3,264 research outputs found
Belief as Willingness to Bet
We investigate modal logics of high probability having two unary modal
operators: an operator expressing probabilistic certainty and an operator
expressing probability exceeding a fixed rational threshold . Identifying knowledge with the former and belief with the latter, we may
think of as the agent's betting threshold, which leads to the motto "belief
is willingness to bet." The logic for has an
modality along with a sub-normal modality that extends
the minimal modal logic by way of four schemes relating
and , one of which is a complex scheme arising out of a theorem due to
Scott. Lenzen was the first to use Scott's theorem to show that a version of
this logic is sound and complete for the probability interpretation. We
reformulate Lenzen's results and present them here in a modern and accessible
form. In addition, we introduce a new epistemic neighborhood semantics that
will be more familiar to modern modal logicians. Using Scott's theorem, we
provide the Lenzen-derivative properties that must be imposed on finite
epistemic neighborhood models so as to guarantee the existence of a probability
measure respecting the neighborhood function in the appropriate way for
threshold . This yields a link between probabilistic and modal
neighborhood semantics that we hope will be of use in future work on modal
logics of qualitative probability. We leave open the question of which
properties must be imposed on finite epistemic neighborhood models so as to
guarantee existence of an appropriate probability measure for thresholds
.Comment: Removed date from v1 to avoid confusion on citation/reference,
otherwise identical to v
The story of Oh: the aesthetics and rhetoric of a common vowel sound
Studies in Musical Theatre is the only peer-reviewed journal dedicated to musical theatre. It was launched in 2007 and is now in its seventh volume. It has an extensive international readership and is edited by Dominic Symonds and George Burrows.
This article investigates the use of the ‘word’ ‘Oh’ in a variety of different performance idioms. Despite its lack of ‘meaning’, the sound is used in both conversation and poetic discourse, and I discuss how it operates communicatively and expressively through contextual resonances, aesthetic manipulation and rhetorical signification. The article first considers the aesthetically modernist work of Cathy Berberian in Bussotti’s La Passion Selon Sade; then it considers the rhetorically inflected use of ‘Oh’ to construct social resonance in popular song;finally, it discusses two important uses of the sound ‘Oh’ which bookend the Broadway musical Oklahoma!, serving to consolidate the allegorical and musico-dramatic narrative of the show
Temperature Dependence of the QCD Coupling
We present a one-loop calculation of a gauge invariant QCD beta function.
Using both momentum and temperature renormalization group equations we
investigate the running coupling in the magnetic sector as a function of
temperature and momentum scale. At fixed momentum scale we find that, in
contrast to or QED, high-temperature QCD is strongly coupled,
even after renormalization group improvement. However, if the momentum scale is
changed simultaneously with temperature in a specified manner, the coupling
decreases. We also point out in what regime dimensional reduction occurs. Both
the cases smaller and larger than are discussed.Comment: 10 pages, LaTeX (5 postscript figures available),
ITFA-93-11,THU-93/0
Critical Temperature and Amplitude Ratios from a Finite-Temperature Renormalization Group
We study \l\f^4 theory using an environmentally friendly finite-temperature
renormalization group. We derive flow equations, using a fiducial temperature
as flow parameter, develop them perturbatively in an expansion free from
ultraviolet and infrared divergences, then integrate them numerically from zero
to temperatures above the critical temperature. The critical temperature, at
which the mass vanishes, is obtained by integrating the flow equations and is
determined as a function of the zero-temperature mass and coupling. We
calculate the field expectation value and minimum of the effective potential as
functions of temperature and derive some universal amplitude ratios which
connect the broken and symmetric phases of the theory. The latter are found to
be in good agreement with those of the three-dimensional Ising model obtained
from high- and low-temperature series expansions.Comment: 14 pages of LaTeX. Postscript figures available upon request form
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A generating functional for ultrasoft amplitudes in hot QCD
The effective amplitudes for gluon momentum p<<gT in hot QCD exhibit damping
as a result of collisions. The whole set of n-point amplitudes is shown to be
generated from one functional K(x,y;A), in addition to the induced current
j(x;A).Comment: 7 pages, no figure (some comments added
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