31 research outputs found
Reasoning Algebraically with Description Logics
Semantic Web applications based on the Web Ontology Language (OWL) often
require the use of numbers in class descriptions for expressing
cardinality restrictions on properties or even classes. Some of these
cardinalities are specified explicitly, but quite a few are entailed and
need to be discovered by reasoning procedures. Due to the Description
Logic (DL) foundation of OWL, those reasoning services are offered by DL
reasoners. Existing DL reasoners employ reasoning procedures that are
arithmetically uninformed and substitute arithmetic reasoning by "don't
know" non-determinism in order to cover all possible cases. This lack of
information about arithmetic problems dramatically degrades the
performance of DL reasoners in many cases, especially with ontologies
relying on the use of Nominals and Qualied Cardinality Restrictions.
The contribution of this thesis is twofold: on the theoretical level, it
presents algebra�ic reasoning with DL (ReAl DL) using a sound, complete,
and terminating reasoning procedure for the DL SHOQ. ReAl DL combines
tableau reasoning procedures with algebraic methods, namely Integer
Programming, to ensure arithmetically better informed reasoning. SHOQ
extends the standard DL ALC with transitive roles, role hierarchies,
qualified cardinality restrictions (QCRs), and nominals, and forms an
expressive subset of OWL. Although the proposed algebraic tableau is
double exponential in the worst case, it deals with cardinalities with
an additional level of information and properties that make the calculus
amenable and well suited for optimizations. In order for ReAl DL to have
a practical merit, suited optimizations are proposed towards achieving
an efficient reasoning approach that addresses the sources of complexity
related to nominals and QCRs. On the practical level, a running
prototype reasoner (HARD) is implemented based on the proposed calculus
and optimizations. HARD is used to evaluate the practical merit of ReAl
DL, as well as the effectiveness of the proposed optimizations.
Experimental results based on real world and synthetic ontologies show
that ReAl DL outperforms existing reasoning approaches in handling the
interactions between nominals and QCRs. ReAl DL also comes with some
interesting features such as the ability to handle ontologies with
cyclic descriptions without adopting special blocking strategies. ReAl
DL can form a basis to provide more efficient reasoning support for
ontologies using nominals or QCRs
A hybrid ABox calculus using algebraic reasoning for the Description Logic SHIQ
We present a hybrid tableau calculus for the description logic (DL) SHIQ. The presented algorithm decides SHIQ ABox consistency and uses an algebraic approach for more informed
reasoning about qualified number restrictions (QNRs). Benefiting from integer linear programming and several optimization techniques to deal with the interaction of QNRs and inverse roles, our approach provides a more deterministic and informed calculus. In addition, a prototype reasoner based on the hybrid calculus has been implemented that decides concept satisfiability for ALCHIQ. We provide a set of benchmarks that demonstrate the effectiveness of our hybrid reasoner in comparison to other DL reasoners
Inference fusion: a hybrid approach to taxonomic reasoning.
We present a hybrid way to extend taxonomic reasoning using inference fusion, i.e. the dynamic combination of inferences from distributed heterogeneous reasoners. Our approach integrates results from a DL-based taxonomic reasoner with results from a constraint solver. Inference fusion is carried out by (i) parsing heterogeneous input knowledge, producing suitable homogeneous subset of the input knowledge for each specialised reasoner; (ii) processing the homogeneous knowledge, collecting the reasoning results and passing them to the other reasoner if appropriate; (iii) combining the results of the two reasoners. We discuss the benefits of our approach to the ontological reasoning and demonstrate our ideas by proposing a hybrid modelling languages, DL(D)=S, and illustrating its use by means of examples
Inductive Logic Programming in Databases: from Datalog to DL+log
In this paper we address an issue that has been brought to the attention of
the database community with the advent of the Semantic Web, i.e. the issue of
how ontologies (and semantics conveyed by them) can help solving typical
database problems, through a better understanding of KR aspects related to
databases. In particular, we investigate this issue from the ILP perspective by
considering two database problems, (i) the definition of views and (ii) the
definition of constraints, for a database whose schema is represented also by
means of an ontology. Both can be reformulated as ILP problems and can benefit
from the expressive and deductive power of the KR framework DL+log. We
illustrate the application scenarios by means of examples. Keywords: Inductive
Logic Programming, Relational Databases, Ontologies, Description Logics, Hybrid
Knowledge Representation and Reasoning Systems. Note: To appear in Theory and
Practice of Logic Programming (TPLP).Comment: 30 pages, 3 figures, 2 tables
Pseudo-contractions as Gentle Repairs
Updating a knowledge base to remove an unwanted consequence is a challenging task. Some of the original sentences must be either deleted or weakened in such a way that the sentence to be removed is no longer entailed by the resulting set. On the other hand, it is desirable that the existing knowledge be preserved as much as possible, minimising the loss of information. Several approaches to this problem can be found in the literature. In particular, when the knowledge is represented by an ontology, two different families of frameworks have been developed in the literature in the past decades with numerous ideas in common but with little interaction between the communities: applications of AGM-like Belief Change and justification-based Ontology Repair. In this paper, we investigate the relationship between pseudo-contraction operations and gentle repairs. Both aim to avoid the complete deletion of sentences when replacing them with weaker versions is enough to prevent the entailment of the unwanted formula. We show the correspondence between concepts on both sides and investigate under which conditions they are equivalent. Furthermore, we propose a unified notation for the two approaches, which might contribute to the integration of the two areas
Concept Descriptions with Set Constraints and Cardinality Constraints
We introduce a new description logic that extends the well-known logic ALCQ by allowing the statement of constraints on role successors that are more general than the qualified number restrictions of ALCQ. To formulate these constraints, we use the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA), in which one can express Boolean combinations of set constraints and numerical constraints on the cardinalities of sets. Though our new logic is considerably more expressive than ALCQ, we are able to show that the complexity of reasoning in it is the same as in ALCQ, both without and with TBoxes.The first version of this report was put online on April 6, 2017. The current version, containing more information on related
work, was put online on July 13, 2017.
This is an extended version of a paper published in the proceedings of FroCoS 2017
Reasoning with Very Expressive Fuzzy Description Logics
It is widely recognized today that the management of imprecision and
vagueness will yield more intelligent and realistic knowledge-based
applications. Description Logics (DLs) are a family of knowledge representation
languages that have gained considerable attention the last decade, mainly due
to their decidability and the existence of empirically high performance of
reasoning algorithms. In this paper, we extend the well known fuzzy ALC DL to
the fuzzy SHIN DL, which extends the fuzzy ALC DL with transitive role axioms
(S), inverse roles (I), role hierarchies (H) and number restrictions (N). We
illustrate why transitive role axioms are difficult to handle in the presence
of fuzzy interpretations and how to handle them properly. Then we extend these
results by adding role hierarchies and finally number restrictions. The main
contributions of the paper are the decidability proof of the fuzzy DL languages
fuzzy-SI and fuzzy-SHIN, as well as decision procedures for the knowledge base
satisfiability problem of the fuzzy-SI and fuzzy-SHIN