Absorption law

Absorption law

In algebra, the absorption law is an identity linking a pair of binary operations.

Any two binary operations, say $ and %, are subject to the absorption law if:

:"a" $ ("a" % "b") = "a" % ("a" $ "b") = "a".

The operations $ and % are said to form a dual pair.

Let there be some set closed under two binary operations. If those operations are commutative, associative, and satisfy the absorption law, the resulting abstract algebra is a lattice, in which case the two operations are sometimes called meet, join; other possibilities include and,or. Since commutativity and associativity are often properties of other algebraic structures (for example, addition and multiplication of real numbers), absorption is the defining property of a lattice. Since Boolean algebras and Heyting algebras are lattices, they too obey the absorption law.

Since classical logic is a model of Boolean algebra, and the same is true of intuitionistic logic and Heyting algebras, the absorption law holds for operations vee and wedge , denoting OR and AND, respectively. Hence:

: a vee (a wedge b) = a wedge (a vee b) = a

where "=" is understood to be logical equivalence over formulae.

The absorption law does not hold for relevance logics, linear logics, and substructural logics. In the last case, there is no one-to-one correspondence between the free variables of the defining pair of identities.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать курсовую

Look at other dictionaries:

  • Henry’s gas absorption law — Henrio dujų sugerties dėsnis statusas T sritis fizika atitikmenys: angl. Henry’s gas absorption law vok. Henrysches Gasabsorptionsgesetz, n rus. закон Генри о поглощении газов, m pranc. loi de Henry d’absorption des gaz, f …   Fizikos terminų žodynas

  • absorption — ab·sorp·tion n: the application to the states of rights guaranteed by the U.S. Constitution while Powell [ v. Alabama ] was sometimes described as having absorbed the right to counsel, the Court there clearly limited any such absorption W. R.… …   Law dictionary

  • absorption of mind — index diligence (care) Burton s Legal Thesaurus. William C. Burton. 2006 …   Law dictionary

  • Absorption — may refer to:Chemistry and biology*Absorption (chemistry), absorption of particles of gas or liquid in liquid or solid material *Absorption (skin), a route by which substances can enter the body through the skin *Absorption (pharmacokinetics),… …   Wikipedia

  • Absorption (chemistry) — Absorption, in chemistry, is a physical or chemical phenomenon or a process in which atoms, molecules, or ions enter some bulk phase gas, liquid or solid material. This is a different process from adsorption, since the molecules are taken up by… …   Wikipedia

  • Absorption (electromagnetic radiation) — An overview of electromagnetic radiation absorption. This example discusses the general principle using visible light as specific example. A white beam source emitting light of multiple wavelengths is focused on a sample (the complementary color… …   Wikipedia

  • Absorption refrigerator — The absorption refrigerator is a refrigerator that utilizes a heat source (e.g., solar, kerosene fueled flame) to provide the energy needed to drive the cooling system rather than being dependent on electricity to run a compressor. These… …   Wikipedia

  • Absorption spectroscopy — An overview of electromagnetic radiation absorption. This example discusses the general principle using visible light as a specific example. A white beam source – emitting light of multiple wavelengths – is focused on a sample (the complementary… …   Wikipedia

  • Absorption coefficient — The absorption coefficient α is a property of a material. It defines the extent to which a material absorbs energy, for example that of sound waves or electromagnetic radiation. Wallace Sabine was a pioneer of this concept in acoustics and… …   Wikipedia

  • law of absorption — sugerties dėsnis statusas T sritis automatika atitikmenys: angl. law of absorption vok. Absorptionsgesetz, n rus. закон поглощения, m pranc. loi d absorption, f …   Automatikos terminų žodynas

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”