Advanced kripke frame for quantum logic

Abstract

Quantum logic has been studied with orthomodular lattices. The semantics required for quantum logic can also be provided by OM-models, whose nature is almost equivalent to the notion of orthomodular lattices. However, the development of OM-models is in its infancy, and important notions of orthomodular lattices such as OM laws, atomicity and covering laws cannot yet be fully described. Thus, in this paper, we develop OM-models in an attempt to solve these problems.