84 research outputs found
Reasoning about Typicality and Probabilities in Preferential Description Logics
In this work we describe preferential Description Logics of typicality, a
nonmonotonic extension of standard Description Logics by means of a typicality
operator T allowing to extend a knowledge base with inclusions of the form T(C)
v D, whose intuitive meaning is that normally/typically Cs are also Ds. This
extension is based on a minimal model semantics corresponding to a notion of
rational closure, built upon preferential models. We recall the basic concepts
underlying preferential Description Logics. We also present two extensions of
the preferential semantics: on the one hand, we consider probabilistic
extensions, based on a distributed semantics that is suitable for tackling the
problem of commonsense concept combination, on the other hand, we consider
other strengthening of the rational closure semantics and construction to avoid
the so-called blocking of property inheritance problem.Comment: 17 pages. arXiv admin note: text overlap with arXiv:1811.0236
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
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 the 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 of the form
p :: T(C) v D, whose intuitive meaning is that “we believe with degree 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 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 standard Description Logic ALC
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