Real Logic and Logic Tensor Networks
Haukur Páll Jónsson
Abstract:
In recent years interest has risen in combining knowledge representation and machine learning and in this thesis we explore Real Logic (RL). RL offers a novel approach to this combination. RL uses first-order logic (FOL) syntax and has a many-valued semantics in which terms are interpreted as real-valued vectors. By making assumptions about the model space and the relation between terms and predicates, we have a well-defined search procedure to search for models to our logical theory in a framework implementing RL called Logic Tensor Networks (LTN).
We evaluate RL and LTN in an empirical setting using the PASCAL-Part dataset and describe the dataset using FOL and then search for a model which satisfies our logical description of the dataset. The task of Semantic Image Interpretation (SII) is used to evaluate RL and compare different instantiations of RL. The goal of SII is to produce a scene graph given an image and prior knowledge about entities in the image. Solutions to this task are expected to take into account the prior knowledge when making predictions based on low-level features. We will model the task using RL and demonstrate that logical constraints improve classification of entities, relation and make predictions more logically consistent. Along the way, we formulate hypotheses about the inner workings of the model and perform experiments to test those hypotheses. The most notable hypotheses are the following four. A model trained with logical constraints will have less variation in performance compared to an unconstrained model. Some instantiations of RL will not work, or work poorly, in a neural network setting. A model trained with logical constraints will produce more logically consistent predictions. The predecessor of the LTN will perform equivalently to the LTN in this setting. We will see from the theoretical results and experimental results that some these hypotheses are incorrect whilst we establish the correctness of the others. We conclude the thesis by summarizing our results and recognize the novel step RL takes in combining knowledge representation and machine learning.