1,125 research outputs found
An Optimal Decision Procedure for MPNL over the Integers
Interval temporal logics provide a natural framework for qualitative and
quantitative temporal reason- ing over interval structures, where the truth of
formulae is defined over intervals rather than points. In this paper, we study
the complexity of the satisfiability problem for Metric Propositional Neigh-
borhood Logic (MPNL). MPNL features two modalities to access intervals "to the
left" and "to the right" of the current one, respectively, plus an infinite set
of length constraints. MPNL, interpreted over the naturals, has been recently
shown to be decidable by a doubly exponential procedure. We improve such a
result by proving that MPNL is actually EXPSPACE-complete (even when length
constraints are encoded in binary), when interpreted over finite structures,
the naturals, and the in- tegers, by developing an EXPSPACE decision procedure
for MPNL over the integers, which can be easily tailored to finite linear
orders and the naturals (EXPSPACE-hardness was already known).Comment: In Proceedings GandALF 2011, arXiv:1106.081
Begin, After, and Later: a Maximal Decidable Interval Temporal Logic
Interval temporal logics (ITLs) are logics for reasoning about temporal
statements expressed over intervals, i.e., periods of time. The most famous ITL
studied so far is Halpern and Shoham's HS, which is the logic of the thirteen
Allen's interval relations. Unfortunately, HS and most of its fragments have an
undecidable satisfiability problem. This discouraged the research in this area
until recently, when a number non-trivial decidable ITLs have been discovered.
This paper is a contribution towards the complete classification of all
different fragments of HS. We consider different combinations of the interval
relations Begins, After, Later and their inverses Abar, Bbar, and Lbar. We know
from previous works that the combination ABBbarAbar is decidable only when
finite domains are considered (and undecidable elsewhere), and that ABBbar is
decidable over the natural numbers. We extend these results by showing that
decidability of ABBar can be further extended to capture the language
ABBbarLbar, which lays in between ABBar and ABBbarAbar, and that turns out to
be maximal w.r.t decidability over strongly discrete linear orders (e.g. finite
orders, the naturals, the integers). We also prove that the proposed decision
procedure is optimal with respect to the complexity class
Maximal decidable fragments of Halpern and Shoham's modal logic of intervals
In this paper, we focus our attention on the fragment of
Halpern and Shoham's modal logic of intervals (HS) that
features four modal operators corresponding to the
relations ``meets'', ``met by'', ``begun by'', and
``begins'' of Allen's interval algebra (AAbarBBbar logic).
AAbarBBbar properly extends interesting interval temporal
logics recently investigated in the literature, such as the
logic BBbar of Allen's ``begun by/begins'' relations and
propositional neighborhood logic AAbar, in its many
variants (including metric ones). We prove that the satisfiability
problem for AAbarBBbar, interpreted over finite linear orders,
is decidable, but not primitive recursive (as a matter of fact,
AAbarBBbar turns out to be maximal with respect to decidability). Then, we show that it becomes undecidable when AAbarBBbar is interpreted over classes of linear orders that contains at least one linear order with an infinitely ascending sequence, thus including the natural time flows N, Z, Q, and R
No temperature fluctuations in the giant HII region H 1013
While collisionally excited lines in HII regions allow one to easily probe
the chemical composition of the interstellar medium in galaxies, the possible
presence of important temperature fluctuations casts some doubt on the derived
abundances. To provide new insights into this question, we have carried out a
detailed study of a giant HII region, H 1013, located in the galaxy M101, for
which many observational data exist and which has been claimed to harbour
temperature fluctuations at a level of t^2 = 0.03-0.06. We have first
complemented the already available optical observational datasets with a
mid-infrared spectrum obtained with the Spitzer Space Telescope. Combined with
optical data, this spectrum provides unprecedented information on the
temperature structure of this giant HII region. A preliminary analysis based on
empirical temperature diagnostics suggests that temperature fluctuations should
be quite weak. We have then performed a detailed modelling using the pyCloudy
package based on the photoionization code Cloudy. We have been able to produce
photoionization models constrained by the observed Hb surface brightness
distribution and by the known properties of the ionizing stellar population
than can account for most of the line ratios within their uncertainties. Since
the observational constraints are both strong and numerous, this argues against
the presence of significant temperature fluctuations in H 1013. The oxygen
abundance of our best model is 12 + log O/H = 8.57, as opposed to the values of
8.73 and 8.93 advocated by Esteban et al. (2009) and Bresolin (2007),
respectively, based on the significant temperature fluctuations they derived.
However, our model is not able to reproduce the intensities of the oxygen
recombination lines . This cannot be attributed to observational uncertainties
and requires an explanation other than temperature fluctuations.Comment: accepted in Astronomy & Astrophysic
The structure and dynamics of the AC114 galaxy cluster revisited
We present a dynamical analysis of the galaxy cluster AC114 based on a
catalogue of 524 velocities. Of these, 169 (32%) are newly obtained at ESO
(Chile) with the VLT and the VIMOS spectrograph. Data on individual galaxies
are presented and the accuracy of the measured velocities is discussed.
Dynamical properties of the cluster are derived. We obtain an improved mean
redshift value z= 0.31665 +/- 0.0008 and velocity dispersion \sigma= 1893+73-82
\kms. A large velocity dispersion within the core radius and the shape of the
infall pattern suggests that this part of the cluster is in a radial phase of
relaxation with a very elongated radial filament spanning 12000 \kms. A radial
foreground structure is detected within the central 0.5/h Mpc radius,
recognizable as a redshift group at the same central redshift value. We analyze
the color distribution for this archetype Butcher-Oemler galaxy cluster and
identify the separate red and blue galaxy sequences. The latter subset contains
44% of confirmed members of the cluster, reaching magnitudes as faint as R_{f}=
21.1 (1.0 magnitude fainter than previous studies). We derive a mass M_{200}=
(4.3 \pm 0.7) x 10^15 Msun/h. In a subsequent paper we will utilize the
spectral data presented here to explore the mass-metallicity relation for this
intermediate redshift cluster.Comment: 17 pages, 11 figures, 4 tables, accepted for publication in MNRA
Metal abundances in extremely distant Galactic old open clusters. II. Berkeley 22 and Berkeley 66
We report on high resolution spectroscopy of four giant stars in the Galactic
old open clusters Berkeley~22 and Berkeley~66 obtained with HIRES at the Keck
telescope. We find that and for
Berkeley~22 and Berkeley~66, respectively. Based on these data, we first revise
the fundamental parameters of the clusters, and then discuss them in the
context of the Galactic disk radial abundance gradient. We found that both
clusters nicely obey the most updated estimate of the slope of the gradient
from \citet{fri02} and are genuine Galactic disk objects.Comment: 20 pages, 6 eps figures, accepted for publication in the Astronomical
Journa
Interval temporal logic model checking: The border between good and bad HS fragments
The model checking problem has thoroughly been explored in the context of standard point-based temporal logics, such as LTL, CTL, and CTL 17, whereas model checking for interval temporal logics has been brought to the attention only very recently. In this paper, we prove that the model checking problem for the logic of Allen\u2019s relations started-by and finished-by is highly intractable, as it can be proved to be EXPSPACE-hard. Such a lower bound immediately propagates to the full Halpern and Shoham\u2019s modal logic of time intervals (HS). In contrast, we show that other noteworthy HS fragments, namely, Propositional Neighbourhood Logic extended with modalities for the Allen relation starts (resp., finishes) and its inverse started-by (resp., finished-by), turn out to have\u2014maybe unexpectedly\u2014the same complexity as LTL (i.e., they are PSPACE-complete), thus joining the group of other already studied, well-behaved albeit less expressive, HS fragments
Complete and Terminating Tableau for the Logic of Proper Subinterval Structures over Dense Orderings
We introduce special pseudo-models for the interval logic of proper subintervals over dense linear orderings. We prove finite model property with respect to such pseudo-models, and using that result we develop a decision procedure based on a sound, complete, and terminating tableau for that logic. The case of proper subintervals is essentially more complicated than the case of strict subintervals, for which we developed a similar tableau-based decision procedure in a recent work
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