Fuzzy Decisions in Modular Neural Networks

Modular neural networks structured as associative memories are capable of processing inputs built from tensorial products of vectors. In this context, the operators of propositional and modal logic can be represented as modular distributed memories that can process not only classical Boolean but also fuzzy evaluations of truth-values of sentences. Furthermore, projecting memory outputs onto unit vectors yield discrete dynamical systems that exhibit varying degrees of complexity. As examples, we analyze outcomes of semantic evaluations in several self-referential systems including modal versions of the chaotic liar, antagonistic decisions and extended dilemmas. By studying these examples we hope to shed some light on the modeling of cognitive decisions.