Interval Logic Tensor Networks
This work addresses the problem of integrating fuzzy temporal reasoning with neural networks for researchers in neuro-symbolic AI, though it appears incremental as it builds on existing logic tensor network approaches.
The paper tackles the problem of reasoning about events with fuzzy durations by introducing Interval Logic Tensor Networks (ILTN), a neuro-symbolic system that learns by propagating gradients through Interval Real Logic (IRL). The results show that ILTN successfully leverages IRL knowledge in synthetic tasks to make events compliant with background temporal knowledge.
In this paper, we introduce Interval Real Logic (IRL), a two-sorted logic that interprets knowledge such as sequential properties (traces) and event properties using sequences of real-featured data. We interpret connectives using fuzzy logic, event durations using trapezoidal fuzzy intervals, and fuzzy temporal relations using relationships between the intervals' areas. We propose Interval Logic Tensor Networks (ILTN), a neuro-symbolic system that learns by propagating gradients through IRL. In order to support effective learning, ILTN defines smoothened versions of the fuzzy intervals and temporal relations of IRL using softplus activations. We show that ILTN can successfully leverage knowledge expressed in IRL in synthetic tasks that require reasoning about events to predict their fuzzy durations. Our results show that the system is capable of making events compliant with background temporal knowledge.