Department of Mathematics and
Boole Centre
University College Cork
3:30pm Thursday 22nd September 2005
Room 2511, JCMB, King's Buildings
It is a challenging and interesting problem to integrate the logic based and neural-network based approaches to computation and artificial intelligence with the intention of combining the advantages to be gained from connectionism and symbolic AI. On the one hand, connectionist systems possess many properties one expects to find in intelligent systems: massive parallelism, the ability to learn, robustness etc. On the other hand, a rather different, but important feature one also expects of intelligent systems is the ability to represent and reason about structured objects and structure-sensitive processes, and this feature is rather well-handled by systems based on computational logic.
One aspect of the integration of these paradigms is the computation, or approximate computation, by neural networks (NN) of the various operators associated with logic programs as these provide the (fixed-point) semantics one associates with such programs. In the case of propositional programs, one can exactly compute the operators in question and, by iteration, their fixed points. This process can also be carried out for first-order programs except that techniques based, usually, on approximation methods must be employed. Furthermore, aside from the issue of integrating artificial and natural models of computation, one can also view these results as a step towards providing logical and fixed-point semantics for NN thought of as a natural model of computation.
In this talk, we discuss first, for propositional programs, the computation by NN of a general operator which encapsulates all the main semantics encountered in logic programming. Second, we consider certain of the various problems posed in attempting to approximate semantic operators in the case of first-order programs. This work relates to that of Hoelldobler, Gabbay, Garcez, Hitzler et al. and the members of the Theory of Computation Group at BCRI (Komendantskaya, Komendantsky, Lane, Woods and the speaker). Finally, we briefly consider the possibility of a categorical semantics for NN based on these ideas, and this is ongoing work with John Power of LFCS.