Schrödinger logics are a kind of
non-classical logic Non-classical logics (and sometimes alternative logics) are formal systems that differ in a significant way from standard logical systems such as propositional and predicate logic. There are several ways in which this is done, including by way of ...
in which the
law of identity
In logic, the law of identity states that each thing is identical with itself. It is the first of the historical three laws of thought, along with the law of noncontradiction, and the law of excluded middle. However, few systems of logic are bui ...
is restricted.
These logics are motivated by the consideration that in quantum mechanics, elementary particles may be indistinguishable, even in principle, on the basis of any measurement. This in turn suggests that such particles cannot be considered as self-identical objects in the way that such things are usually treated within formal logic and set theory.
Schrödinger logics are many-sorted logics in which the expression ''x'' = ''y'' is not a
well-formed formula
In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language. A formal language can be ...
in general. A
formal semantics can be provided using the concept of a quasi-set. Schrödinger logics were introduced by da Costa and Krause.
Schrödinger logic is not related to
quantum logic
In the mathematical study of logic and the physical analysis of quantum foundations, quantum logic is a set of rules for manipulation of propositions inspired by the structure of quantum theory. The field takes as its starting point an observat ...
, which is a propositional logic that rejects the distributivity laws of
classical logic
Classical logic (or standard logic or Frege-Russell logic) is the intensively studied and most widely used class of deductive logic. Classical logic has had much influence on analytic philosophy.
Characteristics
Each logical system in this class ...
.
References
{{Non-classical logic
Non-classical logic
Logic