Thesis (M. S.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2010. / Committee Chair: Paul Hasler; Committee Member: David V Anderson; Committee Member: Saibal Mukhopadhyay. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (leaves 90-92).

Thesis (M.A.)--York University, 2005. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 92-94). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url%5Fver=Z39.88-2004&res%5Fdat=xri:pqdiss &rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:MR11823

M.A. (Philosophy) / Please refer to full text to view abstract

The subject of this dissertation is the theory of Boolean and multiple-valued functions. The main areas considered are: functional completeness, canonical forms, minimization of functions, discrete differences and functional decomposability. The results obtained are used as a foundation for the development of several new algorithms for logic synthesis of combinational logic circuits. These include an efficient algorithm for three-level AND-OR-XOR minimization for Boolean functions, an algorithm for generating the composition trees for Boolean and multiple-valued functions in a certain class, and an algorithm for computing a new canonical form of multiple-valued functions. Several other problems, related to logic synthesis, such as test generation for combinational logic circuits and synthesis of easily testable circuits are also addressed. Possible directions for future research are discussed. / Graduate

Legal reasoning is a method that is applied by legal practitioners to make legal decisions. For a scenario, legal reasoning requires not only the facts of the scenario but also the legal rules to be enforced within it. Formal logic has long been used for reasoning tasks in many domains. Deontic logic is a logic which is often used to formalise legal scenarios with its built-in notions of obligation, permission and prohibition. Within the legal domain, it is important to recognise that there are many exceptions and conflicting obligations. This motivates the enrichment of deontic logic with not only the notion of defeasibility, which allows for reasoning about exceptions, but a stronger notion of typicality which is based on defeasibility. KLM-style defeasible reasoning introduced by Kraus, Lehmann and Magidor (KLM), is a logic system that employs defeasibility while a logic that serves the same role for the stronger notion of typicality is Propositional Typicality Logic (PTL). Deontic paradoxes are often used to examine deontic logic systems as the scenarios arising from the paradoxes' structures produce undesirable results when desirable deontic properties are applied to the scenarios. This is despite the various scenarios themselves seeming intuitive. This dissertation shows that KLM-style defeasible reasoning and PTL are both effective when applied to the analysis of the deontic paradoxes. We first present the background information which comprises propositional logic, which forms the foundation for the other logic systems, as well as the background of KLM-style defeasible reasoning, deontic logic and PTL. We outline the paradoxes along with their issues within the presentation of deontic logic. We then show that for each of the two logic systems we can intuitively translate the paradoxes, satisfy many of the desirable deontic properties and produce reasonable solutions to the issues resulting from the paradoxes.

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The expressive power of logic-programming languages allows utilization of conventional constructs in development of computer systems based on logic programming. However, logic-programming languages have many novel features and capabilities. This thesis investigates how advantage can be taken of these features in the development of a logic-based computer system. It demonstrates that innovative approaches to software, hardware, and computer system design and implementation are feasible in a logic-programming context and often preferable to adaptation of conventional ones. The investigation centers on three main ideas: executable specification, declarative I/O, and implementation through transformation and meta-interpretation. A particular class of languages supporting parallel computation, committed-choice logic-programming languages, are emphasized. One member of this class, Concurrent Prolog, serves as the machine, specification, and implementation language. The investigation has several facets. Hardware, software, and overall system models for a logic-based computer are determined and examined. The models are described by logic programs. The computer system is represented as a goal for resolution. The clauses involved in the subsequent reduction steps constitute its specification. The same clauses also describe the manner in which the computer system is initiated. Frameworks are given for developing models of peripheral devices whose actions and interactions can be declaratively expressed. Interactions do not rely on side-effects or destructive assignment, and are term-based. A methodology is presented for realizing (prototypic) implementations from device specifications. The methodology is based on source-to-source transformation and meta-interpretation. A magnetic disk memory is used as a representative example, resulting in an innovative approach to secondary storage in a logic-programming environment. Building on these accomplishments, a file system for a logic-based computer system is developed. The file system follows a simple model and supports term-based, declarative I/O. Throughout the thesis, features of the logic-programming paradigm are demonstrated and exploited. Interesting and innovative concepts established include: device processes and device processors; restartable and perpetual devices and systems; peripheral devices modelled as function computations or independent logical (inference) systems; unique, compact representations of terms; lazy term expansion; files systems as perpetual processes maintaining local states; and term- and unification-based file abstractions. Logic programs are the sole formalism for specifications and implementations. / Science, Faculty of / Computer Science, Department of / Graduate

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