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From Logic to Algebra: After embedding a KG in its corresponding vector space, each symbolic elements (entities and relations) will be assigned a vector. Moving
by MLres 7y ago
From Logic to Algebra: After embedding a KG in its corresponding vector space, each symbolic elements (entities and relations) will be assigned a vector. Moving from symbols to vectors is equivalent with moving from logic to algebra. In other words, after mapping a KG to a vector space, logical rules can be converted to their corresponding algebraic formula. More concretely, considering the target vector space provided for the KG, one can derive the formula for each logical rules. Therefore, as there is an equivalent vector for each of the symbols, there will be an equivalent algebraic formula for each of the logical rules.
- MLres 7y agoCapability vs practical rule injection: The question is that if the NNs are capable of encoding logical rules? The paper proposes a neural network and proves that the network is capable of expressing any ground truth over encoded rules in the KG. The paper focuses on one class NNs as well as one class of logical rules. Investigation of capability of different class of NNs in encoding different class of logical rules is indeed an important problem which can open a new window in front of ML. When one is sure that the KGE model has enough capability to encode a class of logical rules, deriving a formula for each of logical rules is essential. The derived formula can be used to guide the learning process. The paper reported that injection of rules in the learning process significantly improves performance the learner (KGE model). Therefore, the prior knowledge which is encoded as logical rules significantly improves the performance of the NN.