- From: Peter F. Patel-Schneider <pfps@inf.unibz.it>
- Date: Thu, 04 May 2006 10:22:41 -0400 (EDT)
- To: bry@ifi.lmu.de
- Cc: public-rif-wg@w3.org
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