#
nLab

temporal algebra

# Temporal algebras

## Idea

A temporal algebra is a modal algebra with two operations that reflect the future and past modal operators of a temporal logic.

## Definitions

###### Definition

A **temporal algebra** is a Boolean algebra, $(\mathbb{B}, m_0,m_1)$, with operators, of type $2$, with the condition that the operators are *conjugate*:

$m_0 x \cdot y = 0$ if, and only if, $m_1 y \cdot x = 0$.

Equivalently (and equationally) this can be written as

$x \leq l_0 m_1 x \cdot l_1 m_0 x$

where $l_i$ is the dual of $m_1$.

Last revised on December 24, 2010 at 07:26:36.
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