Conventional embedding-based models approach event time prediction in temporal knowledge graphs (TKGs) as a ranking problem. However, they often fall short in capturing essential temporal relationships such as order and distance. In this paper, we propose TEILP, a logical reasoning framework that naturaly integrates such temporal elements into knowledge graph predictions. We first convert TKGs into a temporal event knowledge graph (TEKG) which has a more explicit representation of time in term of nodes of the graph. The TEKG equips us to develop a differentiable random walk approach to time prediction. Finally, we introduce conditional probability density functions, associated with the logical rules involving the query interval, using which we arrive at the time prediction. We compare TEILP with state-of-the-art methods on five benchmark datasets. We show that our model achieves a significant improvement over baselines while providing interpretable explanations. In particular, we consider several scenarios where training samples are limited, event types are imbalanced, and forecasting the time of future events based on only past events is desired. In all these cases, TEILP outperforms state-of-the-art methods in terms of robustness.

Deep vision models have provided new capability across a spectrum of applications in transportation, manufacturing, agriculture, commerce, and security. However, recent studies have demonstrated that these models are vulnerable to adversarial attack, exposing a risk-of-use in critical applications where untrusted parties have access to the data environment or even directly to the sensor inputs. Existing adversarial defense methods are either limited to specific types of attacks or are too complex to be applied to practical vision models. More importantly, these methods rely on techniques that are not interpretable to humans. In this work, we argue that an effective defense should produce an explanation as to why the system is attacked, and by using a representation that is easily readable by a human user, e.g. a logic formalism. To this end, we propose logic adversarial defense (LogicDef), a defense framework that utilizes the scene graph of the image to provide a contextual structure for detecting and explaining object classification. Our framework first mines inductive logic rules from the extracted scene graph, and then uses these rules to construct a defense model that alerts the user when the vision model violates the consistency rules. The defense model is interpretable and its robustness is further enhanced by incorporating existing relational commonsense knowledge from projects such as ConceptNet. In order to handle the hierarchical nature of such relational reasoning, we use a curriculum learning approach based on object taxonomy, yielding additional improvements to training and performance.

Visual question answering (VQA) has been gaining a lot of traction in the machine learning community in the recent years due to the challenges posed in understanding information coming from multiple modalities (i.e., images, language). In VQA, a series of questions are posed based on a set of images and the task at hand is to arrive at the answer. To achieve this, we take a symbolic reasoning based approach using the framework of formal logic. The image and the questions are converted into symbolic representations on which explicit reasoning is performed. We propose a formal logic framework where (i) images are converted to logical background facts with the help of scene graphs, (ii) the questions are translated to first-order predicate logic clauses using a transformer based deep learning model, and (iii) perform satisfiability checks, by using the background knowledge and the grounding of predicate clauses, to obtain the answer. Our proposed method is highly interpretable and each step in the pipeline can be easily analyzed by a human. We validate our approach on the CLEVR and the GQA dataset. We achieve near perfect accuracy of 99.6% on the CLEVR dataset comparable to the state of art models, showcasing that formal logic is a viable tool to tackle visual question answering. Our model is also data efficient, achieving 99.1% accuracy on CLEVR dataset when trained on just 10% of the training data.