# Re: [RIF] Reaction to the proposal by Boley, Kifer et al

From: Francois Bry <bry@ifi.lmu.de>
Date: Thu, 04 May 2006 08:52:00 +0200
Message-ID: <4459A490.8000609@ifi.lmu.de>

```
Peter F. Patel-Schneider wrote:
> A reference to logics based on infinite Herbrand intepretations that shows
> how they relate to standard first-order logics.
>
I think, you should find this in the following books (the first seems to
be out of print):

John Lloyd. Foundations of Logic Programming, Springer 1984, 1991
Kees Doets. From Logic to Logic Programming, The MIT Press, 1994)*
*http://www.amazon.com/gp/product/0262041421/sr=8-1/qid=1146724851/ref=pd_bbs_1/104-1241285-2467909?%5Fencoding=UTF8**

> In logics where every "domain element" has a name, the substitution
> interpretation of quantifiers is well known.  However, how does this relate
> to logics where there is not necessarily a name for every domain element or
> where there cannot be a name for every domain element?
>
To the best of my understanding, classical logic's model theory is not
such that "every domain element necessarily has a name" (I guess, you
mean a name expressible in the syntax of the logic language).

And, I would dare to  say that the evaulation of existential
quantieifers in classical logic is well-known...
>> To the best of my understanding, the one and the other syntax are both
>> possible. Personally, I would prefer a syntax (subject predicate object)
>> because it is natural and simple.
>>
>
> Is this a (single) ternary predicate?  If not, how does it match the
> proposal?  If so, how can it be considered to be natural?
>
(subject pred object) can be a infix notation for a binary predicate "pred". This is standard in classical logic where, e.g. the binary predicate "+" for addition is often written infix, eg (3 + 4) instead of prefix, eg +(3, 5). To the best of my understanding, such an infix notation would be very convenient for RDF triples. I see it as natural for two reasonsd:

1. it reminds of eg addition
2. it is closed to natural language (where (subject predicate object) orignally come from, first proposed, if I remember well, by Aristotle.)

Francois
```
Received on Thursday, 4 May 2006 06:52:04 UTC

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