Lóxica de clases

A lóxica das clases é considerada a proposición que considera a pertenza ou non dun elemento ou persoa a unha determinada clase ou grupo. É a interpretación dunha frase ou enunciado baixo a formalización da teoría dos conxuntos ou diagramas de Venn.

A clase significa un conxunto de individuos cunha propiedade en común. Cómpre ter en conta que a propiedade define a clase, non o individuo, tornándose esencialmente distinta da lóxica de predicado. Neste caso, polo tanto, o valor de verdade é dada pola adhesión ou non dunha clase. Polo tanto, a táboa de valor de verdade e explícito como táboas de pertenza.

Polo tanto, non é o mesmo que dicir: "Hs = Sócrates é un home" (onde un atributo se refire á calidade do ser de Sócrates), para dicir, "SH = Sócrates pertence á clase dos homes". A clase fai sentido, aínda que non os individuos. Así, o home da clase, como un concepto de home, existe aínda na ausencia dos homes. Da mesma forma, hai o concepto de "cabalos alados", aínda que existan os Pegasos.

Actualmente a chamada lóxica tradicional, a lóxica siloxística interprétase como clases.

Elementos e a súa simbolización

Clase universal
  • Universo: é a clase de todas as clases, de todos os elementos do universo que estemos considerando. Ela e chamada clase universal. U
  • Clase vacía: clase que non posúe ningún elemento : Ø
  • Individuos:
  • Clase: Un conxunto de individuos que teñen unha propiedade común. Pode ser expresada de diversas maneiras:
A = () - Por enumeración
A = (Todos nacidos en Asturias) - Por definición dunha propiedade
A = ( x/naceu en Asturias) - Por un función proposicional cuantificada (lido: Todo x tal que x pertence á clase dos nacidos en Asturias)
  • Pertenza: Non pertenza:
  • Xeralizador: Todo x.
  • Particularizador: Algún x
  • Conectivas : - Definidas de igual forma que na lóxica de enunciados relativas á pertenza ou non pertenza dun individuo a unha clase (estas funcións lóxicas son definidas en Táboa de valores de verdade).
  • A negación é definida como unha transacción entre as clases, a clase adicional.

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