Re: [BLD] proposed text for interpretations

> Michael,
> 
> Herewith a proposal for a definition of interpretations with extensible
> datatype support. Since you dislike datatype maps so much, I avoided
> using them.

Because datatype maps are not needed.

>From the above statement one may conclude that the current version of the
semantics is not extensible with respect to data types. As far as I can
see, the only difference is that you changed the order of some definitions
and removed the condition that value spaces are included in the domain
(which is wrong and is based on a misunderstanding, I believe).

However, some elements in your proposal are good and I used them to improve
the current version.

> Primitive datatypes. Some symbol spaces symsp, called primitive data
> types, have a value space, denoted VSsymsp, and a mapping from the
> lexical space to the VSsymsp, denoted Lsymsp.
> [JB: I think the value space and the lexical-to-value mapping needs to
> be defined before the interpretation is defined, because they do not
> depend on the interpretation]

I totally disagree with this order. First, value spaces and
lexical-to-value mappings are part of the definition of semantic
structures, ***and nothing else***.

Defining them separately (and before the definition of semantic structures)
is putting the cart before the horse.

> Truth values. Interpretations assign a truth value to every formula.
> 
> The set of truth values is denoted by TV. For RIF-BLD, TV includes only
> two values, t (true) and f (false). (See end note on truth values.)
> 
> In RIF, TV has a total or partial order, called the truth order, and
> denoted with <t. In RIF-BLD, f <t t, and it is a total order. (See end
> note on ordering truth values.)
> [JB: I think it is not necessary to intermingle the definition of truth
> values with the definition of an interpretation]

The definition of truth values is, again, part of the definition of
semantic structures, and nothing else. But the previous organization was
not optimal and I moved things around a bit.

> Basic semantic structures. Given a set of datatypes DT which includes
> all data types supported by RIF, a basic semantic structure, I, is a
> tuple of the form <D,IC, IV, IF, IR>, where

As I said, it I believe that it is didactically better to define the effect
of the data types after that piece.

> * D, called the domain of I, is a non-empty countable set of elements,
> 
> * IC is a mapping from Const to elements of D, such that for every
> symbol l^^u in Const,
> 
>   *   if u is a datatype in DT, then IC(l^^u)=3DLu(l),
> 
> * IV is a mapping from Var to elements of D,
> 
> * IF is a mapping from Const to functions from D* into D (here D* is a
> set of all tuples of any length over the domain D), and
> 
> * IR is a mapping from Const to partial truth-valued mappings D*
>  TV.
> 
> The equality predicate is interpreted as identity on D, i.e.: IR
>  is
> a truth-valued mapping such as IR(<a,a>) t for every a
>  D; it maps
> any other pair of elements of D to f. IR is undefined on other
> elements of D* (tuples of length other than 2).
> 
> ....
> 
> Semantic structures and the entailment would also need to be defined
> with respect to a set of datatypes DT.

Hold on. The above was a definition of semantic structures, so I fail to
understand your last sentence. Did you mean truth valuation? What exactly
needs to be changed there?


	--michael  


>                          debruijn@inf.unibz.it
> 
> Jos de Bruijn,        http://www.debruijn.net/

Received on Tuesday, 16 October 2007 05:07:08 UTC