26,729 research outputs found
Qualifying number restrictions in concept languages
We investigate the subsumption problem in logic-based knowledge representation languages of the KL-ONE family. The language presented in this paper provides the constructs for conjunction, disjunction, and negation of concepts, as well as qualifying number restrictions. The latter ones generalize the well-known role quantifications (such as value restrictions) and ordinary number restrictions, which are present in almost all KL-ONE based systems. Until now, only little attempts were made to integrate qualifying number restrictions into concept languages. It turns out that all known subsumption algorithms which try to handle these constructs are incomplete, and thus detecting only few subsumption relations between concepts.
We present a subsumption algorithm for our language which is sound and complete. Subsequently we discuss why the subsumption problem in this language is rather hard from a computational point of view. This leads to an idea of how to recognize concepts which cause tractable problems
Practical Reasoning for Very Expressive Description Logics
Description Logics (DLs) are a family of knowledge representation formalisms
mainly characterised by constructors to build complex concepts and roles from
atomic ones. Expressive role constructors are important in many applications,
but can be computationally problematical. We present an algorithm that decides
satisfiability of the DL ALC extended with transitive and inverse roles and
functional restrictions with respect to general concept inclusion axioms and
role hierarchies; early experiments indicate that this algorithm is well-suited
for implementation. Additionally, we show that ALC extended with just
transitive and inverse roles is still in PSPACE. We investigate the limits of
decidability for this family of DLs, showing that relaxing the constraints
placed on the kinds of roles used in number restrictions leads to the
undecidability of all inference problems. Finally, we describe a number of
optimisation techniques that are crucial in obtaining implementations of the
decision procedures, which, despite the worst-case complexity of the problem,
exhibit good performance with real-life problems
Cardinality restrictions on concepts
The concept description formalisms of existing terminological systems allow the user to express local cardinality restrictions on the fillers of a particular role. It is not possible, however, to introduce global restrictions on the number of instances of a given concept. The paper argues that such cardinality restrictions on concepts are of importance in applications such as configuration of technical systems, an application domain of terminological systems that is currently gaining in interest. It shows that including such restrictions into the description language leaves the important inference problems such as instance testing decidable. The algorithm combines and simplifies the ideas developed for the treatment of qualifying number restrictions and of general terminological axioms
Decidable Reasoning in Terminological Knowledge Representation Systems
Terminological knowledge representation systems (TKRSs) are tools for
designing and using knowledge bases that make use of terminological languages
(or concept languages). We analyze from a theoretical point of view a TKRS
whose capabilities go beyond the ones of presently available TKRSs. The new
features studied, often required in practical applications, can be summarized
in three main points. First, we consider a highly expressive terminological
language, called ALCNR, including general complements of concepts, number
restrictions and role conjunction. Second, we allow to express inclusion
statements between general concepts, and terminological cycles as a particular
case. Third, we prove the decidability of a number of desirable TKRS-deduction
services (like satisfiability, subsumption and instance checking) through a
sound, complete and terminating calculus for reasoning in ALCNR-knowledge
bases. Our calculus extends the general technique of constraint systems. As a
byproduct of the proof, we get also the result that inclusion statements in
ALCNR can be simulated by terminological cycles, if descriptive semantics is
adopted.Comment: See http://www.jair.org/ for any accompanying file
PSPACE Reasoning for Graded Modal Logics
We present a PSPACE algorithm that decides satisfiability of the graded modal
logic Gr(K_R)---a natural extension of propositional modal logic K_R by
counting expressions---which plays an important role in the area of knowledge
representation. The algorithm employs a tableaux approach and is the first
known algorithm which meets the lower bound for the complexity of the problem.
Thus, we exactly fix the complexity of the problem and refute an
ExpTime-hardness conjecture. We extend the results to the logic Gr(K_(R \cap
I)), which augments Gr(K_R) with inverse relations and intersection of
accessibility relations. This establishes a kind of ``theoretical benchmark''
that all algorithmic approaches can be measured against
Knowledge web: realising the semantic web... all the way to knowledge-enhanced multimedia documents
The semantic web and semantic web services are major efforts in order to spread and to integrate knowledge technology to the whole web. The Knowledge Web network of excellence aims at supporting their developments at the best and largest European level and supporting industry in adopting them. It especially investigates the solution of scalability, heterogeneity and dynamics obstacles to the full development of the semantic web. We explain how Knowledge Web results should benefit knowledge-enhanced multimedia applications
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