Quantum logic as a fragment of independence-friendly logic

The working assumption of this paper is that noncommuting variables are irreducibly interdependent. The logic of such dependence relations is the author's independence-friendly (IF) logic, extended by adding to it sentence-initial contradictory negation -(,) over and above the dual (strong) negation Lambda similar to. Then in a Hilbert space similar to turns out to express orthocomplementation. This can be extended to any logical space, which makes it possible to define the dimension fo a logical space. The received Birkhoff and von Neumann 'quantum logic' can be interpreted by taking their 'disjunction' to be -(,) (similar toA & similar toB). Their logic can thus be mapped into a Boolean structure to which an additional operator similar to has been added.