Completeness of Quantum Logic

Ernst-Walther Stachow

Meixing Zhao, Jinchuan Hou, Kan He +1 more

Satoko Titani

Quantum logic is a counterpart of orthomodular lattice and interpreted in a sheaf of complete Boolean algebra. This means that quantum logic is interpreted in a family of classical worlds. The aim of this paper is to prove a sheaf completeness of quantum logic.

E. Giuntini

This paper will take into account the Lindenbaum property in Ortho modular Quantum Logic (OQL) and Partial Classical Logic (PCL). The Lindenbaum property has an interest both from a logical and a physical point of view since it has to do with the problem of the completeness of quantum theory and with the possibi? lity of extending any semantically non-contradictory set of formulas to a semanti? cally non-contradictory complete set of formulas. The main purpose of this paper is4 to show that both OQL and PCL cannot satisfy the Lindenbaum property.

Anatolij Dvurečenskij

Pushkin P.E. Kachroo

This thesis provides an introduction to the concepts of soundness and completeness in the context of quantum logic. As quantum logic is based on a lattice and not Boolean logic as is the case of classical logic, its meta analysis is very different. This thesis is devoted to studying the differences that this structure provides. In terms of quatum computation, the thesis provides an introduction to decidability as it is used in classical computation theory using Turing machines and then presents a comparison to quantum computation structure. The aim of the thesis is to present the existing basic structures of classical and quantum logic, as well as classical and quantum computation that will enable the development of the technical connections between the two in terms of specific models and finally to their relationship to classical and quantum complexity.