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

From: Francois Bry <bry@ifi.lmu.de>
Subject: Re: [RIF] Reaction to the proposal by Boley, Kifer et al
Date: Thu, 04 May 2006 08:52:00 +0200

> 
> 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**

Searching through the second book I couldn't find any use of "infinite"
modifying "Herbrand".  There was a hint - on page 44 the book talks about
the divergence between satisfiability in arbitrary models and
satisfiability in Herbrand models over a small vocabulary - but nothing
more that I could find through Amazon.

> > 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).

Yes, in standard FOL is it not necessary for every domain element to have a
name (in the syntax).

> And, I would dare to  say that the evaulation of existential
> quantieifers in classical logic is well-known...

My question was how are logics where there must be a name for every domain
element (i.e., those based solely on Herbrand interpretations) related to
the more standard logics where this is not necessary.

> >> 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 closer to natural language (where (subject predicate object)
> orignally come from, first proposed, if I remember well, by Aristotle.)  

Fair enough.

> Francois

peter

Received on Thursday, 4 May 2006 14:22:56 UTC