Ontology evolution in physics

With the advent of reasoning problems in dynamic environments, there is an increasing need for automated reasoning systems to automatically adapt to unexpected changes in representations. In particular, the automation of the evolution of their ontologies needs to be enhanced without substantially sacrificing expressivity in the underlying representation. Revision of beliefs is not enough, as adding to or removing from beliefs does not change the underlying formal language. General reasoning systems employed in such environments should also address situations in which the language for representing knowledge is not shared among the involved entities, e.g., the ontologies in a multi-ontology environment or the agents in a multi-agent environment. Our techniques involve diagnosis of faults in existing, possibly heterogeneous, ontologies and then resolution of these faults by manipulating the signature and/or the axioms. This thesis describes the design, development and evaluation of GALILEO (Guided Analysis of Logical Inconsistencies Lead to Evolution of Ontologies), a system designed to detect conflicts in highly expressive ontologies and resolve the detected conflicts by performing appropriate repair operations. The integrated mechanism that handles ontology evolution is able to distinguish between various types of conflicts, each corresponding to a unique kind of ontological fault. We apply and develop our techniques in the domain of Physics. This an excellent domain because many of its seminal advances can be seen as examples of ontology evolution, i.e. changing the way that physicists perceive the world, and case studies are well documented – unlike many other domains. Our research covers analysing a wide ranging development set of case studies and evaluating the performance of the system on a test set. Because the formal representations of most of the case studies are non-trivial and the underlying logic has a high degree of expressivity, we face some tricky technical challenges, including dealing with the potentially large number of choices in diagnosis and repair. In order to enhance the practicality and the manageability of the ontology evolution process, GALILEO incorporates the functionality of generating physically meaningful diagnoses and repairs and, as a result, narrowing the search space to a manageable size

Notes in Pure Mathematics & Mathematical Structures in Physics

These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.Comment: Small improvements and addition

Aspects of Symmetry, Topology and Anomalies in Quantum Matter

In this thesis, we explore the aspects of symmetry, topology and anomalies in quantum matter with entanglement from both condensed matter and high energy theory viewpoints. The focus of our research is on the gapped many-body quantum systems including symmetry-protected topological states and topologically ordered states. Chapter 1. Introduction. Chapter 2. Geometric phase, wavefunction overlap, spacetime path integral and topological invariants. Chapter 3. Aspects of Symmetry. Chapter 4. Aspects of Topology. Chapter 5. Aspects of Anomalies. Chapter 6. Quantum Statistics and Spacetime Surgery. Chapter 7. Conclusion: Finale and A New View of Emergence-Reductionism. (Thesis supervisor: Prof. Xiao-Gang Wen)Comment: Ph.D. thesis, MIT, Dept. of Physics. Defended and submitted in May 2015. Citable URI: http://dspace.mit.edu/handle/1721.1/99285 Partially based on arxiv:1212.4863, arXiv:1306.3695, arxiv:1307.7480, arXiv:1310.8291, arXiv:1403.5256, arXiv:1404.7854, arXiv:1405.7689, arXiv:1408.6514, arXiv:1409.3216. With refinement. 250 page