Editing Quantum logic (section)

{{Short description|Theory of logic to account for observations from quantum theory}}
{{Quantum mechanics|cTopic=[[Interpretation of quantum mechanics|Interpretations]]}}

In the [[Mathematical logic|mathematical study of logic]] and the [[Physics|physical]] analysis of [[quantum foundations]], '''quantum logic''' is a set of rules for manip&shy;ulation of [[proposition]]s inspired by the structure of [[Quantum mechanics|quantum theory]].  The formal system takes as its starting point an obs&shy;ervation of [[Garrett Birkhoff]] and [[John von&nbsp;Neumann]], that the structure of experimental tests in classical mechanics forms a [[Boolean algebra (structure)|Boolean algebra]], but the structure of experimental tests in quantum mechanics forms a much more complicated structure.

A number of other logics have also been proposed to analyze quantum-mechanical phenomena, unfortunately also under the name of "quantum logic(s)".  They are not the subject of this article.  For discussion of the similarities and differences between quantum logic and some of these competitors, see ''{{slink||Relationship to other logics}}''.

Quantum logic has been proposed as the correct logic for propositional inference generally, most notably by the philosopher [[Hilary Putnam]], at least at one point in his career.  This thesis was an important ingredient in Putnam's 1968 paper "[[Is Logic Empirical?]]" in which he analysed the [[epistemology|epistemological]] status of the rules of propositional logic.  Modern philosophers reject quantum logic as a basis for reasoning, because it lacks a [[material conditional]]; a common alternative is the system of [[linear logic]], of which quantum logic is a fragment.

Mathematically, quantum logic is formulated by weakening the [[distributive law]] for a Boolean algebra, resulting in an [[Orthocomplement|ortho&shy;complemented lattice]].   Quantum-mechanical [[observable]]s and [[Quantum state|states]] can be defined in terms of functions on or to the lattice, giving an alternate [[Formalism (mathematics)|formalism]] for quantum computations.