Thesis (Ed.D.)--Boston University

This thesis investigates ways of incorporating reasoning by analogy into Pure (Unary) Inductive Logic. We start with an analysis of similarity as distance, noting that this is the conception that has received most attention in the literature so far. Chapter 4 looks in some detail at the consequences of adopting Hamming Distance as our measure of similarity, which proves to be a strong requirement. Chapter 5 then examines various adaptations of Hamming Distance and proposes a subtle modification, further-away-ness, that generates a much larger class of solutions.

We investigate the Principle of Predicate Exchangeability in the framework of Pure Inductive Logic. While this principle was known to Rudolf Carnap, who started research in Inductive Logic, the principle has been somewhat neglected in the past. After providing the framework of Pure Inductive Logic, we will show Representation Theorems for probability functions satisfying Predicate Exchangeability, filling the gap in the list of Representation Theorems for functions satisfying certain rational principles. We then introduce a new principle, called the Principle of Strong Predicate Exchangeability, which is weaker than the well-known Principle of Atom Exchangeability, but stronger than Predicate Exchangeability and give examples of functions that satisfy this principle. Finally, we extend the framework of Inductive Logic to Second Order languages, which allows for increasing a rational agent’s expressive strength. We introduce Wilmers’ Principle, a rational principle that rational agents might want to adopt in this extended framework, and give a representation theorem for this principle.

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Changes in the engineering industry have motivated the redesign of engineering curriculum in recent years. This report documents the redesign of Mechanical Engineering 574, a graduate course in engineering offered at Brigham Young University. The redesign was divided into four phases and used a design narrative to report the design process. Research conducted by the instructor and designer informed the main content of the course. Although the course originally used mainly deductive methods of instruction, by the final phase of the project, the instruction evolved to be primarily inductive in strategy.

This study compared the accuracy for the two general approaches to criminal profiling, inductive and deductive. Participants were 213 college students who participated in a 1-hour training session. Participants in the experimental groups were trained in either the inductive or deductive approach to profiling. Participants in the control group were trained in a crime topic unrelated to profiling (rape and sexual assault prevention). Following the training session, participants were asked to review a double sexual homicide case and then profile the offender by completing the Profiling Offender characteristics Questionnaire. Participants trained in the inductive profiling approach were more accurate when profiling the offender’s physical characteristics. Furthermore, the inductive profiling approach led to higher overall accuracy scores compared to the control condition. These results suggest that training naïve profilers to use the inductive approach may improve the accuracy of offender profiles in sexual homicide cases.

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SMT-based verification analyzes reachability for transition systems represented by SMT formulae. Depending on the theories and the kinds of systems considered, various approaches have been proposed. Together, they form the Verification Modulo Theory (VMT) framework. This thesis delves into SMT-based verification of parameterized systems, emphasizing the challenges and novel solutions in verifying systems with an unbounded number of components. In this thesis, we first introduce a general framework to model such systems. Then, we introduce two novel algorithms that leverage the strengths of SMT for the verification of parameterized systems, focusing on the automation and reduction of computational complexity inherent in such tasks. These algorithms are designed to improve upon existing verification methods by offering enhanced scalability and automation, making them particularly suited for the analysis of distributed systems, network protocols, and concurrent programming models where traditional approaches may fail. Moreover, we introduce an algorithm for compositional verification that advances the capability to modularly verify complex systems by decomposing the verification task into smaller, more manageable sub-tasks. Additionally, we discuss the potential and ongoing application of these algorithms in an industrial project focusing on the design of interlocking logic. This particular application demonstrates the practical utility of our algorithms in a real-world setting, highlighting their effectiveness in improving the safety and reliability of critical infras- tructure. The theoretical advancements proposed in this thesis are complemented by a rig- orous experimental evaluation, demonstrating the applicability and effectiveness of our methods across a range of verification scenarios. Our work is implemented within an ex- tended framework of the MathSAT SMT solver, facilitating its integration into existing verification workflows. Overall, this research contributes to the theoretical underpinnings of Verification Modulo Theories (VMT) and offers tools and methodologies for the verification community, enhancing the capability to verify complex parameterized systems with greater efficiency and reliability.

Inductive logic programming is a discipline investigating invention of clausal theories from observed examples such that for given evidence and background knowledge we are finding a hypothesis covering all positive examples and excluding all negative ones. In this thesis we extend an existing work on template consistency to general consistency. We present a three-phase algorithm DeMeR decomposing the original problem into smaller subtasks, merging all subsolutions together yielding a complete solution and finally refining the result in order to get a compact final hypothesis. Furthermore, we focus on a method how each individual subtask is solved and we introduce a generate-and-test method based on the probabilistic history-driven approach for this purpose. We analyze each stage of the proposed algorithms and demonstrate its impact on a runtime and a hypothesis structure. In particular, we show that the first phase of the algorithm concentrates on solving the problem quickly at the cost of longer solutions whereas the other phases refine these solutions into an admissible form. Finally, we prove that our technique outperforms other algorithms by comparing its results for identifying common structures in random graphs to existing systems.

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