RE: A Single Foundational Logic for the Semantic Web

Seth Russell wrote,
> How about ?
>
> {{ this a n3:falsehood } a  n3:NonSense }

Nice try, but no cigar.

Declaring paradoxical propositions nonsensical or meaningless or
neither true nor false, has a very long history. Unfortunately it 
doesn't work, because we can easily construct new variants of the 
liar, eg.,

  This sentence is false or meaningless

  * If it's true it's either false or meaningless.

  * If it's false it's true.

  * If it's meaningless it's true (in which case it's not meaningless)

More generally, for any proposed resolution which attributes semantic
property P to the liar sentence, we can construct a strengthened liar,

  This sentence is false or P

which will be paradoxical.

The only "solution" I'm aware of which doesn't have this problem is
the paraconsistent logic approach ... use a logic weak enough that it 
supports local contradictions without being reduced to triviality
(ie. you can't infer an arbitrary Q from P&!P) ... but that has its
own problems.

Cheers,


Miles

Received on Wednesday, 1 May 2002 05:59:52 UTC