Logic Tensor Networks for Sequential Events Modelling

This master's thesis investigates the extension of Logic Tensor Networks (LTN) to sequential data modelling. LTN, a neuro-symbolic system introduced by Serafini et al., utilises Real Logic, a fuzzy first-order logic, to enable learning and reasoning in conventional artificial intelligence tasks such as data clustering, multi-label classification, and embedding learning. To address sequential events detection, some preliminary ideas on how to extend LTN, known as Interval Logic Tensor Networks (ILTN), have been recently proposed. ILTN employs a two-sorted logic to interpret knowledge about sequential properties (traces) and event properties using real-featured sequential data. Simple events are represented as trapezoidal fuzzy intervals, and fuzzy temporal relations are computed based on relationships between the intervals' areas. This thesis contributes to a more precise definition of the ILTN framework by providing a comprehensive PyTorch implementation and introducing enhancements for handling the grounding of sequential data. The research includes exploration of synthetic tasks to demonstrate ILTN's capabilities and effectiveness in leveraging knowledge expressed in Interval Real Logic (IRL).