2,382 research outputs found
Dual Logic Concepts based on Mathematical Morphology in Stratified Institutions: Applications to Spatial Reasoning
Several logical operators are defined as dual pairs, in different types of
logics. Such dual pairs of operators also occur in other algebraic theories,
such as mathematical morphology. Based on this observation, this paper proposes
to define, at the abstract level of institutions, a pair of abstract dual and
logical operators as morphological erosion and dilation. Standard quantifiers
and modalities are then derived from these two abstract logical operators.
These operators are studied both on sets of states and sets of models. To cope
with the lack of explicit set of states in institutions, the proposed abstract
logical dual operators are defined in an extension of institutions, the
stratified institutions, which take into account the notion of open sentences,
the satisfaction of which is parametrized by sets of states. A hint on the
potential interest of the proposed framework for spatial reasoning is also
provided.Comment: 36 page
Belief Revision, Minimal Change and Relaxation: A General Framework based on Satisfaction Systems, and Applications to Description Logics
Belief revision of knowledge bases represented by a set of sentences in a
given logic has been extensively studied but for specific logics, mainly
propositional, and also recently Horn and description logics. Here, we propose
to generalize this operation from a model-theoretic point of view, by defining
revision in an abstract model theory known under the name of satisfaction
systems. In this framework, we generalize to any satisfaction systems the
characterization of the well known AGM postulates given by Katsuno and
Mendelzon for propositional logic in terms of minimal change among
interpretations. Moreover, we study how to define revision, satisfying the AGM
postulates, from relaxation notions that have been first introduced in
description logics to define dissimilarity measures between concepts, and the
consequence of which is to relax the set of models of the old belief until it
becomes consistent with the new pieces of knowledge. We show how the proposed
general framework can be instantiated in different logics such as
propositional, first-order, description and Horn logics. In particular for
description logics, we introduce several concrete relaxation operators tailored
for the description logic \ALC{} and its fragments \EL{} and \ELext{},
discuss their properties and provide some illustrative examples
Resonant infiltration of an opal: reflection lineshape and contribution from in-depth regions
We analyze the resonant variation of the optical reflection on an infiltrated
artificial opal made of transparent nanospheres. The resonant infiltration is
considered as a perturbation in the frame of a previously described
one-dimensional model based upon a stratified effective index. We show that for
a thin slice of resonant medium, the resonant response oscillates with the
position of this slice. We derive that for adequate conditions of incidence
angle, this spatially oscillating behavior matches the geometrical periodicity
of the opal, and hence the related density of resonant infiltration. Close to
these matching conditions, the resonant response of the global infiltration
varies sharply in amplitude and shape with the incidence angle and
polarization. The corresponding resonant reflection originates from a rather
deep infiltration, up to several wavelengths or layers of spheres. Finally, we
discuss the relationship between the present predictions and our previous
observations on an opal infiltrated with a resonant vapor.Comment: to appear in J Chem Phy
A 2D nanosphere array for atomic spectroscopy
We are interested in the spectroscopic behaviour of a gas confined in a
micrometric or even nanometric volume. Such a situation could be encountered by
the filling-up of a porous medium, such as a photonic crystal, with an atomic
gas. Here, we discuss the first step of this program, with the generation and
characterization of a self-organized 2D film of nanospheres of silica. We show
that an optical characterization by laser light diffraction permits to extract
some information on the array structure and represents an interesting
complement to electron microscopy.Comment: accept\'e pour publication \`a Annales de Physique- proceedings of
COLOQ1
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