Theoretical Foundations
Differentiable logic involves the implementation of logical connectives (AND, OR, NOT) as continuous, differentiable functions. This architecture allows for the optimization of symbolic reasoning chains using standard backpropagation techniques.
Logical Neural Networks (LNN)
LNNs, developed by IBM Research, are a neuro-symbolic framework where neurons represent formulas in weighted first-order logic. These networks are inherently interpretable and support both deductive (forward) and abductive (backward) reasoning within a unified learning environment.
Foundational & Specialized Logic Systems
- Tensor Product Representations (TPR): Paul Smolensky's 1990s work on representing structured symbolic information (like trees) within a neural activation space.
- Real-Valued Logic (RVL): Implementing logic gates using continuous values, enabling the use of fuzzy logic in neural architectures.
- Dice (Probabilistic Logic): A library for exact probabilistic inference using discrete logic representations.
- DeepProbLog: A framework that integrates probabilistic logic programming with deep learning, providing an end-to-end differentiable system.
Strategic Goal
The objective is to construct reasoning layers that maintain strict logical semantics while learning from empirical data. LNNs provide a mechanism for verifying that model updates adhere to defined logical constraints, merging probabilistic flexibility with formal consistency.