quantum logic

This is a contributed topic on quantum logic using tools available on the internet.

Quantum Logic description

There are several approaches to quantum logic, and it should be therefore more appropriately called `Quantum Logics'. The following is a short list of such approaches to quantum logics.

Bibliography

1
Hilbert space in QM- a website: Hilbert Space Explorer Home Page

2
``Metamath web site: The Metamath Home Page: automatic theorem proving on the web Inspired by Whitehead and Russell's monumental Principia Mathematica, the Metamath Proof Explorer has over 8,000 completely worked out proofs in logic and set theory, interconnected with over a million hyperlinked cross-references. Each proof is pieced together with razor-sharp precision using a simple substitution rule that practically anyone with patience can follow, not just mathematicians. Every step can be drilled down deeper and deeper into the labyrinth until axioms of logic and set theory-the starting point for all of mathematics-will ultimately be found at the bottom. You could spend literally days exploring the astonishing tangle of logic leading, say, from $ 2+2=4$ back to the axioms.

Essentially everything that is possible to know in mathematics can be derived from a handful of axioms known as Zermelo-Fraenkel set theory, which is the culmination of many years of effort to isolate the essential nature of mathematics and is one of the most profound achievements of mankind.''

The Metamath Proof Explorer starts with such axioms to build up its proofs.

3
Gudrun Kalmbach, ``Orthomodular Lattices'', Academic Press, London (1983).

4
Ladislav Beran, Orthomodular Lattices; Algebraic Approach, D. Reidel, Dordrecht (1985).

5
M. Pavicić, ``Minimal Quantum Logic with Merged Implications,'' Int. J. of Theor. Phys. 26, 845-852 (1987).

6
M. Pavicić and N. Megill, ``Quantum and Classical Implicational Algebras with Primitive Implication,'' Int. J. of Theor. Phys. 37, 2091-2098 (1998).

7
M. Pavicić and N. Megill, ``Non-Orthomodular Models for Both Standard Quantum Logic and Standard Classical Logic: Repercussions for Quantum Computers,'' Helv.Phys.Acta,72,189-210 (1999).

8
N. Megill and M. Pavicić, ``Equations, States, and Lattices of Infinite-Dimensional Hilbert Space,'' Int. J. Theor. Phys. 39, 2337-2379 (2000)

9
B. McKay, N. Megill, and M. Pavicić, ``Algorithms for Greechie Diagrams,'' Int.J. Theor.Phys.39,2393-2417(2000).

10
N. Megill and M. Pavicić, ``Orthomodular Lattices and a Quantum Algebra,'' Int. J. Theor. Phys.40,1387-1410 (2001).



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