3,461 research outputs found
A Neutrosophic Description Logic
Description Logics (DLs) are appropriate, widely used, logics for managing
structured knowledge. They allow reasoning about individuals and concepts, i.e.
set of individuals with common properties. Typically, DLs are limited to
dealing with crisp, well defined concepts. That is, concepts for which the
problem whether an individual is an instance of it is yes/no question. More
often than not, the concepts encountered in the real world do not have a
precisely defined criteria of membership: we may say that an individual is an
instance of a concept only to a certain degree, depending on the individual's
properties. The DLs that deal with such fuzzy concepts are called fuzzy DLs. In
order to deal with fuzzy, incomplete, indeterminate and inconsistent concepts,
we need to extend the fuzzy DLs, combining the neutrosophic logic with a
classical DL. In particular, concepts become neutrosophic (here neutrosophic
means fuzzy, incomplete, indeterminate, and inconsistent), thus reasoning about
neutrosophic concepts is supported. We'll define its syntax, its semantics, and
describe its properties.Comment: 18 pages. Presented at the IEEE International Conference on Granular
Computing, Georgia State University, Atlanta, USA, May 200
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
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
An empirical analysis of terminological representation systems
The family of terminological representation systems has its roots in the representation system KL-ONE. Since the development of this system more than a dozen similar representation systems have been developed by various research groups. These systems vary along a number of dimensions.In this paper, we present the results of an empirical analysis of six such systems. Surprisingly, the systems turned out to be quite diverse leading to problems when transporting knowledge bases from one system to another. Additionally, the runtime performance between different systems and knowledge bases varied more than we expected. Finally, our empirical runtime performance results give an idea of what runtime performance to expect from such representation systems. These findings complement previously reported analytical results about the computational complexity of reasoning in such systems
CTL : a description logic with expressive concrete domains
Compared with frame-based systems, description logics have the advantage of well-defined semantics and powerful inferences. In order to exploit these advantages in technical domains, the ability to use concrete domains is needed, e.g. systems of (in)equalities over (non)linear polynomials to handle physical laws. Existing systems can only cope with comparisons between attributes. We present an approach that considerably improves the expressiveness of the concrete domains. CTL (Configurable (or Constraint-based) Terminological Logic) is based on the ideas presented in [Baader, F. & Hanschke, P. 1991] and [Hanschke, P. 1993]. Concrete domains are realised through a well-defined interface to external algorithms. Constraint Logic Programming (CLP) systems allow us to easily realise a whole range of concrete domains, e.g. over sets of symbols and numbers. In particular, we are able to handle systems of arbitrary linear polynomials. They also enable us to automatically participate in recent and future improvements in the areas of CLP and computer algebra, e.g. systems capable of handling arbitrary non-linear polynomials
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