The effects in a quantum-mechanical system form a partial algebra and a partially ordered
set which is the prototypical example of the effect algebras discussed in this paper. The …

" Is quantum logic really logic?" This book argues for a positive answer to this question once
and for all. There are many quantum logics and their structures are delightfully varied. The …

The papers making up this volume deal with various aspects of what we may call
operational quantum logic. This subject-lying somewhere at the crossroads of mathematics …

As a noncommutative generalization of effect algebras, we introduce pseudoeffect algebras
and list some of their basic properties. For the purpose of a structure theory, we further …

A sequential effect algebra (SEA) is an effect algebra on which a sequential product with
natural properties is defined. The properties of sequential products on Hilbert space effect …

We show that every D-lattice (lattice-ordered effect algebra) P is a set-theoreticunion of
maximal subsets of mutually compatible elements, called blocks. Moreover, blocks are sub …

Mathematically, quantum mechanics can be regarded as a non-classical probability calculus
resting upon a non-classical propositional logic. More specifically, in quantum mechanics …

Intuitionistic logic, in which the double negation law not-not-P= P fails, is dominant in
categorical logic, notably in topos theory. This paper follows a different direction in which …

An effect algebra is a partial algebra modeled on the standard effect algebra of positive self-
adjoint operators dominated by the identity on a Hilbert space. Every effect algebra is …

Effectus theory is a new branch of categorical logic that aims to capture the essentials of
quantum logic, with probabilistic and Boolean logic as special cases. Predicates in effectus …