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

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 $[Fe/H]=-0.32\pm0.19$ and $[Fe/H]=-0.48\pm0.24$ 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

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

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