Vaishak Belle

Randomized trees for real-time one-step face detection and recognition

We present a system for detecting and recognizing faces in images in real-time which is able to learn new identities in instants. In mobile service robotics, interaction with persons is becoming increasingly important, real-time performance is required and the introduction of new persons is a necessary feature for many applications. Although face detection and face recognition are well studied, only a few papers address both problems jointly and only few systems are able to learn to identify new persons quickly. To achieve real-time performance on modest computing hardware, we use random forests for both detection and recognition, and compare with well-known techniques such as boosted face detection and support vector machines for identification. Results are presented on different datasets and compare favorably well to competitive methods.

Robot location estimation in the situation calculus

Location estimation is a fundamental sensing task in robotic applications, where the world is uncertain, and sensors and effectors are noisy. Most systems make various assumptions about the dependencies between state variables, and especially about how these dependencies change as a result of actions. Building on a general framework by Bacchus, Halpern and Levesque for reasoning about degrees of belief in the situation calculus, and a recent extension to it for continuous probability distributions, in this paper we illustrate location estimation in the presence of a rich theory of actions using examples. The formalism also allows specifications with incomplete knowledge and strict uncertainty, as a result of which the agents initial beliefs need not be characterized by a unique probability distribution. Finally, we show that while actions might affect prior distributions in nonstandard ways, suitable posterior beliefs are nonetheless entailed as a side-effect of the overall specification.

On progression and query evaluation in first-order knowledge bases with function symbols

In a seminal paper, Lin and Reiter introduced the notion of progression of basic action theories. Unfortunately, progression is second-order in general. Recently, Liu and Lakemeyer improve on earlier results and show that for the local-effect and normal actions case, progression is computable but may lead to an exponential blow-up. Nevertheless, they show that for certain kinds of expressive first-order knowledge bases with disjunctive information, called proper, it is efficient. However, answering queries about the resulting state is still undecidable. In this paper, we continue this line of research and extend proper KBs to include functions. We prove that their progression wrt local-effect, normal actions, and range-restricted theories, is first-order definable and efficiently computable. We then provide a new logically sound and complete decision procedure for certain kinds of queries.

Semantical considerations on multiagent only knowing

Abstract Levesque introduced the notion of “only knowing” to precisely capture the beliefs of a knowledge base. He also showed how only knowing can be used to formalize nonmonotonic behavior within a monotonic logic. Levesques logic only deals with a single agent, and therefore, a number of attempts have been made to generalize only knowing to the many agent case. However, all these attempts have some undesirable features. Most significantly, these attempts are propositional and it is not clear how they are to be extended to the first-order case. In this work, we propose a new semantical account of multiagent only knowing which, for the first time, has a natural possible-world semantics for a quantified language with equality. Among other things, properties about Levesques logic generalize faithfully to the many agent case with this account. For the propositional fragment, we also provide a sound and complete axiomatization. Finally, we obtain a multiagent first-order version of the nonmonotonicity exhibited by the logic of only knowing.

A Logical Theory of Localization

A central problem in applying logical knowledge representation formalisms to traditional robotics is that the treatment of belief change is categorical in the former, while probabilistic in the latter. A typical example is the fundamental capability of localization where a robot uses its noisy sensors to situate itself in a dynamic world. Domain designers are then left with the rather unfortunate task of abstracting probabilistic sensors in terms of categorical ones, or more drastically, completely abandoning the inner workings of sensors to black-box probabilistic tools and then interpreting their outputs in an abstract way. Building on a first-principles approach by Bacchus, Halpern and Levesque, and a recent continuous extension to it by Belle and Levesque, we provide an axiomatization that shows how localization can be realized wrt a basic action theory, thereby demonstrating how such capabilities can be enabled in a single logical framework. We then show how the framework can also enable localization for multiple agents, where an agent can appeal to the sensing already performed by another agent and the knowledge of their relative positions to localize itself.

Multiagent only knowing in dynamic systems

The idea of only knowing a collection of sentences, as proposed by Levesque, has been previously shown to be very useful in characterizing knowledge-based agents: in terms of a specification, a precise and perspicuous account of the beliefs and non-beliefs is obtained in a monotonic setting. Levesques logic is based on a first-order modal language with quantifying-in, thus allowing for de re versus de dicto distinctions, among other things. However, the logic and its recent dynamic extension only deal with the case of a single agent. In this work, we propose a first-order multiagent framework with knowledge, actions, sensing and only knowing, that is shown to inherit all the features of the single agent version. Most significantly, we prove reduction theorems by means of which reasoning about knowledge and actions in the framework simplifies to non-epistemic, non-dynamic reasoning about the initial situation.

On the projection problem in active knowledge bases with incomplete information

The problem of projection has been identified as a fundamental reasoning concern in dynamical domains, where we are to determine whether or not some conditions will hold after a sequence of actions has been performed starting in some initial state. Solving the problem requires, at the very least, effectively reasoning about how actions transform the world, and inferring the logical consequences of the initial knowledge base (KB). For various reasons, tractability one of them, applications often make the closed-world assumption, thereby limiting the scope of these systems for the real world. In this thesis, using the language of the situation calculus, we investigate the computational properties of a number of unsolved reasoning tasks in the context of projection with incomplete information. We first look at inherently incomplete KBs, where the information provided to the agent may not determine every fact about the world. Projection, then, may involve reasoning about what is believed and also, about what is not believed. We then look at physical agents with unreliable hardware, as a result of which actions lead to certain kinds of incomplete knowledge. Intuitively, beliefs should be (periodically) synchronized with this noise. Finally, we consider the presence of other agents in the environment, whose beliefs may differ arbitrarily, and the formalism should incorporate what others sense and learn during actions. To enable a precise mathematical treatment of incomplete KBs, we appeal to a seminal proposal by Levesque, called only knowing. Building on existing work, we investigate projection wrt extensions to the situation calculus for only knowing, noisy hardware and multiple agents. Our central contribution will be to show that, in spite of the additional expressivity, reasoning about knowledge and action reduces to nonepistemic non-dynamic reasoning about the initial KB. More precisely, we show that when the initial KB is an arbitrary first-order theory, we are able to identify conditions under which projection can be solved by progressing the KB to a sentence reflecting the changes due to actions that have already occurred. Moreover, when effectors are unreliable, we allow the system to maintain probabilistic beliefs and then show how projection can be addressed by means of updating these beliefs. Finally, when there are many agents in the picture, we show that queries about the future can be resolved by regressing the query backwards to a formula about the initial KB. Only knowing comes with a significant result that allows us to reduce queries about knowledge to first-order theorem-proving tasks, which is then made use of when solving projection.

Review of programming with higher-order logic by Dale Miller and Gopalan Nadathur

Formal models of systems in computer science typically involve specifications over syntactic structures, such as formulas in a logic, λ-terms, π-calculus expressions, among others. Logic programming is one way to realize these specifications and studying such models; Prolog, for example, is an important logic programming language heavily used in declarative frameworks in computer science. This book presents deep techniques that take the many ideas at the heart of Prolog, and extend its power and expressivity by elegantly combining these ideas with a simply typed version of higher-order logic. The end result is a rich programming language, called λProlog, that benefits from the paradigms of higher-order logic and logic programming. The technical material in the book is perhaps most readily accessible to readers familiar with Prolog and aspects of functional programming. That is, the book does not deal with introductory material on either of these topics. The proof-theoretic framework used to justify the various derivation rules also require readers to be familiar with logic.

Review of from zero to infinity: what makes numbers interesting by Constance Reid

It would be difficult for anyone to be more profoundly interested in anything than I am in the theory of primes. G. H. Hardy (see book). From Zero to Infinity by Constance Reid has been inspiring the mathematically keen for over 50 years now. Written in informal style, the book offers an introduction to the beauty of natural numbers. It is organized into 12 chapters, with a chapter each for the first ten natural numbers. A special chapter is dedicated to the Euler identity, and another one to Aleph-0. Tracing the discovery of the numbers, the chapters expand upon features and facts, all of which tells us why these numbers are interesting. While perhaps many of such facts can be found in elementary undergraduate texts, it nonetheless attempts a holistic picture describing relations between prime, composite, perfect, rational and irrational numbers. As the author explains in the preface, the book has a story. The advent of computers enabled the discovery of a new set of perfect numbers, which started the chapters. While it may be hard to imagine how a whole chapter could be written about the most common of numbers, the author does so in a very satisfactory manner. The chapters usually end with some notes, open problems and hints about these problems. The reader is often encouraged to tackle them, and not all are that elementary! The discovery of “0” is perhaps well known. It is also known that it serves as an important identity. The chapter introduces the modern positional notation, and goes to explain why this number is so important. Chapter “1” serves to form the foundation of natural numbers, via addition, and also enables discussions about factorization. Chapter “2” not surprisingly speaks of the binary notation, its significance and introduces a novice reader to binary addition and multiplication. Chapter “3” talks about primes and chapter “4”