To address these domains, there have been several proposals to achieve efficiency through loose integrations with efficient declarative solvers such as constraint solvers or satisfiability modulo theories solvers. While these approaches successfully avoid substantial grounding, due to the loose integration, they are not suitable for performing defeasible reasoning on functions. As a result, this expressive reasoning on functions must either be performed using predicates to simulate the functions or in a way that is not elaboration tolerant. Neither compromise is reasonable; the former suffers from the grounding bottleneck when domains are large as is often the case in real-world domains while the latter necessitates encodings to be non-trivially modified for elaborations.
This dissertation presents a novel framework called Answer Set Programming Modulo Theories (ASPMT) that is a tight integration of the stable model semantics and satisfiability modulo theories. This framework both supports defeasible reasoning about functions and alleviates the grounding bottleneck. Combining the strengths of Answer Set Programming and satisfiability modulo theories enables efficient continuous reasoning while still supporting rich reasoning features such as reasoning about defaults and reasoning in domains with incomplete knowledge. This framework is realized in two prototype implementations called MVSM and ASPMT2SMT, and the latter was recently incorporated into a non-monotonic spatial reasoning system. To define the semantics of this framework, we extend the first-order stable model semantics by Ferraris, Lee and Lifschitz to allow "intensional functions" and provide analyses of the theoretical properties of this new formalism and on the relationships between this and existing approaches.
Breast cancer is one of the most common types of cancer worldwide. Early detection and diagnosis are crucial for improving the chances of successful treatment and survival. In this thesis, many different machine learning algorithms were evaluated and compared to predict breast cancer malignancy from diagnostic features extracted from digitized images of breast tissue samples, called fine-needle aspirates. Breast cancer diagnosis typically involves a combination of mammography, ultrasound, and biopsy. However, machine learning algorithms can assist in the detection and diagnosis of breast cancer by analyzing large amounts of data and identifying patterns that may not be discernible to the human eye. By using these algorithms, healthcare professionals can potentially detect breast cancer at an earlier stage, leading to more effective treatment and better patient outcomes. The results showed that the gradient boosting classifier performed the best, achieving an accuracy of 96% on the test set. This indicates that this algorithm can be a useful tool for healthcare professionals in the early detection and diagnosis of breast cancer, potentially leading to improved patient outcomes.