obversion

Helou

Al tratar de hacer algunos de los ejercicios del programa dosbox, me encontré con algunos que me han implicado mayor dificltad, toda vez que no se bien como funcionan algunas operacions lógicas, como es la obversion. Por si hay alguien en ese trance aqui lesdejo unas noras que quizá ayuden.

Una obversión lógica es una de las operaciones que la lógica clásica tradicional admitía como operación lógica.

Consiste en la modificación del juicio aristotélico de forma que cambiando la cualidad del juicio, afirmativo-negativo, y negando el término predicado, obtenemos un juicio equivalente.

De este modo:

Todo S es P \rightarrow se obvierte en \rightarrow Ningún S es no-P

Todos los españoles son europeos \rightarrow Ningún español es no-europeo


Ningún S es P \rightarrow se obvierte en \rightarrow Todo S es no-p

Ningún español es americano \rightarrow Todo español es no-americano


Algún S es P \rightarrow se obvierte en \rightarrow Algún S no es no-p

Algún español es rubio \rightarrow Algún español no es no-rubio



http://academic.csuohio.edu/polen/LC9_Help/4/immediate.htm

Conversion, Obversion, and Contraposition

Conversion is the inference in which the subject and predicate are interchanged. In modern logic it is only valid for the E and I propositions. The valid converse is logically equivalent to the original proposition. In traditional logic, the A proposition has a converse by limitation which is the subaltern of the invalid A-converse; i.e., the corresponding I proposition. The converse by limitation is implied by the original but is not (usually) equivalent to it.
ORIGINAL CONVERSE VALID? BY LIMITATION
All S are P All P are S no Some P are S
No S are P No P are S yes
Some S are P Some P are S yes
Some S are not P Some P are not S no

Obversion is the inference in which the quality of the proposition is changed and the predicate is interchanged with its complement. It is valid for all four forms. The obverse is logically equivalent to the original proposition.
ORIGINAL OBVERSE VALID?
All S are P No S are nonP yes
No S are P All S are nonP yes
Some S are P Some S are not nonP yes
Some S are not P Some S are nonP yes

Contraposition is the inference in which the subject is interchanged with the complement of the predicate and the predicate is interchanged with the complement of the subject. In modern logic it is only valid for the A and O propositions. The valid contrapositive is logically equivalent to the original proposition. In traditional logic, the E proposition has a contrapositive by limitation which is the subaltern of the invalid E-contrapositive; i.e., the corresponding O proposition. The contrapositive by limitation is implied by the original but is not (usually) equivalent to it.
ORIGINAL CONTRAPOSITIVE VALID? BY LIMITATION
All S are P All nonP are nonS yes
No S are P No nonP are nonS no Some nonP are not nonS
Some S are P Some nonP are nonS no
Some S are not P Some nonP are not nonS yes