The main content of this thesis concerns a tableau method for solving the satisfiability problem for the modal μ-calculus. A sound and complete tableau system for the modal μ-calculus is given. Since every tableau in such tableau system is finite and bounded by the length of the formula, the tableau system may be used as a decision procedure for determining the satisfiability of the formula. An alternative proof of the small model property is obtained: every satisfiable formula has a model of size singleexponential in the length of the formula. Contrary to known proofs in literature, the results presented here do not rely on automata theory. Two simplifications of the tableau system are given. One is for the class of aconjunctive formulae. The resulting tableau system has been used to prove the completeness of Kozen’s axiomatisation with respect to the aconjunctive fragment of the modal μ- calculus. Another is for the formulae in the class Πμ 2 . In addition to the tableau method, the thesis explores some model-surgery techniques with the aim that such techniques may be used to directly prove the small model theorem. The techniques obtained so far have been used to show the small model property for Πμ 2 -formulae and for formulae with linear models.

Each volume includes author's previously published papers. / Bibliography: leaves 147-151 (v. 1). / 3 v. : / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (D.Sc.)--University of Adelaide, School of Mathematical Sciences, 2005

Thesis (Ph. D.)--University of California, San Diego, 2008. / Title from first page of PDF file (viewed December 5, 2008). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 160-164).

Thesis (Master)--İzmir Institute of Technology, İzmir, 2006 / Keywords:Temporal logic, modal logic. Includes bibliographical references (leaves 45).

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In this dissertation, we investigate how commonsense reasoning can be formalized by using extended logic programs. In this investigation, we first use extended logic programs to formalize inheritance hierarchies with exceptions by adopting McCarthy's simple abnormality formalism to express uncertain knowledge. In our representation, not only credulous reasoning can be performed but also the ambiguity-blocking inheritance and the ambiguity-propagating inheritance in skeptical reasoning are simulated. In response to the anomalous extension problem, we explore and discover that the intuition underlying commonsense reasoning is a kind of forward reasoning. The unidirectional nature of this reasoning is applied by many reformulations of the Yale shooting problem to exclude the undesired conclusion. We then identify defeasible conclusions in our representation based on the syntax of extended logic programs. A similar idea is also applied to other formalizations of commonsense reasoning to achieve such a purpose.

According to the classical consistency presupposition, contradictions have an explosive character: Whenever they are present in a theory, anything goes, and no sensible reasoning can thus take place. A logic is paraconsistent if it disallows such presupposition, and allows instead for some inconsistent yet non-trivial theories to make perfect sense. The Logics of Formal Inconsistency, LFIs, form a particularly expressive class of paraconsistent logics in which the metatheoretical notion of consistency can be internalized at the object-language level. As a consequence, the LFIs are able to recapture consistent reasoning by the addition of appropriate consistency assumptions. The present monograph introduces the LFIs and provides several illustrations of them and of their properties, showing that such logics constitute in fact the majority of interesting paraconsistent systems in the literature. Several ways of performing the recapture of consistent reasoning inside such inconsistent systems are also illustrated. In each case, interpretations in terms of many-valued, possible-translations, or modal semantics are provided, and the problems related to providing algebraic counterparts to such logics are surveyed. A formal abstract approach is proposed to all related definitions and an extended investigation is made into the logical principles and the positive and negative properties of negation.

Thesis (M.S.)--Florida State University, 2004. / Advisor: Dr. Bing Kwan, Florida State University, College of Engineering, Dept. of Electrical and Computer Engineering. Title and description from dissertation home page (viewed June 16, 2004). Includes bibliographical references.

Thesis (Ph.D.)--Victoria University of Wellington, 2009. / Includes bibliographical references and index.

Thesis (All-College Honors) - - State University of New York College at Cortland, 2006 - - Department of Philosophy.