PhiloWikiConceptsPhilosophersBooksInteractive graph

Concept

MV-algebra

Overview

In abstract algebra, a branch of pure mathematics, an MV-algebra is an algebraic structure with a binary operation

⊕

{\displaystyle \oplus }

, a unary operation

¬

{\displaystyle \neg }

, and the constant

0

{\displaystyle 0}

, satisfying certain axioms. MV-algebras are the algebraic semantics of Łukasiewicz logic; the letters MV refer to the many-valued logic of Łukasiewicz. MV-algebras coincide with the class of bounded commutative BCK algebras.

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

Possible passages

Found by search and not yet checked by a person; they may only mention the idea in passing.

  1. Any such select set is called the set of postulates, or premises, from which the reasoning proceeds. The reasoning is nothing else than the exhibition of the whole pattern of general conditions involved in the pattern derived from the selected postulates.

    Alfred North Whitehead, Science and the modern world

    States what MV-algebra is.

    Read the chapter · Open in the reader

  2. The nature of abstract mathematics (the general division of which will be examined in the following chapter) is clearly and exactly determined. It is composed of what is called the _Calculus_,[2] taking this word in its greatest extent, which reaches from the most simple numerical operations to the most sublime combinations of transcendental analysis. The _Calculus_ has the solution of all questions relating to…

    Auguste Comte, The philosophy of mathematics

    States what MV-algebra is.

    Read the chapter · Open in the reader

  3. Even speech rebels against this idea. A mathematical figure of three dimensions is called a solid--corpus solidum--and hence, according to the Latin, a body capable of being handled. It has a name derived, therefore, by no means from the independent play of imagination but from solid reality.

    Friedrich Engels, Landmarks of Scientific Socialism

    States what MV-algebra is.

    Read the chapter · Open in the reader

Philosophers who discussed MV-algebra

Related ideas

Place in the tradition

Part of Fuzzy logic.

Explore MV-algebra in the interactive graph →