Studies in the Logic of Explanatory Power

Human reasoning often involves explanation. In everyday affairs, people reason to hypotheses based on the explanatory power these hypotheses afford; I might, for example, surmise that my toddler has been playing in my office because I judge that this hypothesis delivers a good explanation of the disarranged state of the books on my shelves. But such explanatory reasoning also has relevance far beyond the commonplace. Indeed, explanatory reasoning plays an important role in such varied fields as the sciences, philosophy, theology, medicine, forensics, and law.This dissertation provides an extended study into the logic of explanatory reasoning via two general questions. First, I approach the question of what exactly we have in mind when we make judgments pertaining to the explanatory power that a hypothesis has over some evidence. This question is important to this study because these are the sorts of judgments that we constantly rely on when we use explanations to reason about the world. Ultimately, I introduce and defend an explication of the concept of explanatory power in the form of a probabilistic measure. This formal explication allows us to articulate precisely some of the various ways in which we might reason explanatorily.The second question this dissertation examines is whether explanatory reasoning constitutes an epistemically respectable means of gaining knowledge. I defend the following ideas: The probability theory can be used to describe the logic of explanatory reasoning, the normative standard to which such reasoning attains. Explanatory judgments, on the other hand, constitute heuristics that allow us to approximate reasoning in accordance with this logical standard while staying within our human bounds. The most well known model of explanatory reasoning, Inference to the Best Explanation, describes a cogent, nondeductive inference form. And reasoning by Inference to the Best Explanation approximates reasoning directly via the probability theory in the real world. Finally, I respond to some possible objections to my work, and then to some more general, classic criticisms of Inference to the Best Explanation. In the end, this dissertation puts forward a clearer articulation and novel defense of explanatory reasoning

Interval-based uncertain reasoning

This thesis examines three interval based uncertain reasoning approaches: reasoning under interval constraints, reasoning using necessity and possibility functions, and reasoning with rough set theory. In all these approaches, intervals are used to characterize the uncertainty involved in a reasoning process when the available information is insufficient for single-valued truth evaluation functions. Approaches using interval constraints can be applied to both interval fuzzy sets and interval probabilities. The notion of interval triangular norms, or interval t-norms for short, is introduced and studied in both numeric and non-numeric settings. Algorithms for computing interval t-norms are proposed. Basic issues on the use of t-norms for approximate reasoning with interval fuzzy sets are studied. Inference rules for reasoning under interval constraints are investigated. In the second approach, a pair of necessity and possibility functions is used to bound the fuzzy truth values of propositions. Inference in this case is to narrow the gap between the pair of the functions. Inference rules are derived from the properties of necessity and possibility functions. The theory of rough sets is used to approximate truth values of propositions and to explore modal structures in many-valued logic. It offers an uncertain reasoning method complementary to the other two

Quick and energy-efficient Bayesian computing of binocular disparity using stochastic digital signals

Reconstruction of the tridimensional geometry of a visual scene using the binocular disparity information is an important issue in computer vision and mobile robotics, which can be formulated as a Bayesian inference problem. However, computation of the full disparity distribution with an advanced Bayesian model is usually an intractable problem, and proves computationally challenging even with a simple model. In this paper, we show how probabilistic hardware using distributed memory and alternate representation of data as stochastic bitstreams can solve that problem with high performance and energy efficiency. We put forward a way to express discrete probability distributions using stochastic data representations and perform Bayesian fusion using those representations, and show how that approach can be applied to diparity computation. We evaluate the system using a simulated stochastic implementation and discuss possible hardware implementations of such architectures and their potential for sensorimotor processing and robotics.Comment: Preprint of article submitted for publication in International Journal of Approximate Reasoning and accepted pending minor revision

Approximate Reasoning with Fuzzy Booleans

This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp antecedents; in case of fuzzy booleans this set contains only two rules. It is shown that Zadeh's extension principle is equivalent to the compositional rule of inference using a complete set of fuzzy rules with singleton crisp antecedents. The results are applied to describe the use of approximate reasoning with fuzzy booleans to object-oriented design methods

The relationship between IR and multimedia databases

Modern extensible database systems support multimedia data through ADTs. However, because of the problems with multimedia query formulation, this support is not sufficient.\ud \ud Multimedia querying requires an iterative search process involving many different representations of the objects in the database. The support that is needed is very similar to the processes in information retrieval.\ud \ud Based on this observation, we develop the miRRor architecture for multimedia query processing. We design a layered framework based on information retrieval techniques, to provide a usable query interface to the multimedia database.\ud \ud First, we introduce a concept layer to enable reasoning over low-level concepts in the database.\ud \ud Second, we add an evidential reasoning layer as an intermediate between the user and the concept layer.\ud \ud Third, we add the functionality to process the users' relevance feedback.\ud \ud We then adapt the inference network model from text retrieval to an evidential reasoning model for multimedia query processing.\ud \ud We conclude with an outline for implementation of miRRor on top of the Monet extensible database system

Predictive intelligence to the edge through approximate collaborative context reasoning

We focus on Internet of Things (IoT) environments where a network of sensing and computing devices are responsible to locally process contextual data, reason and collaboratively infer the appearance of a specific phenomenon (event). Pushing processing and knowledge inference to the edge of the IoT network allows the complexity of the event reasoning process to be distributed into many manageable pieces and to be physically located at the source of the contextual information. This enables a huge amount of rich data streams to be processed in real time that would be prohibitively complex and costly to deliver on a traditional centralized Cloud system. We propose a lightweight, energy-efficient, distributed, adaptive, multiple-context perspective event reasoning model under uncertainty on each IoT device (sensor/actuator). Each device senses and processes context data and infers events based on different local context perspectives: (i) expert knowledge on event representation, (ii) outliers inference, and (iii) deviation from locally predicted context. Such novel approximate reasoning paradigm is achieved through a contextualized, collaborative belief-driven clustering process, where clusters of devices are formed according to their belief on the presence of events. Our distributed and federated intelligence model efficiently identifies any localized abnormality on the contextual data in light of event reasoning through aggregating local degrees of belief, updates, and adjusts its knowledge to contextual data outliers and novelty detection. We provide comprehensive experimental and comparison assessment of our model over real contextual data with other localized and centralized event detection models and show the benefits stemmed from its adoption by achieving up to three orders of magnitude less energy consumption and high quality of inference