90,422 research outputs found
Belief merging within fragments of propositional logic
Recently, belief change within the framework of fragments of propositional
logic has gained increasing attention. Previous works focused on belief
contraction and belief revision on the Horn fragment. However, the problem of
belief merging within fragments of propositional logic has been neglected so
far. This paper presents a general approach to define new merging operators
derived from existing ones such that the result of merging remains in the
fragment under consideration. Our approach is not limited to the case of Horn
fragment but applicable to any fragment of propositional logic characterized by
a closure property on the sets of models of its formulae. We study the logical
properties of the proposed operators in terms of satisfaction of merging
postulates, considering in particular distance-based merging operators for Horn
and Krom fragments.Comment: To appear in the Proceedings of the 15th International Workshop on
Non-Monotonic Reasoning (NMR 2014
Multi-scale initial conditions for cosmological simulations
We discuss a new algorithm to generate multi-scale initial conditions with
multiple levels of refinements for cosmological "zoom-in" simulations. The
method uses an adaptive convolution of Gaussian white noise with a real space
transfer function kernel together with an adaptive multi-grid Poisson solver to
generate displacements and velocities following first (1LPT) or second order
Lagrangian perturbation theory (2LPT). The new algorithm achieves RMS relative
errors of order 10^(-4) for displacements and velocities in the refinement
region and thus improves in terms of errors by about two orders of magnitude
over previous approaches. In addition, errors are localized at coarse-fine
boundaries and do not suffer from Fourier-space induced interference ringing.
An optional hybrid multi-grid and Fast Fourier Transform (FFT) based scheme is
introduced which has identical Fourier space behaviour as traditional
approaches. Using a suite of re-simulations of a galaxy cluster halo our real
space based approach is found to reproduce correlation functions, density
profiles, key halo properties and subhalo abundances with per cent level
accuracy. Finally, we generalize our approach for two-component baryon and
dark-matter simulations and demonstrate that the power spectrum evolution is in
excellent agreement with linear perturbation theory. For initial baryon density
fields, it is suggested to use the local Lagrangian approximation in order to
generate a density field for mesh based codes that is consistent with
Lagrangian perturbation theory instead of the current practice of using the
Eulerian linearly scaled densities.Comment: 22 pages, 24 figures. MNRAS in press. Updated affiliation
A synchronous program algebra: a basis for reasoning about shared-memory and event-based concurrency
This research started with an algebra for reasoning about rely/guarantee
concurrency for a shared memory model. The approach taken led to a more
abstract algebra of atomic steps, in which atomic steps synchronise (rather
than interleave) when composed in parallel. The algebra of rely/guarantee
concurrency then becomes an instantiation of the more abstract algebra. Many of
the core properties needed for rely/guarantee reasoning can be shown to hold in
the abstract algebra where their proofs are simpler and hence allow a higher
degree of automation. The algebra has been encoded in Isabelle/HOL to provide a
basis for tool support for program verification.
In rely/guarantee concurrency, programs are specified to guarantee certain
behaviours until assumptions about the behaviour of their environment are
violated. When assumptions are violated, program behaviour is unconstrained
(aborting), and guarantees need no longer hold. To support these guarantees a
second synchronous operator, weak conjunction, was introduced: both processes
in a weak conjunction must agree to take each atomic step, unless one aborts in
which case the whole aborts. In developing the laws for parallel and weak
conjunction we found many properties were shared by the operators and that the
proofs of many laws were essentially the same. This insight led to the idea of
generalising synchronisation to an abstract operator with only the axioms that
are shared by the parallel and weak conjunction operator, so that those two
operators can be viewed as instantiations of the abstract synchronisation
operator. The main differences between parallel and weak conjunction are how
they combine individual atomic steps; that is left open in the axioms for the
abstract operator.Comment: Extended version of a Formal Methods 2016 paper, "An algebra of
synchronous atomic steps
Twisted actions and regular Fell bundles over inverse semigroups
We introduce a new notion of twisted actions of inverse semigroups and show
that they correspond bijectively to certain regular Fell bundles over inverse
semigroups, yielding in this way a structure classification of such bundles.
These include as special cases all the stable Fell bundles.
Our definition of twisted actions properly generalizes a previous one
introduced by Sieben and corresponds to Busby-Smith twisted actions in the
group case. As an application we describe twisted etale groupoid C*-algebras in
terms of crossed products by twisted actions of inverse semigroups and show
that Sieben's twisted actions essentially correspond to twisted etale groupoids
with topologically trivial twists.Comment: 35 page
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