The Universe of Approximations

AbstractThe idea of approximate entailment has been in [13] as a way of modeling the reasoning of an agent with limited resources. They proposed a system in which a family of logics, parameterized by a set of propositional letters, approximates classical logic as the size of the set increases.In this paper, we take the idea further, extending two of their systems to deal with full propositional logic, giving them semantics and sound and complete proof methods based on tableaux. We then present a more general system of which the two previous systems are particular cases and show how it can be used to formalize heuristics used in theorem proving

A conditional perspective of belief revision

Belief Revision is a subarea of Knowledge Representation and Reasoning (KRR) that investigates how to rationally revise an intelligent agent's beliefs in response to new information. There are several approaches to belief revision, but one well-known approach is the AGM model, which is rooted in work by Alchourrón, Gärdenfors, and Makinson. This model provides a set of axioms defining desirable properties of belief revision operators, which manipulate the agent's belief set represented as a set of propositional formulas. A famous extension to the classical AGM framework of Belief Revision is Darwiche and Pearl's approach to iterated belief revision. They uncovered that the key to rational behavior under iteration is adequate preservation of conditional beliefs, i.e., beliefs the agent is willing to accept in light of (hypothetical) new information. Therefore, they introduced belief revision operators modifying the agent's belief state, built from conditional beliefs. Kern-Isberner fully axiomatized a principle of conditional preservation for belief revision, which captures the core of adequate treatment of conditional beliefs during the revision. This powerful axiom provides the necessary conceptual framework for revising belief states with sets of conditionals as input, and it shows that conditional beliefs are subtle but essential for studying the process of belief revision. This thesis provides a conditional perspective of Belief Revision for different belief revision scenarios. In the first part, we introduce and investigate a notion of locality for belief revision operators on the semantic level. Hence, we exploit the unique features of conditionals, which allow us to set up local cases and revise according to these cases, s.t., the complexity of the revision task is reduced significantly. In the second part, we consider the general setting of belief revision with respect to additional meta-information accompanying the input information. We demonstrate the versatility and flexibility of conditionals as input for belief revision operators by reducing the parameterized input to a conditional one for two well-known parameterized belief revision operators who are similarly motivated but very different in their technical execution. Our results show that considering conditional beliefs as input for belief revision operators provides a gateway to new insights into the dynamics of belief revision

Optimal Sensor Allocation for Fault Detection and Isolation

Automatic fault diagnostic schemes rely on various types of sensors (e.g., temperature, pressure, vibration, etc) to measure the system parameters. Efficacy of a diagnostic scheme is largely dependent on the amount and quality of information available from these sensors. The reliability of sensors, as well as the weight, volume, power, and cost constraints, often makes it impractical to monitor a large number of system parameters. An optimized sensor allocation that maximizes the fault diagnosibility, subject to specified weight, volume, power, and cost constraints is required. Use of optimal sensor allocation strategies during the design phase can ensure better diagnostics at a reduced cost for a system incorporating a high degree of built-in testing. In this paper, we propose an approach that employs multiple fault diagnosis (MFD) and optimization techniques for optimal sensor placement for fault detection and isolation (FDI) in complex systems. Keywords: sensor allocation, multiple fault diagnosis, Lagrangian relaxation, approximate belief revision, multidimensional knapsack problem

Advanced optimization techniques with applications to organizational design and graph-based inference

This dissertation is divided into two parts: (i) modeling and the concomitant optimization algorithms for designing Command & Control ( C2) organizations; and (ii) disease diagnosis and discovering organizational networks and their processes from noisy observations (i.e., negative /positive findings, or uncertain message data) using inference techniques from graphical models. In the first part, we seek to design organizational (C2) structures with the ability to conduct dynamic action synchronization, achieve organization agility, and increase speed of command over a robust, decentralized architecture. The key components to design and evaluation of C2 organizational structure are: (i) mathematical modeling of the mission and organization and explicitly formulating the design optimization problem; (ii) develop algorithms for finding the optimal or near-optimal design. The search space of the optimization problem is very high-dimensional with discrete and continuous attributes. The shape of the high-dimensional surface that corresponds to the optimized function is usually very complex. The focus of this part of the dissertation is to provide mathematical modeling of missions and organizations, and to develop systematic procedures based on evolutionary algorithm (EA), specifically nested genetic algorithm (GA) and multi-objective EA, for designing organizations. The following three topics will be addressed: (1) explore various command & control organization models, i.e., hierarchy, heterarchy, and holarchy; (2) obtain congruent heterarchical organizational structures by applying concepts from group technology; (3) achieve flexibility of holonic structure and the concomitant distributed scheduling scheme by employing multiple objective optimization techniques. ^ In the second part of the thesis, we extend our optimization techniques to inference in network models. The networks include a QMR-DT (Quick Medical Reference-Decision Theoretic) network,1 where identifying the correct diagnoses is hard due to its large and loopy structure. A computationally efficient algorithm is developed to achieve fast inference in a QMR-DT network. Probabilistic graphical models and computationally efficient solution methods are also developed to discover C 2 organizational structures from noisy observations that include activities, communications and command decisions. The contributions of this part of the thesis are the following: (a) Lagrangian Relaxation Algorithm ( LRA) generates an upper bound for the objective function by relaxing the original problem via a set of Lagrange multipliers. The near-optimal diagnosis (configuration) is found by minimizing the duality gap via a subgradient method. (b) Approximate belief revision (ABR) algorithm, incorporating mean field theory and a novel message-passing mechanism, estimates the beliefs (pseudo marginal posterior probabilities) for each disease of interest; (c) A Hidden Markov Random Field (HMRF) model and a graph matching algorithm are employed to discover the attributes of and relationships among organizational members, assets, environment areas, and mission tasks. The focus is on identifying the mapping between a set of hypothesized networks and the observed data, and selecting the maximum a posteriori hypothesis as the matching network. ^ 1The QMR-DT network [82] is a large two-level (or bi-partite) graph model based on expert and statistical knowledge in internal medicine.