The realization of transparent deep learning models faces a substantial challenge when used in domains that depend on human trust alongside requirement for high transparency. The current explainable AI (XAI) solutions reveal model decision details but they lack the capability to distinguish between conscious explicit and unconscious implicit knowledge. The review fills a knowledge gap by examining research published previously to evaluate neural network cognitive representations according to their handling of explicit and implicit information. This systematic review establishes symbolic (explicit) and sub-symbolic (implicit) and hybrid frameworks using criteria derived from cognitive theories of dual-processes and Global Workspace Theory and neuro-symbolic integration according to PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses). Research shows that symbolic models make up 26% of models while implicit feature representations without clear human-interpretable logic exist in 41% of models and no distinction can be found in 33% of models. Studies demonstrate hybrid reasoning systems which unite symbolic and sub-symbolic methods deliver an 18% boost to interpretation outcomes such as human trust assessment and experience satisfaction ratings along with a 6.3% enhancement in predictive accuracy across healthcare and NLP and computer vision tasks. The revealed findings show why cognitive principles need to become part of XAI systems and thus this study introduces a taxonomy approach to support neural architecture development which aligns better with human reasoning processes.