A Simple Separation Logic

International audience

We present quantitative separation logic (QSL). In contrast to classical separation logic, QSL employs quantities which evaluate to real numbers instead of predicates which evaluate to Boolean values. The connectives of classical separation logic, separating conjunction and separating implication, are lifted from predicates to quantities. This extension is conservative: Both connectives are backward compatible to their classical analogs and obey the same laws, e.g. modus ponens, adjointness, etc. Furthermore, we develop a weakest precondition calculus for quantitative reasoning about probabilistic pointer programs in QSL. This calculus is a conservative extension of both Ishtiaq’s, O’Hearn’s and Reynolds’ separation logic for heap-manipulating programs and Kozen’s / McIver and Morgan’s weakest preexpectations for probabilistic programs. Soundness is proven with respect to an operational semantics based on Markov decision processes. Our calculus preserves O’Hearn’s frame rule , which enables local reasoning. We demonstrate that our calculus enables reasoning about quantities such as the probability of terminating with an empty heap, the probability of reaching a certain array permutation, or the expected length of a list.

Stone-type duality theorems, which relate algebraic and relational/topological models, are important tools in logic because -- in addition to elegant abstraction -- they strengthen soundness and completeness to a categorical equivalence, yielding a framework through which both algebraic and topological methods can be brought to bear on a logic. We give a systematic treatment of Stone-type duality for the structures that interpret bunched logics, starting with the weakest systems, recovering the familiar BI and Boolean BI (BBI), and extending to both classical and intuitionistic Separation Logic. We demonstrate the uniformity and modularity of this analysis by additionally capturing the bunched logics obtained by extending BI and BBI with modalities and multiplicative connectives corresponding to disjunction, negation and falsum. This includes the logic of separating modalities (LSM), De Morgan BI (DMBI), Classical BI (CBI), and the sub-classical family of logics extending Bi-intuitionistic (B)BI (Bi(B)BI). We additionally obtain as corollaries soundness and completeness theorems for the specific Kripke-style models of these logics as presented in the literature: for DMBI, the sub-classical logics extending BiBI and a new bunched logic, Concurrent Kleene BI (connecting our work to Concurrent Separation Logic), this is the first time soundness and completeness theorems have been proved. We thus obtain a comprehensive semantic account of the multiplicative variants of all standard propositional connectives in the bunched logic setting. This approach synthesises a variety of techniques from modal, substructural and categorical logic and contextualizes the "resource semantics" interpretation underpinning Separation Logic amongst them.

\n Belief Revision deals with the problem of how a rational agent should proceed in face of new information. In the AGM paradigm, the most used framework in Belief Revision, given a set of beliefs, there are three possible epistemic changes in relation to a new belief: expansion, contraction and revision. Among them, we are particularly interested in the latter. A revision occurs when an agent receives new information possibly inconsistent with its epistemic state and has to change it in order to accommodate the new belief in a consistent way. However, new information may come as a set of beliefs (instead of a single one), a problem known as Multiple Revision, in which, unlike Iterated Revision, all new pieces of information are processed simultaneously. This thesis starts with a survey on the topic of Multiple Revision. The purpose is to bring and organize the state-of-the-art of the area, showing the different approaches developed since 1988 and the open problems that still exist. After that, different contributions on non-prioritized multiple revision are proposed. One of AGM revision\\'s main properties is success, which guarantees that new information is always accepted by a rational agent, even when it has to give up a reasonable belief previously held. However, in more realistic scenarios, when dealing with a new belief that contradicts previous ones, an agent has the option to reject it, an approach called non-prioritized revision. Among the possible operations for this approach, Choice Revision is the one that deals with the case in which it is enough for the agent to absorb only a subset of the input set. We propose an axiomatic characterization of Choice Multiple Revision through two different constructions: one based on remainder sets and the other on kernel sets, along with algorithms for both of them. The approach was developed for belief bases and is not restricted to classical propositional logic. Still about the possible operations for non-prioritized multiple revision and the option the agent has to accept or reject a new information, Selective Revision came up as a third possibility, allowing the agent to accept only a part of the new belief. The operation was initially defined for single sentences as inputs and for belief sets. This thesis proposes a generalization of Selective Revision to the multiple case for both belief sets (theories) and belief bases. We provide constructions, postulates and representation theorems for different classes of Multiple Selective Revision.\n

In ‘belief revision’ a theory \( \mathcal{K} \) is revised with a formula ϕ resulting in a revised theory \( \mathcal{K}*\phi \). Typically, ¬ϕ is in \( \mathcal{K} \), one has to give up belief in ¬ϕ by a process of retraction, and ϕ is in \( \mathcal{K}*\phi \). We propose to model belief revision in a dynamic epistemic logic. In this setting, we typically have an information state (pointed Kripke model) for the theory \( \mathcal{K} \) wherein the agent believes the negation of the revision formula, i.e., wherein B¬ϕ is true. The revision with ϕ is a program *ϕ that transforms this information state into a new information state. The transformation is described by a dynamic modal operator [*ϕ], that is interpreted as a binary relation 〚*ϕ〛 between information states. The next information state is computed from the current information state and the belief revision formula. If the revision is successful, the agent believes ϕ in the resulting state, i.e., B ϕ is then true. To make this work, as information states we propose ‘doxastic epistemic models’ that represent both knowledge and degrees of belief. These are multi-modal and multi-agent Kripke models. They are constructed from preference relations for agents, and they satisfy various characterizable multi-agent frame properties. Iterated, revocable, and higher-order belief revision are all quite natural in this setting. We present, for an example, five different ways of such dynamic belief revision. One can also see that as a non-deterministic epistemic action with two alternatives, where one is preferred over the other, and there is a natural generalization to general epistemic actions with preferences.

Current and future satellite sensors provide measurements in and around the oxygen A-band on a global basis. These data are commonly used for the determination of cloud and aerosol properties. In this paper, we assess the information content in the oxygen A-band for the retrieval of macrophysical cloud parameters using precise radiative transfer simulations covering a wide range of geophysical conditions in conjunction with advance inversion techniques. The information content of the signal with respect to the retrieved parameters is analyzed in a stochastic framework using two common criteria: the degrees of freedom for a signal and the Shannon information content. It is found that oxygen A-band measurements with moderate spectral resolution (0.2 nm) provide two pieces of independent information that allow the accurate retrieval of cloud-top height together with either cloud optical thickness or cloud fraction. Additionally, our results confirm previous studies indicating that the retrieval of cloud geometrical thickness (CGT) from single-angle measurements is not reliable in this spectral region. Finally, a sensitivity study shows that the retrieval of macrophysical cloud parameters is slightly sensitive to the uncertainty in the CGT and very sensitive to the uncertainty in the surface albedo.

Abstract. In this paper, we analyze the performance of the Infrared Atmospheric Sounding Interferometer (IASI), launched in October 2006 on board METOP-A, for the monitoring of carbon monoxide (CO) during extreme fire events, focusing on the record-breaking fires which devastated thousands of square kilometers of forest in Greece during the last week (23–30) of August 2007. After an assessment of the quality of the profiles retrieved using the Fast Optimal Retrievals on Layers for IASI (FORLI) algorithm, the information provided on fire emissions and subsequent pollution outflow is discussed. Large CO plumes were observed above the Mediterranean Basin and North Africa, with total CO columns exceeding 24×1018 molecules/cm2 and absolute volume mixing ratios up to 4 ppmv on the 25 August. Up to 30×1018 molecules/cm2 and 22 ppmv in the lower troposphere are retrieved close to the fires above the Peloponnese, but with larger uncertainty. The average root-mean-square (RMS) difference between simulated and observed spectra is close to the estimated radiometric noise level, slightly increasing (by ~14%) in the fresh fire plumes. CO profiles are retrieved with a vertical resolution of about 8 km, with ~1.7 pieces of independent information on the vertical in the region considered and a maximum sensitivity in the free troposphere (~4–5 km). Using the integrated total amount, the increase in CO burden due to these fires is estimated to 0.321 Tg, ~40% of the total annual anthropogenic emissions in Greece. The patterns of these CO enhancements are in good agreement with the aerosol optical depth (AOD) retrieved from the MODIS measurements, highlighting a rapid transport of trace gases and aerosols across the Mediterranean Basin (less than one day). While the coarse vertical resolution will not allow the location of the exact plume height, the large CO enhancements observed in the lower troposphere are consistent with the maximum aerosol backscatter coefficient at ~2 km detected by the CALIPSO lidar in space (CALIOP).

The total intensities of the H, K, and infrared triplet lines of the Ca ii atom emitted from a finite uniform plane-parallel atmosphere are calculated for electron temperatures between 4,000°K and 20,000°K, for electron densities between 1010 cm-3 and 1012 cm-3, and for optical thicknesses in the K line between 0.1 and 100. The atmosphere, standing vertically upon the solar surface, is illuminated by the photospheric radiation. In the atmosphere the steady-state equations and the transfer equations in the lines are simultaneously solved by using an iterative method. The effect of the 3D levels upon the intensities of the H and K lines is studied. It is found that their intensities for an atom with the 3D levels are higher than those for an atom without the 3D levels. Hence the absence of the 3D levels leads to an overestimate of one or more among electron temperature, electron density, and optical thickness. The relative intensities of the infrared triplet lines to the K line are sensitive to the optical thickness, and are not sensitive to the electron temperature and density. The total intensity of each line is comparatively sensitive to all the physical parameters. The intensities of lines in each multiplet share an essentially common variation, so that the Ca ii-line intensities can yield us only two pieces of independent information on the physical state of the emitting atmosphere. Comparisons of the calculated intensities with the solar observations show that the Ca ii-line intensities may be used to determine the optical thickness and electron temperature of the emitting atmosphere for any assumed electron density.

Vertically constrained CO2 retrievals from TCCON measurements

Journal Article Dose Evaluation in Fluoroscopy Get access F.R. Verdun, F.R. Verdun Search for other works by this author on: Oxford Academic PubMed Google Scholar P. Capasso, P. Capasso Search for other works by this author on: Oxford Academic PubMed Google Scholar J.-F. Valley, J.-F. Valley Search for other works by this author on: Oxford Academic PubMed Google Scholar P. Schnyder P. Schnyder Search for other works by this author on: Oxford Academic PubMed Google Scholar Radiation Protection Dosimetry, Volume 80, Issue 1-3, 1 November 1998, Pages 139–141, https://doi.org/10.1093/oxfordjournals.rpd.a032488 Published: 01 November 1998

It is widely assumed that party identification and loyalty can distort partisans' information processing, diminishing their receptivity to counter-partisan arguments and evidence. Here we empirically evaluate this assumption. We test whether American partisans' receptivity to arguments and evidence is diminished by countervailing cues from in-party leaders (Donald Trump or Joe Biden), using a survey experiment with 24 contemporary policy issues and 48 persuasive messages containing arguments and evidence (N = 4,531; 22,499 observations). We find that, while in-party leader cues influenced partisans' attitudes, often more strongly than the persuasive messages, there was no evidence that the cues meaningfully diminished partisans' receptivity to the messages-despite them directly contradicting the messages. Rather, persuasive messages and countervailing leader cues were integrated as independent pieces of information. These results generalized across policy issues, demographic subgroups and cue environments, and challenge existing assumptions about the extent to which party identification and loyalty distort partisans' information processing.

Interactive Information Design

On characterizing the error in a remotely sensed liquid water content profile

Pulse width modulation (PWM) is widely used in different applications. PWM transforms the information in the amplitude of a bounded input signal into the pulse width output signal without suffering from quantization noise. The frequency of the output signal is usually constant. In this paper, the new PWM system with frequency changing (PWMFM) is described. In such PWMFM the pulse width and also the carrier frequency are changed. Therefore, two independent pieces of information can be simultaneously transmitted over one channel; hence PWM and frequency modulation (FM) are simultaneously used. But such system needs 2 demodulators, one for PWM and the second for FM. PWMFM can be used in the following applications: LED light intensity control via PWM and several LED block switching by FM PWMFM is highly useful in motor speed control applications by PWM and direction of rotation with FM. PWMFM can be used also in a class-D audio amplifier for power control, e.g. coarse by means of FM and fine by PWM. PWMFM can be used for the simultaneous transmission of two independent information between all, mutual combinations of analog and digital circuits. The analog and digital circuits for modulation and demodulation of PWMF signal are described and measuring results are presented in this work.

Nonstandard Reasoning