Neural Networks, Penalty Logic and Optimality Theory
Reinhard Blutner

Abstract:

Ever since the discovery of neural networks, there has been a
controversy between two modes of information processing. On the one
hand, symbolic systems have proven indispensable for our understanding
of higher intelligence, especially when cognitive domains like
language and reasoning are examined. On the other hand, it is a matter
of fact that intelligence resides in the brain, where computation
appears to be organized by numerical and statistical principles and
where a parallel distributed architecture is appropriate. The present
claim is in line with researchers like Paul Smolensky and Peter
Gärdenfors and suggests that this controversy can be resolved by a
unified theory of cognition - one that integrates both aspects of
cognition and assigns the proper roles to symbolic computation and
numerical neural computation.  The overall goal in this contribution
is to discuss formal systems that are suitable for grounding the
formal basis for such a unified theory. It is suggested that the
instruments of modern logic and model theoretic semantics are
appropriate for analyzing certain aspects of dynamical systems like
inferring and learning in neural networks. Hence, I suggest that an
active dialogue between the traditional symbolic approaches to logic,
information and language and the connectionist paradigm is possible
and fruitful. An essential component of this dialogue refers to
Optimality Theory (OT) - taken as a theory that likewise aims to
overcome the gap between symbolic and neuronal systems.  In the light
of the proposed logical analysis notions like recoverability and
bidirection are explained, and likewise the problem of founding a
strict constraint hierarchy is discussed. Moreover, a claim is made
for developing an 'embodied' OT closing the gap between symbolic
representation and embodied cognition.

Keywords: connectionism, Optimality Theory, nonmontonic logic, symbolism,
  cognitive architecture