Neural Networks, Penalty Logic and Optimality Theory

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.