Interval Logic Tensor Networks

TL;DR

This paper introduces Interval Logic Tensor Networks, a neuro-symbolic system that learns to reason about fuzzy temporal intervals and event durations using a differentiable logic framework.

Contribution

It presents a novel neuro-symbolic approach combining fuzzy interval logic with neural networks for temporal reasoning tasks.

Findings

ILTN successfully predicts fuzzy event durations in synthetic tasks.

The system enforces temporal knowledge constraints effectively.

ILTN demonstrates the ability to learn and reason about fuzzy temporal intervals.

Abstract

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.