Re: Monotonicity of semantic extensions

On 09/12/2012 12:30 PM, Richard Cyganiak wrote:
> On 12 Sep 2012, at 16:31, Peter F. Patel-Schneider wrote:
>>>> With the direct graph semantics you propose, it is a non-monotonic extension because when you switch this semantics on, the entailments you could do with the "minimal" semantics are not valid anymore.
>>>> I don't think that's how people think of an extension. They probably do not expect that extensions make you lose what you had before.
>>> Well, yes, there are cases where the minimal semantics says that A entails B, and the “direct graph” semantics says that A contradicts B.
>> Note that this last statement does not in itself indicate that there are entailments in the minimal semantics that are not entailments in the direct graph semantics.   It could just be the case that A is inconsistent in the direct graph semantics.
> No, there are indeed cases here where A is consistent under either semantics, A entails B in the minimal semantics, and A contradicts B in the stronger semantic extension.
>
> Does that make the semantic extension non-monotonic?
>
> Richard
Even this doesn't make the extension non-monotonic, but it does make it 
strange, in that you wouldn't get the following theorem

If A entails B then A & B entails C implies A entails C

As with Pat, I thought that the above theorem was an essential part of logical 
deduction, but stranger things have happened.

peter

Received on Wednesday, 12 September 2012 20:37:35 UTC