[FOM] paraconsistent logic and computer science

Hartley Slater slaterbh at cyllene.uwa.edu.au
Sat Oct 13 20:15:47 EDT 2007

Arnon Avron takes Nuel Belnap's line on the applicability of 
paraconsistent logic:

>  Turning now to CS and AI, I think that the answer to your question
>is here much simpler, and was given by Belnap long ago. The knowledge
>store in a KB (Knowledge Base)  usually comes from different sources,
>and so might be contradictory. Now even if one thinks that consistency
>should eventually be restored to the KB, doing this in a reliable
>and efficient way might take time, and during that time the KB
>must continue to function as efficiently and reliably as possible.
>This can be done only if it uses during that time an inference mechanism that
>tolerates the existence of contradiction (and since a KB
>is frequently updated, such a mechanism might be practically needed
>all the time).

But this will not do, for at least four reasons.

First, one cannot have in the KB a series of facts including the fact 
that p and the fact that -p, if '-' is classical negation, i.e. 
contradiction, since just that is what is ruled out in that case.

On the other hand, if there are traces of the 'knowledge' sources 
then what there might be in the KB are a series of facts of the form 
'Snp', saying that source n claims that p.  But then, while one might 
have S1p, S1q...S2-p, S2q, etc., it would need not a paraconsistent 
logic to arrive at consequences, but some kind of intensional logic.

What one more likely has in a KB, however, is not a series of facts, 
but just a series of sentences, maybe with some indication of their 
sources.  And then, if both 'p', and '-p' are there, for some 'p', no 
consequence at all follows without an interpretation being given to 
the '-'.  So while it might be convenient to give a temporary, 
paraconsistent interpretation to the '-' for the purposes Avron 
indicates, what he forgets is that this might be the quite proper 
interpretation, given the intention of the source that says '-p'. 
And in that case the given sentences would be quite consistent as 
they stand.  There is nothing in the *sentences* 'p' and '-p' to make 
them contradictory, i.e. to make the fact expressed by the one rule 
out the fact expressed by the other.  Why should the source that says 
'-p' be using classical negation?

Of course one might (indeed one should) distinguish classical and 
paraconsistent negations syntactically.  But then, if the negative 
sentence has a classical negation in it, every other proposition 
follows necessarily, no matter what else, and any 'inference 
mechanism' that is imposed on the case that does not respect this is 
distorting the data.  If one distinguishes the negations 
syntactically then the relevant consequences are inherent in the 
sentences themselves, since the syntactic discrimination then itself 
indicates what rules of inference apply.

Barry Hartley Slater
Honorary Senior Research Fellow
Philosophy, M207 School of Humanities
University of Western Australia
35 Stirling Highway
Crawley WA 6009, Australia
Ph: (08) 6488 2107 (W), 9386 4812 (H)
Fax: (08) 6488 1057
Url: http://www.philosophy.uwa.edu.au/staff/slater

More information about the FOM mailing list