On the Logic of Belief and Propositional Quantification

We consider extending the modal logic KD45, commonly taken as the baseline system for belief, with propositional quantifiers that can be used to formalize natural language sentences such as “everything I believe is true” or “there is some-thing that I neither believe nor disbelieve.” Our main results are axiomatizations of the logics with propositional quantifiers of natural classes of complete Boolean algebras with an operator (BAOs) validating KD45. Among them is the class of complete, atomic, and completely multiplicative BAOs validating KD45. Hence, by duality, we also cover the usual method of adding propositional quantifiers to normal modal logics by considering their classes of Kripke frames. In addition, we obtain decidability for all the concrete logics we discuss

Satellite-based Cloud Remote Sensing: Fast Radiative Transfer Modeling and Inter-Comparison of Single-/Multi-Layer Cloud Retrievals with VIIRS

This dissertation consists of three parts, each of them, progressively, contributing to the problem of great importance that satellite-based remote sensing of clouds. In the first section, we develop a fast radiative transfer model specialized for Visible Infrared Imaging Radiometer Suite (VIIRS), based on the band-average technique. VIIRS, is a passive sensor flying aboard the NOAA’s Suomi National Polar-orbiting Partnership (NPP) spacecraft. This model successfully simulates VIIRS solar and infrared bands, in both moderate (M-bands) and imagery (I-bands) spatial resolutions. Besides, the model is two orders of magnitude faster than Line-by-line & discrete ordinate transfer (DISORT) method with a great accuracy. The second and third parts are going to investigate the retrieval of single-/multi- layer cloud optical properties, especially, cloud optical thickness (τ) and cloud effective particle size (De) with different methods. By presenting the comparison between results derived from VIIRS measurements and benchmark products, potential applications of Bayesian and OE retrieval methods for cloud property retrieval are discussed. It has proved that Bayesian method is more suitable for single-layer scenarios with fewer variables with fast speed, while Optimal Estimation method is superior to Bayesian method for more complicated multi-layer scenarios

On the Logics with Propositional Quantifiers Extending S5Π

Scroggs's theorem on the extensions of S5 is an early landmark in the modern mathematical studies of modal logics. From it, we know that the lattice of normal extensions of S5 is isomorphic to the inverse order of the natural numbers with infinity and that all extensions of S5 are in fact normal. In this paper, we consider extending Scroggs's theorem to modal logics with propositional quantifiers governed by the axioms and rules analogous to the usual ones for ordinary quantifiers. We call them Π-logics. Taking S5Π, the smallest normal Π-logic extending S5, as the natural counterpart to S5 in Scroggs's theorem, we show that all normal Π-logics extending S5Π are complete with respect to their complete simple S5 algebras, that they form a lattice that is isomorphic to the lattice of the open sets of the disjoint union of two copies of the one-point compactification of N, that they have arbitrarily high Turing-degrees, and that there are non-normal Π-logics extending S5Π

Logics of Imprecise Comparative Probability

This paper studies connections between two alternatives to the standard probability calculus for representing and reasoning about uncertainty: imprecise probability andcomparative probability. The goal is to identify complete logics for reasoning about uncertainty in a comparative probabilistic language whose semantics is given in terms of imprecise probability. Comparative probability operators are interpreted as quantifying over a set of probability measures. Modal and dynamic operators are added for reasoning about epistemic possibility and updating sets of probability measures

Tight Bounds for The Price of Fairness

A central decision maker (CDM), who seeks an efficient allocation of scarce resources among a finite number of players, often has to incorporate fairness criteria to avoid unfair outcomes. Indeed, the Price of Fairness (POF), a term coined in Bertsimas et al. (2011), refers to the efficiency loss due to the incorporation of fairness criteria into the allocation method. Quantifying the POF would help the CDM strike an appropriate balance between efficiency and fairness. In this paper we improve upon existing results in the literature, by providing tight bounds for the POF for the proportional fairness criterion for any $n$, when the maximum achievable utilities of the players are equal or are not equal. Further, while Bertsimas et al. (2011) have already derived a tight bound for the max-min fairness criterion for the case that all players have equal maximum achievable utilities, we also provide a tight bound in scenarios where these utilities are not equal. Finally, we investigate the sensitivity of our bounds and Bertsimas et al. (2011) bounds for the POF to the variability of the maximum achievable utilities

PMP: Privacy-Aware Matrix Profile against Sensitive Pattern Inference

Recent rapid development of sensor technology has allowed massive fine-grained time series (TS) data to be collected and set the foundation for the development of data-driven services and applications. During the process, data sharing is often involved to allow the third-party modelers to perform specific time series data mining (TSDM) tasks based on the need of data owner. The high resolution of TS brings new challenges in protecting privacy. While meaningful information in high-resolution TS shifts from concrete point values to local shape-based segments, numerous research have found that long shape-based patterns could contain more sensitive information and may potentially be extracted and misused by a malicious third party. However, the privacy issue for TS patterns is surprisingly seldom explored in privacy-preserving literature. In this work, we consider a new privacy-preserving problem: preventing malicious inference on long shape-based patterns while preserving short segment information for the utility task performance. To mitigate the challenge, we investigate an alternative approach by sharing Matrix Profile (MP), which is a non-linear transformation of original data and a versatile data structure that supports many data mining tasks. We found that while MP can prevent concrete shape leakage, the canonical correlation in MP index can still reveal the location of sensitive long pattern. Based on this observation, we design two attacks named Location Attack and Entropy Attack to extract the pattern location from MP. To further protect MP from these two attacks, we propose a Privacy-Aware Matrix Profile (PMP) via perturbing the local correlation and breaking the canonical correlation in MP index vector. We evaluate our proposed PMP against baseline noise-adding methods through quantitative analysis and real-world case studies to show the effectiveness of the proposed method