Gradient-Based Optimization on G\"odel Logic as Discrete Local Search

ArXi:2503.01817v2 Announce Type: replace A fundamental challenge in neurosymbolic systems is applying continuous gradient-based optimization to discrete logical domains. While fuzzy relaxations provide differentiability, they often lack a formal structural alignment with classical logic. In this work, we show that G\"odel semantics addresses this limitation through a homomorphism that maps its continuous interpretations to Boolean ones, allowing discrete variables to be encoded while maintaining full differentiability.