implementation of Modus ponens and Modus tollens
Can we have in Prelude - Booleans, Modus ponens and Modus tollens implemented? Or in another module?
reminder:[[BR]]
P is a proposition and v(p) is the logic value of P.[[BR]]
P is true, v(P) = 1[[BR]]
P is false, v(P) = 0[[BR]]
P -> Q is always true in propositional logic.
Modus ponens:[[BR]] v(P) = 1[[BR]]
v(P -> Q) = 1[[BR]]
v(Q) = 1[[BR]]
v(P) and v(P -> q) are premiss, v(q) is the conclusion.[[BR]] or in a more general form[[BR]]
P : X is A[[BR]]
P -> Q : A -> B[[BR]]
Q : X is B[[BR]]
Modus tollens:[[BR]] v(Q) = 0[[BR]]
v(P -> Q) = 1[[BR]]
v(P) = 0[[BR]]
v(Q) and v(P -> Q) are premiss, v(P) is the conclusion.[[BR]] or in a more general form[[BR]]
not Q : X is not B[[BR]]
P -> Q : A -> B[[BR]]
not P : X is not A[[BR]][[BR]]
As well as using the numbers 0 and 1 for the respective values false and true, we'll use the letters F for False and T for True.[[BR]]
We are always:[[BR]] v(F) = 0[[BR]]
v(T) = 1[[BR]]
v(P -> Q) = 1[[BR]]
Trac metadata
Trac field | Value |
---|---|
Version | 8.0.1 |
Type | FeatureRequest |
TypeOfFailure | OtherFailure |
Priority | normal |
Resolution | Unresolved |
Component | libraries/base |
Test case | |
Differential revisions | |
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Blocking | |
CC | |
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