Tse, Ming Fun. / Thesis submitted in: December 2001. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 142-146). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Problem Definition --- p.2 / Chapter 1.2 --- Contributions --- p.3 / Chapter 1.3 --- Thesis Outline --- p.4 / Chapter 2 --- Literature Review --- p.6 / Chapter 2.1 --- Representing Inexact Knowledge --- p.7 / Chapter 2.1.1 --- Nature of Inexact Knowledge --- p.7 / Chapter 2.1.2 --- Probability Based Reasoning --- p.8 / Chapter 2.1.3 --- Certainty Factor Algebra --- p.11 / Chapter 2.1.4 --- Fuzzy Logic --- p.13 / Chapter 2.2 --- Machine Learning Paradigms --- p.13 / Chapter 2.2.1 --- Classifications --- p.14 / Chapter 2.2.2 --- Neural Networks and Gradient Descent --- p.15 / Chapter 2.3 --- Related Learning Systems --- p.21 / Chapter 2.3.1 --- Relational Concept Learning --- p.21 / Chapter 2.3.2 --- Learning of Fuzzy Concepts --- p.24 / Chapter 2.4 --- Fuzzy Logic --- p.26 / Chapter 2.4.1 --- Fuzzy Set --- p.27 / Chapter 2.4.2 --- Basic Notations in Fuzzy Logic --- p.29 / Chapter 2.4.3 --- Basic Operations on Fuzzy Sets --- p.29 / Chapter 2.4.4 --- "Fuzzy Relations, Projection and Cylindrical Extension" --- p.31 / Chapter 2.4.5 --- Fuzzy First Order Logic and Fuzzy Prolog --- p.34 / Chapter 3 --- Knowledge Representation and Learning Algorithm --- p.43 / Chapter 3.1 --- Knowledge Representation --- p.44 / Chapter 3.1.1 --- Fuzzy First-order Logic ´ؤ A Powerful Language --- p.44 / Chapter 3.1.2 --- Literal Forms --- p.48 / Chapter 3.1.3 --- Continuous Variables --- p.50 / Chapter 3.2 --- System Architecture --- p.61 / Chapter 3.2.1 --- Data Reading --- p.61 / Chapter 3.2.2 --- Preprocessing and Postprocessing --- p.67 / Chapter 4 --- Global Evaluation of Literals --- p.71 / Chapter 4.1 --- Existing Closeness Measures between Fuzzy Sets --- p.72 / Chapter 4.2 --- The Error Function and the Normalized Error Functions --- p.75 / Chapter 4.2.1 --- The Error Function --- p.75 / Chapter 4.2.2 --- The Normalized Error Functions --- p.76 / Chapter 4.3 --- The Nodal Characteristics and the Error Peaks --- p.79 / Chapter 4.3.1 --- The Nodal Characteristics --- p.79 / Chapter 4.3.2 --- The Zero Error Line and the Error Peaks --- p.80 / Chapter 4.4 --- Quantifying the Nodal Characteristics --- p.85 / Chapter 4.4.1 --- Information Theory --- p.86 / Chapter 4.4.2 --- Applying the Information Theory --- p.88 / Chapter 4.4.3 --- Upper and Lower Bounds of CE --- p.89 / Chapter 4.4.4 --- The Whole Heuristics of FF99 --- p.93 / Chapter 4.5 --- An Example --- p.94 / Chapter 5 --- Partial Evaluation of Literals --- p.99 / Chapter 5.1 --- Importance of Covering in Inductive Learning --- p.100 / Chapter 5.1.1 --- The Divide-and-conquer Method --- p.100 / Chapter 5.1.2 --- The Covering Method --- p.101 / Chapter 5.1.3 --- Effective Pruning in Both Methods --- p.102 / Chapter 5.2 --- Fuzzification of FOIL --- p.104 / Chapter 5.2.1 --- Analysis of FOIL --- p.104 / Chapter 5.2.2 --- Requirements on System Fuzzification --- p.107 / Chapter 5.2.3 --- Possible Ways in Fuzzifing FOIL --- p.109 / Chapter 5.3 --- The α Covering Method --- p.111 / Chapter 5.3.1 --- Construction of Partitions by α-cut --- p.112 / Chapter 5.3.2 --- Adaptive-α Covering --- p.112 / Chapter 5.4 --- The Probabistic Covering Method --- p.114 / Chapter 6 --- Results and Discussions --- p.119 / Chapter 6.1 --- Experimental Results --- p.120 / Chapter 6.1.1 --- Iris Plant Database --- p.120 / Chapter 6.1.2 --- Kinship Relational Domain --- p.122 / Chapter 6.1.3 --- The Fuzzy Relation Domain --- p.129 / Chapter 6.1.4 --- Age Group Domain --- p.134 / Chapter 6.1.5 --- The NBA Domain --- p.135 / Chapter 6.2 --- Future Development Directions --- p.137 / Chapter 6.2.1 --- Speed Improvement --- p.137 / Chapter 6.2.2 --- Accuracy Improvement --- p.138 / Chapter 6.2.3 --- Others --- p.138 / Chapter 7 --- Conclusion --- p.140 / Bibliography --- p.142 / Chapter A --- C4.5 to FOIL File Format Conversion --- p.147 / Chapter B --- FF99 example --- p.150

Thesis (Ph.D.)--McMaster University, 2003. / Advisor: David L. Hitchcock. Includes bibliographical references (leaves 144-147). Also available via World Wide Web.

Equational reasoning with string diagrams provides an intuitive method for proving equations between morphisms in various forms of monoidal category. !-Graphs were introduced with the intention of reasoning with infinite families of string diagrams by allowing repetition of sub-diagrams. However, their combinatoric nature only allows commutative nodes. The aim of this thesis is to extend the !-graph formalism to remove the restriction of commutativity and replace the notion of equational reasoning with a natural deduction system based on first order logic. The first major contribution is the syntactic !-tensor formalism, which enriches Penrose's abstract tensor notation to allow repeated structure via !-boxes. This will allow us to work with many noncommutative theories such as bialgebras, Frobenius algebras, and Hopf algebras, which have applications in quantum information theory. A more subtle consequence of switching to !-tensors is the ability to definitionally extend a theory. We will demonstrate how noncommutativity allows us to define nodes which encapsulate entire diagrams, without inherently assuming the diagram is commutative. This is particularly useful for recursively defining arbitrary arity nodes from fixed arity nodes. For example, we can construct a !-tensor node representing the family of left associated trees of multiplications in a monoid. The ability to recursively define nodes goes hand in hand with proof by induction. This leads to the second major contribution of this thesis, which is !-Logic (!L). We extend previous attempts at equational reasoning to a fully fledged natural deduction system based on positive intuitionistic first order logic, with conjunction, implication, and universal quantification over !-boxes. The key component of !L is the principle of !-box induction. We demonstrate its application by proving how we can transition from fixed to arbitrary arity theories for monoids, antihomomorphisms, bialgebras, and various forms of Frobenius algebras. We also define a semantics for !L, which we use to prove its soundness. Finally, we reintroduce commutativity as an optional property of a morphism, along with another property called symmetry, which describes morphisms which are not affected by cyclic permutations of their edges. Implementing these notions in the !-tensor language allows us to more easily describe theories involving symmetric or commutative morphisms, which we then demonstrate for recursively defined Frobenius algebra nodes.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND HUMANITIES / Bibliography: leaves 175-176. / by Lon A. Berk. / Ph.D.

Here we consider the verification and semantic integration for the set of first-order time ontologies by Allen-Hayes, Ladkin, and van Benthem that axiomatize time as points, intervals, or a combination of both within an ontology repository environment. Semantic integration of the set of time ontologies is explored via the notion of theory interpretations using an automated reasoner as part of the methodology. We use the notion of representation theorems for verification by characterizing the models of the ontology up to isomorphism and proving that they are equivalent to the intended structures for the ontology. Provided is a complete account of the meta-theoretic relationships between ontologies along with corrections to their axioms, translation definitions, proof of representation theorems, and a discussion of various issues such as class-quantified interpretations, the impact of namespacing support for Common Logic, and ontology repository support for semantic integration as related to the time ontologies examined.

Here we consider the verification and semantic integration for the set of first-order time ontologies by Allen-Hayes, Ladkin, and van Benthem that axiomatize time as points, intervals, or a combination of both within an ontology repository environment. Semantic integration of the set of time ontologies is explored via the notion of theory interpretations using an automated reasoner as part of the methodology. We use the notion of representation theorems for verification by characterizing the models of the ontology up to isomorphism and proving that they are equivalent to the intended structures for the ontology. Provided is a complete account of the meta-theoretic relationships between ontologies along with corrections to their axioms, translation definitions, proof of representation theorems, and a discussion of various issues such as class-quantified interpretations, the impact of namespacing support for Common Logic, and ontology repository support for semantic integration as related to the time ontologies examined.

Thesis (Ph. D.)--Missouri University of Science and Technology, 2008. / Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed May 28, 2009) Includes bibliographical references.

Made available in DSpace on 2014-06-12T15:48:50Z (GMT). No. of bitstreams: 2 arquivo2717_1.pdf: 481883 bytes, checksum: bb9d70f42c1cda245b5340284b5dc431 (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2011 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesta tese, provamos que todo domínio infinito finitamente gerado é bi-interpretável com a estrutura dos números naturais. Usando este argumento, demonstramos que todo anel f.g. R que tem um ideal primo nilpotente I tal que R/I é um domínio é Quase-Finitamente Axiomatizável

Background: Community resilience to a disaster is a complex phenomenon studied using a variety of research lenses, such as psychological and ecological, resulting in a lack of consensus about what the key factors are that make a community resilient. Formally representing this knowledge will allow researchers to better understand the links between the knowledge generated using different lenses and help to integrate new findings into the existing body of knowledge. Objective: Using ontology engineering methods to represent this knowledge will provide a tool to aid researchers in the field. Methods: An ontology is a structured way of organizing and representing knowledge in the field of community resilience to a disaster. The model created using this method can be read by a computer, which allows a reasoner to manipulate and infer new knowledge. Results: When using these methods to structure community resilience knowledge some of the complexities and ambiguities were identified. These included semantic ambiguities, such as two distinct factors being used interchangeably or two terms being used to describe the same factor, making the distinction between what are the factors and the characteristics of those factors, and finally, the inherited characteristics and relationships associated with hierarchical relationships. Conclusions: Having the knowledge about community resilience to a disaster represented in an ontology will aid researchers when operationalizing this knowledge in the future.

Thesis. 1976. Ph.D.--Massachusetts Institute of Technology. Dept. of Philosophy. / Microfiche copy available in Archives and Humanities. / Bibliography: leaves 165-170. / Ph.D.