In logic, a (functionally) complete set of logical connectives or Boolean operators is one which can be used to express all possible truth tables by combining members of the set into a Boolean expression. A well known complete set of connectives is { AND, OR, NOT }, consisting of binary conjunction, binary disjunction and negation. The set consisting only of the binary operator NAND is also functionally complete.

PropertyValue
dbpprop:abstract
  • In logic, a (functionally) complete set of logical connectives or Boolean operators is one which can be used to express all possible truth tables by combining members of the set into a Boolean expression. A well known complete set of connectives is { AND, OR, NOT }, consisting of binary conjunction, binary disjunction and negation. The set consisting only of the binary operator NAND is also functionally complete. In a context of propositional logic, functionally complete sets of connectives are also called (expressively) adequate. From the point of view of digital electronics, functional completeness means that every possible logic gate can be realized as a network of gates of the types prescribed by the set. In particular all logic gates can be assembled from binary NAND gates.
  • A maioria das lógicas encontradas nos livros modernos tomam como conectivos primitivos: a conjunção (<math>\land</math>), disjunção (<math>\lor</math>), negação(<math>\lnot</math>), implicação(<math>\to</math>) e a bi-implicação (<math>\leftrightarrow</math>). Esse conjunto de conectivos goza da propriedade de completude funcional. Porém, esse não é um conjunto mínimo, já que a implicação e bi-implicação podem ser definidos como: :<math>A \to B := \neg A \lor B</math> <math>A \leftrightarrow B := (A \to B) \land (B \to A)</math> Já a disjunção, por sua vez, pode ser definida utilizando a conjunção: :<math>A \lor B := \neg(\neg A \land \neg B)</math> A conjunção pode ser expressa em termos da disjunção de modo semelhante: :<math>A \land B:= \neg(\neg A \lor \neg B)</math> Já os conectivos binários NOR e NAND sozinhos, possuem a propriedade da completude funcional, e são chamados Anfeque.
dbpprop:hasPhotoCollection
rdfs:comment
  • In logic, a (functionally) complete set of logical connectives or Boolean operators is one which can be used to express all possible truth tables by combining members of the set into a Boolean expression. A well known complete set of connectives is { AND, OR, NOT }, consisting of binary conjunction, binary disjunction and negation. The set consisting only of the binary operator NAND is also functionally complete.
  • A maioria das lógicas encontradas nos livros modernos tomam como conectivos primitivos: a conjunção (<math>\land</math>), disjunção (<math>\lor</math>), negação(<math>\lnot</math>), implicação(<math>\to</math>) e a bi-implicação (<math>\leftrightarrow</math>). Esse conjunto de conectivos goza da propriedade de completude funcional.
rdfs:label
  • Functional completeness
  • Completude funcional
owl:sameAs
skos:subject
foaf:page
is dbpprop:redirect of