Functional properties of quantum logics

Ahmed M. Al-Adilee, Mustafa G. Al-Mousawi

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.

PEKKA J. LAHTI

Andrei Galiautdinov

Ahmed Al-Adilee, Sami Kadhem Kareem Althabhaw

Our paper is concerned with a generalization of the boundaries of copula that are well-known by Frechet-Hoeffding conditions [4], and study copula boundaries as functions defined on quantum logic ., While there are many properties that have been presented according to our proposed generalization throughout these modified functions and show that some important propositions that have different forms to those of classical copulas. Indeed, it has been shown two main results relevant to the lower and upper boundaries of what we have defined and named by quantum logic copulas, see [1].

Anatolij Dvurečenskij

Christopher John Isham, Noah Linden

The recent suggestion that a temporal form of quantum logic provides the natural mathematical framework within which to discuss the proposal by Gell-Mann and Hartle for a generalized form of quantum theory based on the ideas of histories and decoherence functionals is analyzed and developed herein. Particular stress is placed on properties of the space of decoherence functionals, including one way in which certain global and topological properties of a classical system are reflected in a quantum history theory.