Re: [ontolog-forum] mKR proof of correctness

[Adrian Walker <adriandwalker@xxxxxxxxx>]

Hi Pat & All,

+1 to that.

Here's an example of doing more or less what Pat has described:

  Backchain Iteration: Towards a Practical Inference Method that is Simple
  Enough to be Proved Terminating, Sound and Complete. Journal of Automated Reasoning, 11:1-22

                Cheers,  -- Adrian

On Wed, Apr 2, 2014 at 11:21 PM, Pat Hayes <phayes@xxxxxxx> wrote:

On Apr 2, 2014, at 5:10 PM, Richard H. McCullough <rhmccullough@xxxxxxxxx> wrote:

> John
>
> I don't want there to be any doubt about what I'm saying,
> so I'm devoting one extra email to this topic.
>
> The mKR language is proved semantically correct
> because the mKR run-time system guarantees
> that the Objectivist Axioms are satisfied.

I actually laughed out loud when I read this. First, I have no idea what you mean by proving a language to be semantically correct, but claiming anything semantic **because some axioms are present** misses the entire point of having semantics in the first place, which is to connect formal sentences with claims about the actual world. Then again there is your conflation of semantics with a 'run-time system', which I take it means a system that performs inferences. But without an independent semantics, how does one know that these inferences are valid or complete? The general problem of proving that a program is correct is still open, of course, but any approach to even defining what this means requires that the language of the program has some kind of separate semantics. If the run-time system *Is* the semantics then 'correctness' is trivial to prove - the program does what the program does - but also trivially meaningless. But the final howler here is the idea that Ayn Rand's
  thoughts might have anything, even the shred of a remotest connection, to do with correctness, in any sense of that word.

IF your notation had a semantic theory that would enable an objective check to be made on its validity, and IF you could then show that those axioms were satisfied AND that your run-time system preserved truth (or whatever your semantics calls it), then you might reasonably claim that mKE had a property that one might call Randianicity: conformity to the thoughts of Ayn Rand. But to call this property "semantic correctness" is simply farcical.

Pat Hayes

>
>  Dick McCullough
> Context Knowledge Systems
> mKE and the mKR language
> mKR/mKE tutorial

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