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While deep neural networks have led to major advances in image recognition,language translation, data mining, and game playing, there are well-knownlimits to the paradigm such as lack of explainability, difficulty ofincorporating prior knowledge, and modularity. Neuro symbolic hybrid systemshave recently emerged as a straightforward way to extend deep neural networksby incorporating ideas from symbolic reasoning such as computational logic. Inthis paper, we propose a list desirable criteria for neuro symbolic systems andexamine how some of the existing approaches address these criteria. We thenpropose an extension to generalized annotated logic that allows for thecreation of an equivalent neural architecture comprising an alternate neurosymbolic hybrid. However, unlike previous approaches that rely on continuousoptimization for the training process, our framework is designed as a binarizedneural network that uses discrete optimization. We provide proofs ofcorrectness and discuss several of the challenges that must be overcome torealize this framework in an implemented system.

Extensions to Generalized Annotated Logic and an Equivalent Neural Architecture