164 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
Fuzzy Description Logics with General Concept Inclusions
Description logics (DLs) are used to represent knowledge of an application domain and provide standard reasoning services to infer consequences of this knowledge. However, classical DLs are not suited to represent vagueness in the description of the knowledge. We consider a combination of DLs and Fuzzy Logics to address this task. In particular, we consider the t-norm-based semantics for fuzzy DLs introduced by Hájek in 2005. Since then, many tableau algorithms have been developed for reasoning in fuzzy DLs. Another popular approach is to reduce fuzzy ontologies to classical ones and use existing highly optimized classical reasoners to deal with them. However, a systematic study of the computational complexity of the different reasoning problems is so far missing from the literature on fuzzy DLs. Recently, some of the developed tableau algorithms have been shown to be incorrect in the presence of general concept inclusion axioms (GCIs). In some fuzzy DLs, reasoning with GCIs has even turned out to be undecidable. This work provides a rigorous analysis of the boundary between decidable and undecidable reasoning problems in t-norm-based fuzzy DLs, in particular for GCIs. Existing undecidability proofs are extended to cover large classes of fuzzy DLs, and decidability is shown for most of the remaining logics considered here. Additionally, the computational complexity of reasoning in fuzzy DLs with semantics based on finite lattices is analyzed. For most decidability results, tight complexity bounds can be derived
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
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
Gödel Description Logics
In the last few years there has been a large effort for analysing the computational properties of reasoning in fuzzy Description Logics. This has led to a number of papers studying the complexity of these logics, depending on their chosen semantics. Surprisingly, despite being arguably the simplest form of fuzzy semantics, not much is known about the complexity of reasoning in fuzzy DLs w.r.t. witnessed models over the Gödel t-norm. We show that in the logic G-IALC, reasoning cannot be restricted to finitely valued models in general. Despite this negative result, we also show that all the standard reasoning problems can be solved in this logic in exponential time, matching the complexity of reasoning in classical ALC
Consistency in Fuzzy Description Logics over Residuated De Morgan Lattices
Fuzzy description logics can be used to model vague knowledge in application domains. This paper analyses the consistency and satisfiability problems in the description logic SHI with semantics based on a complete residuated De Morgan lattice. The problems are undecidable in the general case, but can be decided by a tableau algorithm when restricted to finite lattices. For some sublogics of SHI, we provide upper complexity bounds that match the complexity of crisp reasoning
A Description Logic Framework for Commonsense Conceptual Combination Integrating Typicality, Probabilities and Cognitive Heuristics
We propose a nonmonotonic Description Logic of typicality able to account for
the phenomenon of concept combination of prototypical concepts. The proposed
logic relies on the logic of typicality ALC TR, whose semantics is based on the
notion of rational closure, as well as on the distributed semantics of
probabilistic Description Logics, and is equipped with a cognitive heuristic
used by humans for concept composition. We first extend the logic of typicality
ALC TR by typicality inclusions whose intuitive meaning is that "there is
probability p about the fact that typical Cs are Ds". As in the distributed
semantics, we define different scenarios containing only some typicality
inclusions, each one having a suitable probability. We then focus on those
scenarios whose probabilities belong to a given and fixed range, and we exploit
such scenarios in order to ascribe typical properties to a concept C obtained
as the combination of two prototypical concepts. We also show that reasoning in
the proposed Description Logic is EXPTIME-complete as for the underlying ALC.Comment: 39 pages, 3 figure
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