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, (𝔹,m 0,m 1)(\mathbb{B}, m_0,m_1), with operators, of type 22, with the condition that the operators are conjugate:

m 0xy=0m_0 x \cdot y = 0 if, and only if, m 1yx=0m_1 y \cdot x = 0.

Equivalently (and equationally) this can be written as

xl 0m 1xl 1m 0xx \leq l_0 m_1 x \cdot l_1 m_0 x

where l il_i is the dual of m 1m_1.

Revised on December 24, 2010 07:26:36 by Toby Bartels (75.88.75.53)