- From: Francois Bry <bry@ifi.lmu.de>
- Date: Fri, 05 May 2006 13:12:58 +0200
- To: public-rif-wg@w3.org
Chris Menzel wrote: > > On 5/4/06, Francois Bry <bry@ifi.lmu.de> wrote: >> ...[PFPS:] >> > Variable maps are needed to assist in giving meaning to free >> variables. >> > >> Not only to free variables, also to quantified variables. In fact, the >> very idea of Tarskian models does not need formulas free variables. Such >> formulas are considered only so as to define the interpretation function >> (assigning a truth value to a formulain an interpretation) recursively >> on the formulas structure. >> >> As a consequence, one finds in the logic literature both >> "interpretation" offormulas with free variables: >> >> - their free variables are considered existentially quantified (this is >> usual in computer sceince) >> - their free variables are considered universally quantified (this used >> to be usual in German logic of the 19th and beginning of the 20th >> century). > > There's a third option, and that is not to distinguish free variables > semantically from constants. There is then no need for variable maps > at all. Chris is right. This 3rd approach is standard in logic and used in some logic textbooks. It has the advantage of keeping things simple. It has two drawbacks: 1. A didactic drawback (not too dramatic because the appaoch cvan be explained). 2. It does not corresponds to a widespread tratment of free variuables in Computer Science in general, in the theory of relational databases and in logic programming in particular. Francois
Received on Friday, 5 May 2006 11:13:10 UTC