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.