[SCL] abstract vocabulary and interpretation

[Pat Hayes]

>If we define object position, for either names or terms, as anything
>potentially denoting

That is the idea, yes. The terminology of 'position' is slightly 
obsolete at his point.

Pat

>, then by following the somewhat elaborate definitions
>in my previous message, we can define simpler abstract notions of vocabulary
>and interpretation.
>
>The (concrete) vocabulary of any SCL text T is the triple (O, R, F)
>where O is the set of terms appearing in T,
>where R is the set of terms of T in relation position, and
>where F is the set of terms of T in function position,
>
>For any set of names N,
>an (abstract) vocabulary is a triple (O, R, F)
>where O is a set of N-terms, both R and F are subsets of O
>and for any composite N-term (t, t1, ... tn) in O,
>t is in F and ti is in O for 1 <= i <= n.
>
>For any set of names N,
>an interpretation for a vocabulary (O, R, F) has
>a nonempty set U called the universe,
>three maps
>int : O --> U, rel : R --> rel(U), and fun : F --> fun(U),
>and two partial maps (folds)
>relation : U --> rel(U) and function : U --> fun(U),
>where
>the value of int on any composite term (t, seq) in O
>is the value of fun[t] applied to the sequential extension int[seq],
>the image of R under int is a subset of the domain of relation
>and relation[int[t]] = rel[t] for any t in R,
>the image of F under int is a subset of the domain of function
>and function[int[t]] = fun[t] for any t in F.
>
>Robert E. Kent
>rekent at ontologos.org
>
>
>
>
>
>
>
>
>
>_______________________________________________
>SCL mailing list
>SCL at philebus.tamu.edu
>http://philebus.tamu.edu/mailman/listinfo/scl


-- 
---------------------------------------------------------------------
IHMC	(850)434 8903 or (650)494 3973   home
40 South Alcaniz St.	(850)202 4416   office
Pensacola			(850)202 4440   fax
FL 32501			(850)291 0667    cell
phayes at ihmc.us       http://www.ihmc.us/users/phayes