The foregoing tour of LAI impels us to
conclude that logic and AI are still passionately married.
But should they *stay* married?
We now turn, as promised, to some brief reflection on AI's other mate,
connectionism, some proponents of which would be inclined to dissolve
the logic-AI union we have found to be still-vibrant.Of
course, some LAIniks with
low regard for the connectionist-AI knot would similarly welcome
the dissolution of a
marriage they view as
a mésalliance.

In a previous paper one of us (Bringsjord) argued that the CAI-LAI
clash is one of AI's ``wonderful red herrings''
(Bringsjord 1991).
At the core of that
argument was a chain of mathematical equivalence holding between
Turing machines, *k*-tape Turing machines, cellular automata, and
(standard)*Non-standard* neural nets
(cf. Siegelmann 1995) perhaps promise to vindicate
some of
Smolensky's wilder speculation (and to muddy the
analysis of Bringsjord 1991), as in, for example:

I believe that there is a reasonable chance that connectionist models will lead to the development of new somewhat-general-purpose self-programming, massively parallel analog computers, and a new theory of analog parallel computation: They may possibly even challenge the strong construal of Church's Thesis as the claim that the class of well-defined computations is exhausted by those of Turing machines (Smolensky 1988a, p.3).

neural
nets - a chain that played a
role in an argument designed to show that, at bottom,
CAI and LAI are, *contra* Smolensky (author of the CAI
manifestos Smolensky 1988a and 1988b),
perfectly consistent with each other. Even
now, six years later, we know of no demonstration that
LAI and CAI are inconsistent. We *do* know that
in order for such a demonstration to be compelling, it would itself need
to be based on logic. How many mathematical proofs, after all, do you
see expressed as information flow in a neural net? In this section we
hone this question with help from a simple thought-experiment involving
a robotic detective of the future.
Before moving on
to this gedankenexperiment, however, we briefly compare CAI and LAI with help from
a generalization of the definition of `Implemented LAI System' we presented above.

Mon Nov 17 14:57:06 EST 1997