Topics in Many-valued and Quantum Algebraic Logic

dc.contributor.authorLu, Weiyun
dc.description.abstractIntroduced by C.C. Chang in the 1950s, MV algebras are to many-valued (Łukasiewicz) logics what boolean algebras are to two-valued logic. More recently, effect algebras were introduced by physicists to describe quantum logic. In this thesis, we begin by investigating how these two structures, introduced decades apart for wildly different reasons, are intimately related in a mathematically precise way. We survey some connections between MV/effect algebras and more traditional algebraic structures. Then, we look at the categorical structure of effect algebras in depth, and in particular see how the partiality of their operations cause things to be vastly more complicated than their totally defined classical analogues. In the final chapter, we discuss coordinatization of MV algebras and prove some new theorems and construct some new concrete examples, connecting these structures up (requiring a detour through effect algebras!) to boolean inverse semigroups.
dc.publisherUniversité d'Ottawa / University of Ottawa
dc.subjectmv algebra
dc.subjecteffect algebra
dc.subjectmany valued-logic
dc.subjectquantum logic
dc.subjectalgebraic logic
dc.subjectmathematical logic
dc.subjectcategory theory
dc.subjectcategorical logic
dc.titleTopics in Many-valued and Quantum Algebraic Logic
dc.contributor.supervisorScott, Philip / Science
uottawa.departmentMathématiques et statistique / Mathematics and Statistics
CollectionThèses, 2011 - // Theses, 2011 -