This is a contributed topic on quantum logic using tools available on the internet.
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.
The axioms of this standard version of quantum logic (QL) can be specified as three distinct groups of axioms:
, where N stands for the logical negation; ax-a2 and ax-a3 are respectively the commutativity and associativity axioms; the ax-r1 ro ax-r5 axioms are implication axioms, such as:
for ax-r1.
(interestingly, without ax-r3, the quantum logic becomes decidable), and
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.
As of this snapshot date, this entry was owned by bci1.