Quantum Logic Maps and Triangular Norms on D-posets

Abstract

Abstract In this paper, we propose a type of generalization of triangular norms and quantum logic functions on d-poset algebra. We compare the modified constructions, and properties to the classical properties of the generalized concepts. We show several structures with proof of each type of the proposed generalization. We show several relationships that connect the triangular norms to the quantum logic maps, and also show their relationships to the classical probability space. We provide some explanatory examples that show each structure on d-poset with extra properties that depends on a definition of state.