. Semantic Web techniques facilitate merging different sources of knowledge and extract implicit information, thereby putting at risk security and the privacy of individuals. But the same reasoning capabilities can be exploited to protect the confidentiality of knowledge.
Both nonmonotonic inference and secure knowledge base access rely on nonstandard reasoning procedures. The design and realization of these algorithms in a scalable way (appropriate to the ever-increasing size of ontologies and knowledge bases) is carried out by means of a diversified range of optimization techniques such as appropriate module extraction and incremental reasoning. Extensive experimental evaluation shows the efficiency of the developed optimization techniques: (i) for the first time performance compatible with real-time reasoning is obtained for large nonmonotonic ontologies, while (ii) the secure ontology access control proves to be already compatible with practical use in the e-health application scenario.