SUO: Re: Theory Query
Robert and Jon,
I believe that the three of us are in violent agreement about at least
one point, which Jon has stated quite well:
JA> Notice that the very definition of a theory is stated
> relative to a given first-order predicate language $L$.
> Until such a common language has been established, all
> talk of lattices or other orders is just so much Babel.
Robert has reiterated that point with more technical window dressing:
RK> we are dealing with a _fibered structure_ here. I have proposed that
> the truth concept lattice be used in SUO as John Sowa's potentially
> infinite open-ended lattice of theories. However, there is no single
> lattice here but an infinite collection of lattices, where each truth
> classification "truth-classification(L)" and each truth concept
> lattice "truth-lattice(L)" is based upon (indexed by) a particular
> 1st-order language L.
The language I have in mind is the common abstract syntax of the
proposed Common Language Standard. More specifically, I am *only*
considering the FOL core of CL without the metalevel extensions
as the language of the lattice of theories.
I plan to use the metalevel extensions of CL for the purpose of
talking about the relationships among theories in the lattice --
for doing abduction, belief revision, metaphors, learning, and many
other clever kinds of AI reasoning.
The FOL core of CL is an uninterpreted language (i.e., no constant
symbols for predicates, individuals, etc.). For the lattice of
theories that I have been talking about, I am assuming that all
such symbols are taken from the infinite vocabulary of strings
that are supported by the CL naming conventions.
John Sowa