1,012 research outputs found
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
Infinitely Valued Gödel Semantics for Expressive Description Logics
Fuzzy Description Logics (FDLs) combine classical Description Logics with the semantics of Fuzzy Logics in order to represent and reason with vague knowledge. Most FDLs using truth values from the interval [0; 1] have been shown to be undecidable in the presence of a negation constructor and general concept inclusions. One exception are those FDLs whose semantics is based on the infinitely valued Gödel t-norm (G). We extend previous decidability results for the FDL G-ALC to deal with complex role inclusions, nominals, inverse roles, and qualified number restrictions. Our novel approach is based on a combination of the known crispification technique for finitely valued FDLs and an automata-based procedure for reasoning in G-ALC
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
Bounded Rationality and Heuristics in Humans and in Artificial Cognitive Systems
In this paper I will present an analysis of the impact that the notion of “bounded rationality”,
introduced by Herbert Simon in his book “Administrative Behavior”, produced in the
field of Artificial Intelligence (AI). In particular, by focusing on the field of Automated
Decision Making (ADM), I will show how the introduction of the cognitive dimension into
the study of choice of a rational (natural) agent, indirectly determined - in the AI field - the
development of a line of research aiming at the realisation of artificial systems whose decisions
are based on the adoption of powerful shortcut strategies (known as heuristics) based
on “satisficing” - i.e. non optimal - solutions to problem solving. I will show how the
“heuristic approach” to problem solving allowed, in AI, to face problems of combinatorial
complexity in real-life situations and still represents an important strategy for the design
and implementation of intelligent systems
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
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
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