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

Possibilistic and fuzzy multi-sensor fusion for humanitarian mine action

Non

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