3,102 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
Public Employees\u27 Right to Strike
In a society which demands constantly increased services from its government, work stoppages in the public sector are cause for growing concern. Public employees are involved in myriad of service jobs. Yet, public employees are the largest group of employees in Ohio who lack basic labor rights
Mechanical Copying, Copyright Law, and the Teacher
This article deals with the infringement problems encountered by a teacher in duplicating copyrighted material for his class. Since the teacher is the real party in interest, we have attempted to avoid legalistic language (at least without explanation), so as to produce a paper to which the layman, as well as the lawyer may turn for understanding
Mechanical Copying, Copyright Law, and the Teacher
This article deals with the infringement problems encountered by a teacher in duplicating copyrighted material for his class. Since the teacher is the real party in interest, we have attempted to avoid legalistic language (at least without explanation), so as to produce a paper to which the layman, as well as the lawyer may turn for understanding
Coherent light scattering from a two-dimensional Mott insulator
We experimentally demonstrate coherent light scattering from an atomic Mott
insulator in a two-dimensional lattice. The far-field diffraction pattern of
small clouds of a few hundred atoms was imaged while simultaneously laser
cooling the atoms with the probe beams. We describe the position of the
diffraction peaks and the scaling of the peak parameters by a simple analytic
model. In contrast to Bragg scattering, scattering from a single plane yields
diffraction peaks for any incidence angle. We demonstrate the feasibility of
detecting spin correlations via light scattering by artificially creating a
one-dimensional antiferromagnetic order as a density wave and observing the
appearance of additional diffraction peaks.Comment: 4 pages, 4 figure
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