Rajiv Bagai

A paraconsistent relational data model

We present a generalisation of the relational data model based on a 4-valued paraconsistent logic. Our data model is capable of manipulating incomplete as well as inconsistent information. For this model, we define algebraic operators that are generalisations of the usual operators, such as union, selection, join, on ordinary relations. Our data model can underlie any database management system that deals with incomplete or inconsistent information. As another application of our model and its algebra, we present a bottom-up method for constructing the weak well-founded model of general deductive databases. This method can be very simply extended to construct the well-founded model.

Bottom-up computation of the Fitting model for general deductive databases

General logic programs are those that contain both positive and negative subgoals in their clause bodies. For such programs Fitting proposed an elegant 3-valued minimum model semantics that avoids some impracticalities of previous approaches. Here we present a method to compute this Fitting model for deductive databases. We introducepartial relations, which are the semantic objects associated with predicate symbols, and define algebraic operators over them. The first step in our model computation method is to convert the database rules into partial relation definitions involving these operators. The second step is to build the minimum model iteratively. We give algorithms for both steps and show their termination and correctness. We also suggest extensions to our method for computing the well-founded model proposed by van Gelder, Ross and Schlipf.

An accurate system-wide anonymity metric for probabilistic attacks

We give a critical analysis of the system-wide anonymity metric of Edman et al. [3], which is based on the permanent value of a doubly-stochastic matrix. By providing an intuitive understanding of the permanent of such a matrix, we show that a metric that looks no further than this composite value is at best a rough indicator of anonymity. We identify situations where its inaccuracy is acute, and reveal a better anonymity indicator. Also, by constructing an information-preserving embedding of a smaller class of attacks into the wider class for which this metric was proposed, we show that this metric fails to possess desirable generalization properties. Finally, we present a new anonymity metric that does not exhibit these shortcomings. Our new metric is accurate as well as general.

Automatic Theorem Generation in Plane Geometry

We introduce a conceptual framework for discovery of theorems in geometry and a mechanism which systematically discovers such theorems. Our mechanism incrementally generates geometrical situations, makes conjectures about them, uses a geometry theorem prover to determine the consistency of situations, and keeps valid conjectures as theorems. We define geometry situations, situation descriptions, theorems, and their relationships important to understand our discovery task. An exhaustive generator of situation descriptions has enormous combinatorial complexity. We analyze various ways to reduce that complexity. Ideally, the generator should create a single description of each situation, should generate more general situations before more specific ones, and should use the previously discovered theorems to constrain its generation mechanism. We describe our generator which possesses most of these properties, and we outline further improvements. Our theorem prover is based on Wus algebraic method for proving geometry theorems. We discuss the interface between our situation generator and theorem prover and the limitations of our discovery system. Examples of theorems discovered by our system are also presented.

Declarative Object-Oriented Programming: Inheritance, Subtyping and Prototyping

A design and implementation of a declarative object-oriented language is presented. The language is strongly and mostly statically typed and supports software reuse techniques such as inheritance, subtype and parametric polymorphism. It differs significantly from the existing strongly typed object-oriented languages in its declarative constraint language which is based on a suitably extended logic programming paradigm. Behavioral subtyping and advanced polymorphic facilities (such as, for example, F-bounded polymorphism) now fit naturally into this general paradigm. The underlying implementation technique produces a powerful prototyping tool for object-oriented software development and generalizes logic programming architectures by an algebraic automata based model for representing object states and state transitions.

COMPUTING THE WELL-FOUNDED MODEL OF DEDUCTIVE DATABASES

The well-founded model is one of the most popular models of general logic programs, i.e. logic programs with negation in the bodies of clauses. We present a method for constructing this model for general deductive databases, which are logic programs without any function symbols. The method adopts paraconsistent relations as the semantic objects associated with the predicate symbols of the database. Paraconsistent relations are a generalization of ordinary relations in that they allow manipulation of incomplete as well as inconsistent information. The first step in the model construction method is to transform the database clauses into paraconsistent relation definitions involving these operators. The second step is to build the well-founded model iteratively. Algorithms for both steps are presented and their termination and correctness is also established.

Data Caching for Enhancing Anonymity

The benefits of caching for reducing access time to frequently needed data, in order to improve system performance, are already well-known. In this paper, a proposal for employing data caching for increasing the level of anonymity provided by an anonymity system is presented. This technique is especially effective for user sessions containing bidirectional communication, such as anonymous web browsing. A framework is first constructed for capturing the effect of attacks on anonymity systems that have the ability to serve some incoming user requests from their cache. A system-wide metric is then presented for measuring the anonymity provided by such systems. It is shown that the anonymity level of such systems rises with the amount of data caching performed by them. This behavior is illustrated in an example threshold mix network.

Data preservation in intermittently connected sensor networks with data priority

Data generated in sensor networks may have different importance and priority. Different types of data contribute differently for scientists to analyze the physical environment. In a challenging environment, wherein sensor nodes do not always have connected paths to the base station, and not all the data can be preserved inside the network due to severe energy constraints and storage constraints at sensor nodes, how to preserve data with maximum priority is a new and challenging problem. In this paper, we study how to preserve data that yield maximum total priorities, under the constraints that each sensor node has limited energy level and storage capacity. We design an efficient optimal algorithm and prove its optimality. The core of the problem is a maximum weighted flow problem, which is to maximize the total weight of flow in the network considering different flows have different weights. Maximum weighted flow is a generalization of the classic maximum flow problem, wherein each unit of flow has the same weight. To the best of our knowledge, our work is the first to study and solve the maximum weighted flow problem. We propose a more time efficient heuristic algorithm. Via simulation, we show that it performs comparably to the optimal algorithm and performs better than the classic maximum flow algorithm, which does not consider data priority. Finally we design a distributed data preservation algorithm based on push-relabel algorithm, analyze its time and message complexities, and empirically show that it outperforms the push-relabel distributed maximum flow algorithm in terms of the total preserved priorities.

A three dimensional sender anonymity metric

Measuring the degree of anonymity provided by various anonymous systems on the web, is a challenging task. We first illustrate using examples that existing measures in literature are not sufficient to fully characterise the anonymity provided by a system. We then propose a new isolation measure, based upon outliers in a distribution, and show that this measure is critical towards quantifying the overall anonymity level. We provide justification for three distinct aspects of anonymity, important from the perspectives of a user, a system designer, and an attacker, leading to a three-dimensional approach towards measuring sender anonymity. We outline various properties of the proposed three-dimensional metric and illustrate how the metric, along with adjustable weights, can be used to compare different anonymous systems. Finally, we apply the proposed metric to existing anonymous systems and discuss insights which should prove useful in the design of future anonymous systems.

On the Sender Cover Traffic Countermeasure against an Improved Statistical Disclosure Attack

The Statistical Disclosure Attack against a particular user of an anonymity system is known to be very effective in determining, after long-term observation of the system, the set of receivers that user sends messages to. This paper first presents an improvement over this attack that, by employing a weighted mean of the observed relative receiver popularity, is more accurate than the original one based upon arithmetic mean. Second, a mathematical analysis is presented of this attack on a model, in which senders blend dummy messages with real ones. It is shown that despite such sender-generated dummy cover traffic, the attack can proceed almost unhindered. The analysis substantiates earlier empirical indications of the ineffectiveness of this countermeasure.