# Re: Rules are *not* Horn clauses!

From: Pat Hayes <phayes@ai.uwf.edu>
Date: Wed, 19 Sep 2001 10:35:02 -0500
Message-Id: <p05101011b7ce69c9a340@[205.160.76.182]>
To: "Wagner, G.R." <G.R.Wagner@tm.tue.nl>

```>  > I would say that the languages of queries and rules in Prolog
>>  were *identical*: both consist of Horn clauses.
>
>Please notice that Prolog rules (as well as any other practical
>computational rule concept such as SQL views and OCL implications)
>are *not* Horn clauses! They are, for good reasons, more expressive,
>allowing for negation in their body/antecedent (and other things,
>such as quantifiers, as in the case of SQL views).

I replied to the above in a different message, but:.

>We should consider the concept of a rule as a basic one that
>is not derived from that of a Horn clause (which happens to be
>a very restricted/simplified type of rule). The concept of a
>Horn clause is tight to classical (two-valued) logic. But rules
>play a role in all kinds of formalism with a non-classical
>logic semantics (such as intuitionistic, partial, temporal,
>inconsistency-tolerant logic, etc.).

Hold on a minute there. There is no single notion of 'rule' that
plays a role in a variety of logics. Each of these logics can express
implications, and implications (especially those with a single
consequent) can often be thought of as 'rules', if you like, once one
has also settled on a particular implementation of a particular proof
theory for a particular logic. But all those 'rules' are different,
and all of them have some nonlogical assumptions underlying their use.

BTW, the notion of Horn clause is not restricted to classical
two-valued logic. It applies to any logic which has conjunction,
disjunction and negation, which includes all those you mention here
and many others.

Also, for what its worth, these 'rules' are not what a logician would
call an inference rule. Just a heads-up in case of possible confusion.

Pat Hayes
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Received on Wednesday, 19 September 2001 11:35:06 GMT

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