Belief Revision in Expressive Knowledge Representation Formalisms

We live in an era of data and information, where an immeasurable amount of discoveries, findings, events, news, and transactions are generated every second. Governments, companies, or individuals have to employ and process all that data for knowledge-based decision-making (i.e. a decision-making process that uses predetermined criteria to measure and ensure the optimal outcome for a specific topic), which then prompt them to view the knowledge as valuable resource. In this knowledge-based view, the capability to create and utilize knowledge is the key source of an organization or individual’s competitive advantage. This dynamic nature of knowledge leads us to the study of belief revision (or belief change), an area which emerged from work in philosophy and then impacted further developments in computer science and artificial intelligence. In belief revision area, the AGM postulates by Alchourrón, Gärdenfors, and Makinson continue to represent a cornerstone in research related to belief change. Katsuno and Mendelzon (K&M) adopted the AGM postulates for changing belief bases and characterized AGM belief base revision in propositional logic over finite signatures. In this thesis, two research directions are considered. In the first, by considering the semantic point of view, we generalize K&M’s approach to the setting of (multiple) base revision in arbitrary Tarskian logics, covering all logics with a classical model-theoretic semantics and hence a wide variety of logics used in knowledge representation and beyond. Our generic formulation applies to various notions of “base”, such as belief sets, arbitrary or finite sets of sentences, or single sentences. The core result is a representation theorem showing a two-way correspondence between AGM base revision operators and certain “assignments”: functions mapping belief bases to total — yet not transitive — “preference” relations between interpretations. Alongside, we present a companion result for the case when the AGM postulate of syntax-independence is abandoned. We also provide a characterization of all logics for which our result can be strengthened to assignments producing transitive preference relations (as in K&M’s original work), giving rise to two more representation theorems for such logics, according to syntax dependence vs. independence. The second research direction in this thesis explores two approaches for revising description logic knowledge bases under fixed-domain semantics, namely model-based approach and individual-based approach. In this logical setting, models of the knowledge bases can be enumerated and can be computed to produce the revision result, semantically. We show a characterization of the AGM revision operator for this logic and present a concrete model-based revision approach via distance between interpretations. In addition, by weakening the KB based on certain domain elements, a novel individual-based revision operator is provided as an alternative approach

Interactive Event Sequence Query and Transformation

In our burgeoning world of pervasive sensors and affordable data storage, records of timestamped events are being produced across nearly every domain of personal and professional computing. This temporal event data is a fundamental component of electronic health records, process logs, sports analytics, and more. Across all domains, however, are two overarching needs: (1) to understand population-level trends and patterns, and (2) to identify important subsets of individual records. Visual analytics tools are billed as the solution to both of these problems. A huge volume of work has demonstrated the ability of these tools to facilitate user-guided data exploration and hypothesis generation across a wide range of data types. What is typically ignored however, is the process that takes place between the data collection and this exploration stage, a process frequently referred to as data wrangling. For many data types, wrangling consists mostly of restructuring spreadsheet columns and renaming fields. For temporal event data though, this wrangling process can extend much further---to the data itself---where event patterns must be transformed to better reflect either the real world events that generated them or the perspective of a given study. Without this step, population-level trends can be obscured beyond the point of recognition, and important subsets of records are impossible to discern. Temporal event data wrangling, however, is deceivingly difficult and error prone even for expert users. Standard, command-based query languages are poorly suited for specifying even the simplest event patterns and, in systems that are not precisely designed for handling temporal constructs, these queries are executed using a series of slow and inefficient self-join operations. Attempts at more accessible query languages frequently omit critical features such as events that occur over a period of time (intervals) or the absence of an event. Perhaps most importantly is that query alone is not enough to get users through a typical temporal event data wrangling process. Event patterns not only need to be found, but also transformed and re-represented. Temporal event wrangling is just as much about revisal as it is about retrieval, and given the ubiquity of this data type, an effective solution on this front has the potential to hugely impact the way that we utilize this data to inform future decisions. An improved query and wrangling process would not only benefit database professionals, but also dramatically increase the range of users who can access this type of data, particularly domain expert medical researchers. This dissertation demonstrates the ability of the EventFlow visualization tool to extend beyond the typical bounds of data exploration, and serve as a critical aid for both temporal event query and data transformation. I begin by establishing a better understanding of why these two processes are innately error prone, and introduce a simple set of powerful yet usable mechanisms that can help reduce an initial portion of these errors. I then show that by coupling these mechanisms with interactive visualizations, users are able to both identify remaining errors and leverage those errors to construct more accurate queries and transformations. The direct contributions of this dissertation are (1) a graphic-based query capabilities over points, intervals, and absences, (2) an integer programming strategy for processing temporal queries, (3) a Find & Replace system for transforming event sequences, and (4) eight case studies that demonstrate the utility and validity of these approaches. However, this work is designed more broadly to open new avenues of research in how visualization and visual analytics tools can be leveraged for tasks beyond data exploration