In quantum mechanics, the consistent histories or simply "consistent quantum theory" interpretation generalizes the complementarity aspect of the conventional Copenhagen interpretation. The approach is sometimes called decoherent histories and in other work decoherent histories are more specialized.

First proposed by Robert Griffiths in 1984, this interpretation of quantum mechanics is based on a consistency criterion that then allows probabilities to be assigned to various alternative histories of a system such that the probabilities for each history obey the rules of classical probability while being consistent with the Schrödinger equation. In contrast to some interpretations of quantum mechanics, the framework does not include "wavefunction collapse" as a relevant description of any physical process, and emphasizes that measurement theory is not a fundamental ingredient of quantum mechanics. Consistent histories allows predictions related to the state of the universe needed for quantum cosmology.

The interpretation rests on three assumptions:

The third assumption generalizes complementarity and this assumption separates consistent histories from other quantum theory interpretations.

A homogeneous history ${\displaystyle H_{i}}$ (here ${\displaystyle i}$ labels different histories) is a sequence of Propositions ${\displaystyle P_{i,j}}$ specified at different moments of time ${\displaystyle t_{i,j}}$ (here ${\displaystyle j}$ labels the times). We write this as:

${\displaystyle H_{i}=(P_{i,1},P_{i,2},\ldots ,P_{i,n_{i}})}$

and read it as "the proposition ${\displaystyle P_{i,1}}$ is true at time ${\displaystyle t_{i,1}}$ and then the proposition ${\displaystyle P_{i,2}}$ is true at time ${\displaystyle t_{i,2}}$ and then ${\displaystyle \ldots }$". The times ${\displaystyle t_{i,1}<t_{i,2}<\ldots <t_{i,n_{i}}}$ are strictly ordered and called the temporal support of the history.

Inhomogeneous histories are multiple-time propositions which cannot be represented by a homogeneous history. An example is the logical OR of two homogeneous histories: ${\displaystyle H_{i}\lor H_{j}}$.