Humans definitely feel truth but cannot define truth properly. That is what Alfred Tarski
explained to us in the 1930s. Mathematics pursues truth by way of proof, as wittily phrased …

We give a new algorithm for generating Greechie diagrams with arbitrary chosennumber of
atoms or blocks (with 2, 3, 4,... atoms) and provide a computerprogram for generating the …

We show that one can formulate an algebra with lattice ordering so as to contain one
quantum and five classical operations as opposed to the standard formulation of the Hilbert …

This note answers questions on whether three identities known to hold for orthomodular
lattices are true also for ortholattices. One identity is shown to fail by MACE, a program that …

We show that for every orthogonal lub-complete poset P=(P,≤,′, 0, 1), we can introduce
multiple-valued implications sharing properties with quantum implications presented for …

Thirty-seven years ago, Richard Greechie and Stanley Gudder wrote a paper entitled Is a
Quantum Logic a Logic?[Greechie and Gudder, 1971] in which they strengthen a previous …

It is shown that propositional calculuses of both quantum and classical logics are non-
categorical. We find that quantum logic is in addition to an orthomodular lattice also modeled …

This paper presents a natural deduction system for orthomodular quantum logic. The system
is shown to be provably equivalent to Nishimura's quantum sequent calculus. Through the …

We provide several new result on quantum state space, on the lattice of subspacesof an
infinite-dimensional Hilbert space, and on infinite-dimensional Hilbert spaceequations as …

We consider a proper propositional quantum logic and show that it has multiple disjoint
lattice models, only one of which is an orthomodular lattice (algebra) underlying Hilbert …